Portfolio Investment Management

BBPM4103

PORTFOLIO INVESTMENT MANAGEMNET

Dr Lau Wee Yeap

First Printing, May 2009 Second Printing, July 2009 Third Printing, November 2009 Fourth Printing, February 2010

Copyright © Open University Malaysia (OUM), February 2010, BBPM4103 All rights reserved. No part of this work may be reproduced in any form or by any means without the written permission of the President, Open University Malaysia (OUM). Version February 2010

Project Directors: Prof Dr Mansor Fadzil Prof Dr Shaari Abd. Hamid Open University Malaysia Module Writer: Dr Lau Wee Yeap Universiti Malaya Moderator: Nuradli Ridzwan Universiti Sains Islam Malaysia Developed by: Centre for Instructional Design and Technology Open University Malaysia Printed by: Meteor Doc. Sdn. Bhd. Lot 47-48, Jalan SR 1/9, Seksyen 9, Jalan Serdang Raya, Taman Serdang Raya, 43300 Seri Kembangan, Selangor Darul Ehsan

Table of Content Course Guide xi-xiv

Topic 1 Introduction to Financial Market and Securities 1 1.1 The Economics of Financial Market 3 1.2 Types of Investor and Financing 4 1.3 Types of Financial Market and Instrument 6 1.4 Unit Trust Investment 10 1.4.1 The Regulatory Framework 11 1.4.2 Types of Funds 12 1.4.3 Risk and Return in Unit Trust Investment 14 1.5 Capital Market Master Plan (CMP) 14 1.5.1 Background 14 1.5.2 Implementation 15 1.6 Types of Profession in Capital Market 17 Summary 18 Key Terms 18 Self-Test 1 19 Self-Test 2 19 Topic 2 Risk and Return 20

2.1 Risk and Return 22 2.1.1 The Concept of Volatility 23 2.1.2 Definition and Type of Risk 23 2.2 Measuring Return 25 2.2.1 Rate of Return 25 2.2.2 The Certain and Uncertain Outcomes 26 2.2.3 Expected Return 27 2.3 Measuring Risk 28 2.3.1 Investment Risk 28 2.3.2 Standard Deviation 29 2.3.3 Frequency of Means and Standard Deviation 30 2.4 InvestorÊs Behaviour and Utility Function 30 2.4.1 The Concept of Utility 31 2.4.2 Why the Knowledge of Utility Function is Important? 31 2.5 Covariance and Correlation 34 2.5.1 Covariance 34 2.5.2 Relationship Between Variance and Covariance 36 2.5.3 Correlation 36

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2.6 Mean-variance Analysis 37 Summary 38 Key Terms 39 Self-Test 1 39 Self-Test 2 39

Topic 3 Portfolio Theory and Diversification 41 3.1 Introduction to Portfolio Theory 42 3.2 Diversification 43 3.3 Portfolio Return 44 3.3.1 Example 45 3.4 Portfolio Risk 45 3.5 Correlation and Return: Two Asset Case 46 3.6 Investment Opportunities Set for Two Securities 47 3.7 Minimum Variance Portfolios 50 3.8 Diversifiable and Non-diversifiable Risk 53 Summary 55 Key Terms 56 Self-Test 1 56 Self-Test 2 57

Topic 4 Efficient Frontier and Asset Allocation 58 4.1 The Efficient Frontier and Markowitz Portfolio Theory 59 4.1.1 Portfolio Construction with More than Two Assets in the Portfolio 60 4.1.2 Quantifying the Efficient Frontier 62 4.2 Capital Allocation versus Asset Allocation 66 4.2.1 The Capital Allocation Line (CAL) 67 4.2.2 Reward-to-Risk Ratio 69 4.3 The Capital Market Line (CML) 70 4.3.1 The Derivation of The CML 70 4.3.2 The Capital Market Line and the Separation Theorem 72 4.4 Optimal Complete Portfolios 72 4.4.1 Risk Tolerance and Asset Allocation 72 4.4.2 Optimal Composition (Weightings) in a Portfolio 74 4.5 Construction and Use of Market Indices 75 Summary 79 Key Terms 79 Self-Test 1 79 Self-Test 2 81

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Topic 5 Capital Asset Pricing Model 81 5.1 Capital Asset Pricing Model (CAPM) 82 5.1.1 The Assumptions of the CAPM 83 5.2 Market Portfolio and Market Risk Premium 85 5.2.1 The Excess Return on Individual Stocks 86 5.2.2 The Expected Return on Individual Stocks 87 5.2.3 The Ex-aante and Ex-post Versions of the CAPM 88 5.3 The Security Market Line (SML) 89 5.3.1 Graphing the SML 89 5.3.2 The Investment Decision-making Process 90 5.4 Systematic Risk 92 5.4.1 The Estimation of the Beta Coefficient 93 5.5 Extensions of the CAPM 96 5.5.1 The CAPM for a Portfolio 96 5.5.2 The Beta Stability Problem 98 5.6 The Relaxation of CAPM Assumptions 98 Summary 101 Key Terms 101 Self-Test 1 101 Self-Test 2 102

Topic 6 The Arbitrage Pricing Model APT 105 6.1 Arbitrage Pricing Theory 105 6.2 Factor Sensitivities in APT 107 6.2.1 Passive Management 108 6.2.2 Active Management 108 6.2.3 Performance Evaluation 109 6.3 Comparison Between CAPM and APT 109 Summary 110 Key Terms 111 Self-Test 1 111 Self-Test 2 111

Topic 7 Efficient Markets Hypothesis 112 7.1 Efficient Markets 113 7.1.1 The Effect of Efficiency 114 7.2 Degrees of Efficiency 115 7.3 Empirical Tests of EMH 117 7.3.1 The Test for Weak Efficiency 117 7.3.2 The Test for Semi-strong and Strong Efficiency 120 7.4 Implication of EMH to Investment Strategies 120 7.5 Market Rationality 121 7.5.1 Behavioural Finance and Market Anomalies 121

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Summary 122 Key Terms 123 Self-Test 1 123 Self-Test 2 124

Topic 8 Fundamental Analysis and Security Selection 125 8.1� Fundamental Analysis 127 8.1.1 The Top-down Approach to Analysis 128 8.2 Economic Analysis 130 8.2.1 Aggregate Expenditure 130 8.2.2 Key Economic Variables and Economic Indicators 132 8.2.3 Business Cycles 133 8.3 Industry Analysis 136 8.4 Company Analysis 138 8.5 Valuation of Common Stocks Using Dividend Discount Models 139 8.5.1 The Zero Growth Model 140 8.5.2 The Constant Growth Model 140 8.5.3 The Variable Growth Model 141 8.6 Tax Exemptions on Real Property Gains Tax 143 8.6.1 The Constant Growth Earnings Valuation Model 144 8.7 Valuation of Common Stocks Using Price/Earnings Ratio 144 8.7.1 How Practitioners Use The P/E Ratio 145 Summary 146 Key Terms 147 Self-Test 1 147 Self-Test 2 148

Topic 9 Managing Portfolios Active and Passive Strategies 149 9.1 Individual Investors 150 9.2 Institutional Investors 151 9.2.1 Pension Funds 151 9.2.2 Insurance Firms 152 9.2.3 Mutual Funds 153 9.2.4 Banks 153 9.3 Objectives of Active Portfolio Management 153 9.4 Approaches to Active Management 154 9.4.1 Approaches to Active Management from the Perspective of an Individual Investor 154 9.4.2 Approaches to Active Management from the Perspective of an Institutional Investor 156 9.5 Active Equity Portfolio Strategies Management 161 9.5.1 Fundamental Analysis 162

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9.5.2 Technical Analysis 162 9.5.3 Anomalies and Attributes 164 9.6 Active Bond Portfolio Management Strategies 164 9.7 Passive Strategies for Equity Portfolios 166 9.7.1 Buy and Hold 166 9.7.2 Dollar-cost Averaging 168 9.7.3 Constant Beta 168 Summary 168 Key Terms 169 Self-Test 1 169 Self-Test 2 170

Topic 10 Evaluation of Portfolio Performance 171 10.1 The Importance of Performance Evaluation 175 10.1.1 Historical Results 175 10.1.2 Measuring Fund Performance 176 10.2 Institutional Investors 177 10.2.1 Dollar-weighted Returns Method 179 10.2.2 Time-weighted Returns Method 179 10.2.3 Comparison 179 10.3 Benchmarking 180 10.3.1 New Indices 180 10.3.2 Measuring Portfolio Return 185 10.3.3 Risk Adjusted Return 185 10.4 Sharpe Ratio 186 10.5 TreynorÊs Measure 186 10.6 JensenÊs Alpha 187 10.6.1 Application of Risk-adjusted Returns 188 10.6.2 Criticisms of Risk-adjusted Returns 189 10.7 Market Timing and Stock Selection 189 10.7.1 Market Timing 189 10.7.2 Stock Selection 190 Summary 191 Key Terms 192 Self-Test 1 192 Self-Test 2 192

Answers 194 References 225

COURSE GUIDE

PANDUAN KURSUS x

COURSE GUIDE xi

COURSE GUIDE DESCRIPTION

You must read this Course Guide carefully from the beginning to the end. It tells you briefly what the course is about and how you can work your way through the course material. It also suggests the amount of time you are likely to spend in order to complete the course successfully. Please keep on referring to Course Guide as you go through the course material as it will help you to clarify important study components or points that you might miss or overlook.

INTRODUCTION

BBPM4103 Portfolio Investment Management is one of the courses offered by Faculty of Business and Management at Open University Malaysia (OUM). This course is worth 3 credit hours and should be covered over 15 weeks.

COURSE AUDIENCE

This is a core course for students pursuing the degree in Bachelor of Accounting program. As an open and distance learner, you should be acquainted with learning independently and being able to optimise the learning modes and environment available to you. Before you begin this course, please confirm the course material, the course requirements and how the course is conducted. STUDY SCHEDULE

It is a standard OUM practice that learners accumulate 40 study hours for every credit hour. As such, for a three-credit hour course, you are expected to spend 120 study hours. Table 1 gives an estimation of how the 120 study hours could be accumulated.

COURSE GUIDE

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Table 1: Estimation of Time Accumulation of Study Hours

STUDY ACTIVITIES STUDY HOURS

Briefly go through the course content and participate in initial discussions

3

Study the module 60

Attend 3 to 5 tutorial sessions 10

Online participation 12

Revision 15

Assignment(s), Test(s) and Examination(s) 20

TOTAL STUDY HOURS ACCUMULATED 120

COURSE OBJECTIVES

By the end of this course, you should be able to: 1. Explain the basic concepts used in financial market and securities markets; 2. Calculate risk and return of any given asset or portfolio; 3. Appraise the effect of portfolio diversification; 4. Formulate efficient frontier of portfolio; 5. Apply capital asset pricing model to any given security, single-index, multi-

index and APT model to estimate portfolio return; 6. Appraise the usefulness of Efficient Market Hypothesis from the

perspective of portfolio investment; 7. Analyse an investment from the perspective of fundamental analysis; 8. Identify the different investment strategies such as active and passive

management strategies; and 9. Evaluate the performance of any given portfolio.

COURSE GUIDE xiii

COURSE SYNOPSIS

This course is divided into 10 topics. The synopsis for each topic can be listed as follows: Topic 1 explains the economics of the financial market. It also describes the types of investing and financing, and the types of financial markets and assets. It also explains the concept of unit trust funds and investment risk. Lastly it touches on Capital Market Plan and the type of career this field offers. Topic 2 explains the underlying concept of risk and return. It also states the methods on how to measure risk and return. It goes further by discussing the investorÊs behaviour and utility function. Concepts such as covariance and correlation and mean-variance analysis are also introduced and explained. Topic 3 examines the concept of portfolio formation. It explores the idea of diversification. It touches on the method on how to formulate portfolio return and risk. It discusses the role of correlation and covariance in portfolio diversification. It examines the role of correlation and covariance in portfolio diversification. Minimum variance portfolio is introduced. In addition, the differences between diversifiable risk and non-diversifiable risk are discussed. Topic 4 explains the concept of efficient frontier and Markowitz portfolio theory. It also applies the concept of capital allocation line (CAL). Furthermore, it derives capital market line (CML). Lastly, this topic applies asset allocation strategies in forming optimal portfolios and evaluates the usefulness of market indices. Topic 5 explains the concepts of Capital Asset Pricing Model (CAPM) and its assumptions. It derives from the Security Market Line (SML). It also applies SML for investment decision making. It analyses empirical evidence of CAPM. It appraises the implications that CAPM has for investors and evaluates the limitations of CAPM. Topic 6 explains the concept of single-index model. It also discusses the concept of Arbitrage Pricing Theory Model (APT), factor sensitivities, usage and empirical issues in APT. This topic also compares between CAPM and APT. Lastly, it discusses the concept of behavioural finance. Topic 7 explains the concept of efficient markets, the degrees of efficiency and the empirical tests of EMH. This topic also discusses the implication of EMH to investment strategies. Lastly, it touches on market rationality in relation to EMH.

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Topic 8 discusses the meaning of fundamental analysis. It analyses the economic environment of investment. It also touches on industrial analysis and the business cycle. It also analyses companies based by applying the principles of valuation. Lastly, this topic evaluates investment decision process and investment policy. Topic 9 discusses the Active and Passive Strategies. This topic compares individual and institutional investors. It touches on how to construct a portfolio. It formulates active management strategies for equity portfolios and bond portfolios. Lastly, this topic analyses and applies passive strategies in equity portfolio management. Topic 10 explains the importance of performance evaluation. It describes the methods of measuring returns and adjusted returns. It describes the meaning of benchmarking in the context of investment management. It applies the concept of TreynorÊs measure, Sharpe ratio and JensenÊs Alpha in the evaluation of portfolio performance. Lastly, it explains security selection and market timing.

TEXT ARRANGEMENT GUIDE

Before you go through this module, it is important that you note the text arrangement. Understanding the text arrangement should help you to organise your study of this course to be more objective and more effective. Generally, the text arrangement for each topic is as follows: Learning Outcomes: This section refers to what you should achieve after you have completely gone through a topic. As you go through each topic, you should frequently refer to these learning outcomes. By doing this, you can continuously gauge your progress of digesting the topic. Self-Check: This component of the module is inserted at strategic locations throughout the module. It is inserted after you have gone through one sub-section or sometimes a few sub-sections. It usually comes in the form of a question that may require you to stop your reading and start thinking. When you come across this component, try to reflect on what you have already gone through. When you attempt to answer the question prompted, you should be able to gauge whether you have understood what you have read (clearly, vaguely or worse you might find out that you had not comprehended or retained the sub-section(s) that you had just gone through). Most of the time, the answers to the questions can be found directly from the module itself.

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Activity: Like Self-Check, activities are also placed at various locations or junctures throughout the module. Compared to Self-Check, Activity can appear in various forms such as questions, short case studies or it may even ask you to conduct an observation or research. Activity may also ask your opinion and evaluation on a given scenario. When you come across an Activity, you should try to widen what you have gathered from the module and introduce it to real situations. You should engage yourself in higher order thinking where you might be required to analyse, synthesise and evaluate instead of just having to recall and define. Summary: You can find this component at the end of each topic. This component helps you to recap the whole topic. By going through the summary, you should be able to gauge your knowledge retention level. Should you find points inside the summary that you do not fully understand, it would be a good idea for you to revisit the details from the module. Key Terms: This component can be found at the end of each topic. You should go through this component to remind yourself of important terms or jargons used throughout the module. Should you find terms here that you are not able to explain, you should look for the terms from the module. References: References is where a list of relevant and useful textbooks, journals, articles, electronic contents or sources can be found. This list can appear in a few locations such as in the Course Guide (at References section), at the end of every topic or at the back of the module. You are encouraged to read and refer to the suggested sources to elicit the additional information needed as well as to enhance your overall understanding of the course.

PRIOR KNOWLEDGE

Learners of this course are required to pass BBPW3103 Financial Management I and BBPW3203 Financial Management II course.

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ASSESSMENT METHOD

The assessment method and evaluation distribution for this course can be listed as follows:

OLP 5% Assignment 30% Mid Term 26% Final Examination 39% Total 100%

REFERENCES

Elton, E.J., Gruber M. J., Brown S. J., & W.N. Goetzmann. (2007). Modern portfolio theory and investment analysis. (7th ed.). USA: John Wiley & Sons, Inc.

Reilly, F. K., & K. C. Brown. (2006). Investment analysis and portfolio

management. (8th ed.)., Thomson South-Western. Bodie, Z., Kane, A., & Marcus, A. J. (2005). Investments, (6th ed.). USA: Irwin

McGraw-Hill. Sivalingam A. (1990), Modern portfolio management. Longman Publication. Sharpe, W.F., Alexander, G. J., & J. V. Bailey. (1999). Investments. (6th ed.).,

New Jersey: Prentice Hall.

INTRODUCTION

Welcome to Portfolio Investment Management. This is a very interesting subject because it is a combination of many concepts from the field of economics, finance and accounting. Portfolio Investment Management is a body of knowledge developed by many scholars and researchers since 1950s, and today it is a field belongs to what is known as financial economics. Harry Markowitz, one of the scholars who had contributed significantly to this field, won the Nobel Prize in Economics in 1990. In the United States, some of students who have studied this subject ended up having careers in the Wall Street. Today, undergraduate students in finance select this subject as part of their course, and so do many accounting and economics students. Some of you may have invested monies in unit trust fund or „amanah saham‰ such as Amanah Saham Bumiputera (ASB), Amanah Saham Malaysia (ASM) or Amanah Saham Wawasan 2020 (ASW 2020) (Figure 1.1). But do you know

TTooppiicc

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Introduction to Financial Market and Securities

LEARNING OUTCOMES By the end of this topic, you should be able to:1. Explain the economics of financial market; 2. Discuss the two main types of investors; 3. Assess the four types of financial markets and assets; 4. Examine the concept of unit trust fund; 5. Describe the Capital Market Plan; and 6. Analyse the types of career in capital market.

Figure 1.1 : Examples of amanah saham in Malaysia

TOPIC 1 INTRODUCTION TO FINANCIAL MARKET AND SECURITIES

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that the fund managers use the knowledge acquired from Portfolio Management in managing your funds. You can also be a good investor if you master this subject. Therefore, you need to have the required patience and passion to learn this subject. We will begin this subject by introducing some background knowledge such as the economics of financial market, types of investors and financing, as well as the concepts of financial instruments and asset classes. We will also discuss in quite details on unit trust fund investment and the risks related to this type of investment. There will be also an introduction to Capital Market Plan. Lastly, we will talk on the types of career available in capital market.

Harry Markowitz is awarded the Nobel Prize in Economics (1990) for having developed the theory of portfolio choice.

The contribution for which Harry Markowitz now receives his award was first published in an essay entitled "Portfolio Selection" (1952), and later, more extensively, in his book, Portfolio Selection: Efficient Diversification (1959). The so-called theory of portfolio selection that was developed in this early work was originally a normative theory for investment managers, i.e., a theory for optimal investment of wealth in assets which differ in regard to their expected return and risk. On a general level, of course, investment managers and academic economists have long been aware of the necessity of taking returns as well as risk into account: "all the eggs should not be placed in the same basket". Markowitz's primary contribution consisted of developing a rigorously formulated, operational theory for portfolio selection under uncertainty - a theory which evolved into a foundation for further research in financial economics.

Markowitz showed that under certain given conditions, an investor's portfolio choice can be reduced to balancing two dimensions, i.e., the expected return on the portfolio and its variance. Due to the possibility of reducing risk through diversification, the risk of the portfolio, measured as its variance, will depend not only on the individual variances of the return on different assets, but also on the pairwise covariances of all assets.

TOPIC 1 INTRODUCTION TO FINANCIAL MARKET AND SECURITIES 3

THE ECONOMICS OF FINANCIAL MARKET

Underlying the concept of portfolio investment management is the existence of financial market. The understanding of the interaction between different economic agents like individual, households, firms and governments, is fundamental in understanding the interaction of various agents in an economic system. Economic Agents like individuals, households and firms have different needs for funds at different times. They also have surplus of funds at different times. When there is a surplus of funds, they would like to keep or invest those funds in some forms of financial instruments that exist in financial market. On the contrary, when they are in need of funds or in deficit of funds, they would like to borrow the required funds through some forms of financial instruments, from the financial market.

1.1

Hence, the essential aspect pertaining to the risk of an asset is not the risk of each asset in isolation, but the contribution of each asset to the risk of the aggregate portfolio. However, the "law of large numbers" is not wholly applicable to the diversification of risks in portfolio choice because the returns on different assets are correlated in practice. Thus, in general, risk cannot be totally eliminated, regardless of how many types of securities are represented in a portfolio. In this way, the complicated and multidimensional problem of portfolio choice with respect to a large number of different assets, each with varying properties, is reduced to a conceptually simple two-dimensional problem - known as mean-variance analysis. In an essay in 1956, Markowitz also showed how the problem of actually calculating the optimal portfolio could be solved. (In technical terms, this means that the analysis is formulated as a quadratic programming problem; the building blocks are a quadratic utility function, expected returns on the different assets, the variance and covariance of the assets and the investor's budget restrictions.) The model has won wide acclaim due to its algebraic simplicity and suitability for empirical applications. Generally speaking, Markowitz's work on portfolio theory may be regarded as having established financial micro analysis as a respectable research area in economic analysis.

Source: www.nobelprize.org (Retrieved 7 August 2007)

www.wsecurities.com/image9.gif(Retrieved 7 August 2007) www.ifa.com/.../12steps/Step2/harrymarkowitz.jpg(Retrieved 7 August 2007)


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The surplus units will lend their funds to financial markets, while the deficit units will borrow their funds from the markets. The demand and supply of funds through various financial instruments are the fundamental reasons for the existence of financial markets.

TYPES OF INVESTOR AND FINANCING

We assume typical economic agent is rational and it means he or she will always choose to maximise his or her utility. This is an important assumption regarding the behaviour of an economic agent. It is important to have a clear understanding of the types of investors that exist in the market. On a broad basis, investors are divided into retail investors and institutional investors. Figure 1.2 below summarises the main types of investors and its examples.

1.2

Discuss the following question in myLMS.

1. Do you think financial market is important?

2. Imagine if there is no financial market, what will you do if you have excess fund? On the other hand, what will you do if you are in need of extra fund?

ACTIVITY 1.1


Figure 1.2: Main type of investors

Retail investors usually refer to individual and household. Institutional investors usually refer to investors from commercial banks, investment banks, pension funds, insurance companies, asset management companies, unit trust funds, Lembaga Tabung Haji and other government linked organisations such as Permodalan Nasional Berhad (PNB) and Khazanah. Institutional investors comprise of professionally trained fund managers. We can further classify investors into local and foreign investors. Here, local investors refer to domestic investors originating from the home country, and foreign investors refer to investors from overseas market. Foreign investors deal with portfolio investment in Malaysia capital market and they are mostly institutional investors. Their portfolio investment can be from short to medium term in nature, varying from a few months to years and as such, their portfolio investments sometimes are also known as hot money. Moreover, there is also a demarcation between the types of financing. When an investor participates directly in the financial markets through investing in stocks or savings bond, it is known as direct finance/investment. However, when an investor purchases unit trust funds which hold a number of underlying financial assets, this is known as indirect finance/investment.


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TYPES OF FINANCIAL MARKET AND INSTRUMENT

Figure 1.3: Types of Financial Market

In general, there are four types of financial market as shown in Figure 1.3. They are money market, capital market, derivative market and foreign exchange market. All these markets complement each other in day-to-day market transactions. However, in line with this subject on Portfolio Investment Management, we will focus more to the discussion on capital market. Having an understanding of the financial market existence and the needs of various economic agents, the subsequent question now is how these economic agents fulfill their needs by participating in the financial market. As mentioned in the earlier section, economic agents have to invest in financial assets to fulfill their financial needs. Financial institutions offer financial instruments to investors. When investors buy or put monies into these instruments, they become the financial assets to the investors. The decision of investing in different financial assets depends on various factors such as investment horizon, purpose of holding these instruments and availability. We can divide financial instruments into several types. They are (i) debt, (ii) cash and cash-equivalent, (iii) equity, (iv) derivatives, (v) commodity and (vi) precious metal. All of them are shown in Table 1.1, 1.2 and 1.3 respectively.

1.3

1. What kind of behaviour do we assume for an economic agent?

2. A company issues new shares to the public in order to be listed in Bursa Malaysia. What type of financing is this?

SELF-CHECK 1.1


Table 1.1: Types of Financial Instruments Debt, Cash and Cash-Equivalent

Type Descriptions

Savings Account An account held with a financial institution.

Safe vehicle for short-term savings of any amount. High liquidity (easy to cash).

Savings Bond (SB)

A special type of bond issued by federal government, purchased through financial institutions.

Available only at specific times. Pay a fixed interest rate, subject to periodic adjustment by the goverment.

Government Treasury Bill (T-Bill)

Short-term investment: terms of one month to a year (considered a cash-equivalent).

Safe, government-backed.

T-Bills have a face value; you purchase it at a „discount‰ (less than the face value) and then redeem it at face value; the difference is your return (e.g. you may pay $90 for a $100 face value T-Bill you receive the face value upon maturity).

Term Deposit / Fixed Deposit

You invest a sum of money with a financial institution for a set period.

Interest and principal are guaranteed.

BankersÊ Acceptance (BA)

Short-term debt issued by corporations that is guaranteed by a bank.

Highly liquid (terms to maturity of less than a year).

Considered safe, low-risk. Purchased on a „discounted basis‰ to mature on a specific date; your

return is fixed.

Commercial Paper

Similar to BAs, but without the guarantee of a bank.

Available through financial institutions.

Government/ Municipal Bond

Issued by the federal government and provincial government and available through most financial institutions.

Set at fixed interest rate, for a specified term.

Safe (guaranteed to maturity by the issuing government and liquid). Come in terms of one to 30 years.

Can be sold in the bond market before maturity.

Corporate Bond Sued by a corporation and available through a brokerage house.

Set at fixed interest rate, for a specified term. Backed by specific assets of the issuing company.

Come in terms of one to 30 years and in various types.

Can be sold in the bond market before maturity.

Debenture Type of corporate bond, but not secured by specific company assets.

Simply based on the general reputation of the issuing company.

Mortgage-Backed Securities Cagamas

Fixed rate investments that represent an ownership share in a pool of mortgages insured by the federal governmentÊs Canada Mortgage and Housing Corporation.


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Table 1.2: Types of Financial Instruments Equity

Type Descriptions

Common Shares/ Stock

With common shares, you typically have voting rights.

Common shares are usually purchased for potential capital appreciation. If the company makes money you will share in the profits either by seeing the

value of your shares rise, by being paid dividends, or both; if the company suffers a poor year or the market decline, your share values may fall and dividends are unlikely (resulting in a potential capital loss). There are three different stocks:

(i) Blue Chip Stock – Typically stocks of large, stable and actively-traded companies with a

record of regular dividend payments.

– Tend to be conservative equity investments (ii) Penny Stock – Low-cost common shares (typically under $1), usually purchased for

speculative purposes. – Issued by start-up or unproven corporations seeking capital for

expansion (iii) Smalls, Mid and Large-Cap Stock – Corporations of all sizes issue common shares to raise money;

generally, the smaller the corporation, the higher the risk. Preferred Shares/ Stocks

Differ from common shares in several ways and in fact are regarded as bond-like investments.

Normally purchased by investors who want a steady stream of dividends, rather than capital appreciation.

Pay a dividend, which is higher-yielding than a common share. Value and share price influenced more by interest rate trends than by

companyÊs earnings. DonÊt typically give voting rights. They are preferred because you get a preferential claim to the assets/profits

ahead of common shareholders.

As shown in Table 1.2, shares or stocks are issued by corporations; investor becomes a partial owner in the corporation by buying shares (also called stocks) of the company. There are two main categories of shares: „common‰ and „preferred.‰ One word of caution is that share prices and returns fluctuate, and there is no guarantee as to income. Shares are traded on stock exchanges or over-the-counter markets. In addition, we can observe that shares or stocks can be classified into several types, namely the blue chip stock, penny stock, small stock, mid-cap stock and large-cap stock.


Table 1.3: Types Of Financial Instruments Commodities, Derivatives and Precious Metal

Types Descriptions

Commodities Bulk goods such as grains, metals, oil and foods.

Traded on commodities exchanges.

Held in the form of a contract.

Derivatives A security whose value depends on the market value of something else, such as a stock or commodity.

They are complex investments used by sophisticated investors for speculative purposes or to help manage risk (as a hedge against changing market conditions).

„Options‰ and „futures‰ are examples of derivatives; an option gives the investor the right to buy or sell a specific security at a given price before a specified date; a futures contract obligates the investor to buy or sell a specified amount of an asset at a set price on a certain date.

Precious Metals Gold, silver and other precious metals.

Held in form of bullion (the actual metal) or certificates of ownership.

UNIT TRUST INVESTMENT

Unit trust fund is an investment tool that pools monies from individual investor, household or sometimes institution, and those monies then are invested in stock market, bond market or other financial markets. The process of how mutual fund works is shown in Figure 1.4. In United Kingdom and Commonwealth countries like Malaysia, it is called unit trust fund, while in the United States it is better known as mutual fund.

1.4

1. Why do you think we need different type of financial market?

2. Check out from internet, what are the functions of these markets?

ACTIVITY 1.2


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Figure 1.4: The operation of unit trust fund/mutual fund

Source: www.mtbfunds.com/images/charts_graphs/mfp.gif

1.4.1 The Regulatory Framework

Figure 1.5: Flowchart on how unit trust funds are regulated

Source: www.oneinvest.com.my/images/framework.gif


As shown in Figure 1.5, there are three parties involved in unit trust investment. They are the asset management companies, an independent trustee and the unit holders. Asset Management Companies (AMC) which is also known as „Plan Sponsors‰, initiates the fund and looks for investors, while an independent trustee is the custodian of the funds operation. The unit holders are individual investors, or institutions. All the three parties are tied together through a trust deed and Securities Commission (SC) acts as the regulatory body for the unit trust industry.

1.4.2 Types of Funds

In this section, we will look at the different types of funds. Table 1.4 summarises several types of funds available. As shown in Table 1.4, there are basically seven types of funds in the market, namely equity funds, fixed income funds, money market funds, real estate investment trusts (REITs), exchange traded funds (ETF), balanced funds and Syariah funds. In addition, within equity funds, there are aggressive growth funds, index funds and International equity funds.

1. What are asset management companies (AMC)?

2. What are the two legislations related to unit trust industry?

SELF-CHECK 1.2


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Table 1.4: Types of Unit Trust Funds

No Type of Unit Trust Funds

Descriptions

1. Equity Funds An equity unit trust is the most common type of unit trust. The major portion of its assets is generally held in equities or securities of listed companies.

Equity unit trust funds are popular in Malaysia as they provide investors with exposure to the companies listed on Bursa Malaysia. The performance of the units is therefore linked to the performance of Bursa Malaysia. A rising market will normally give rise to an increase in the value of the unit and vice-versa.

There is a wide array of equity unit trusts available in the market, ranging from funds with higher risk, higher returns to funds with lower risk, lower returns.

(a) Aggressive growth funds These funds invest generally in companies with higher

capital growth potential but with associated higher risk.

(b) Index funds These funds invest in a range of companies that closely

match (or „track‰) companies comprising a particular index.

(c) International equity funds These funds invested primarily in overseas share markets.

2. Fixed Income Funds

These funds invest mainly in Malaysian Government Securities, corporate bonds, and money market instruments such as bankers acceptance and fixed deposits. The objective of a fixed income (or bond) funds is usually to provide regular income, with less emphasis on producing capital growth for investors. It is possible, however, for fixed income funds to generate both capital gains and losses during a period of volatile interest rate.

3. Money Market Funds

Money market funds operate in a similar way to a bank account the unit price is normally set at a fixed amount. Money market funds invest in low risk money market instruments that are in effect short-term deposits (loans) to banks and other low risk financial institutions, and in short-term government securities.


4. Real Estate Investment Trusts (REITS)

REITs invest in real properties, usually prominent commercial (office) properties and provide the investor with an opportunity to participate in the property market in a way which is normally impossible to the small time investor. By acquiring units in a listed REITs, however, it is possible to invest a small amount to gain exposure to the property market and have diversification in your portfolio.

5. Exchange Traded Funds (ETF)

ETF is linked unit trust fund whose investment objective is to achieve the same return as a particular market index. ETF often have low expense ratios, and can be bought and sold throughout the trading day through a stockbroker on an exchange.

6. Balanced Funds

Some investors may wish to have an investment in all the major asset classes to reduce the risk of investing in a single asset class. A balanced unit trust fund generally has a portfolio comprising equities, fixed income securities, and cash.

7. Syariah Funds The main objective of Syariah funds is to provide an alternative avenue for investors sensitive to Syariah requirements. Syariah funds will exclude those companies involved in activities, products or services related to conventional banking, insurance and financial services, gambling, alcoholic beverages and non-halal food products.

Source: http://www.fmutm.com.my

1.4.3 Risk and Return in Unit Trust Investment

In general, there is a relationship between risk and return in unit trust investment. As shown in Figure 1.6, aggressive growth funds are riskier than balanced funds. Balanced funds are riskier than bond funds and lastly, bond funds are said to be riskier than money market funds.


14

Figure 1.6: Balancing Risk and Return Between Various Types of Funds

Source: http://www.cba.ca/en/viewPub.asp?fl=6&sl=23&docid=26&pg=2#F

CAPITAL MARKET MASTER PLAN (CMP)

In this section, we will learn about the Capital Market Master Plan (CMP). Firstly, we will read a little bit regarding CMP background. Following that, we will look at how it is implemented.

1.5.1 Background

The Capital Market Master Plan or CMP is a comprehensive plan in charting the strategic positioning and future direction of the Malaysian capital market for the next 10 years. It will prioritise the immediate needs of the capital market and will chart its direction and long-term growth in anticipation of deregulation and liberalisation.

1.5

Among other things, the CMP aims to:

Address weaknesses in the capital market that were previously highlighted by the financial crisis;

Provide a strategic road map to facilitate future business development; and

Assist in the creation of an efficient and competitive capital market.


The CMP was first announced by the then Minister of Finance II and the Chairman of the SC on 6 August 1999 during the closing of the 1999 Securities Commission Annual Dialogue, and was subsequently approved by the Minister of Finance in December 2000. The CMP was then launched by the Minister of Finance on 22 February 2001.

1.5.2 Implementation

As at 30 June 2007, total of 122 recommendations (80%) of the CMP have been completed, with the remaining 30 (20%) in progress. The successful implementation of the CMP was achieved due to the strong commitment and support from major stakeholders in the Malaysian capital market. Details of the completed recommendations are shown in Figure 1.7. The CMP is a strategic blueprint charting the 10-year development of MalaysiaÊs capital market. It adopts a phased approach of implementing 152 recommendations to achieve its vision of a capital market that is:

Internationally competitive;

Highly efficient conduit for the mobilisation and allocation of funds; and

Supported by a strong and facilitative regulatory framework.

Figure 1.7: The implementation of the Capital Market Masterplan (CMP)

Source: http://www.sc.com.my/ENG/html/cmp/cmp_update.html

2007 marks the second year of the implementation of the third phase of the CMP, which spans from 2006 to 2010. CMP Phase 3, which is aligned with the 9th Malaysian Plan, focuses on further broadening and deepening of the capital


16

market and on enhancing the international competitiveness of the Malaysian capital market. In this context, technological change and globalisation are already re-shaping industry structures and boundaries transforming capital market industry competitive dynamics around the world. Similarly, the rapid growth of the Asian economies and capital markets are already having a substantial impact on regional order-flows and portfolio allocations. It is the intention of the SC to adopt and implement forward-looking policies that maintains a balance of optimism and imbues a willingness to adapt so that Malaysia will be positioned to face the challenges and to capitalise on opportunities thrown up by a fast-changing financial and economic landscape. This approach will also increase the extent of Malaysian industry participation in global capital markets. The building of efficient and competitive market mechanisms is required to support the efficient intermediation of the large pools of domestic and regional savings. A developed capital market, attractive to domestic and international investors and issuers, will complement MalaysiaÊs highly international economy and will increase the overall level of wealth creation and growth generation. CMP Phase 3 will also continue with further initiatives to further strengthen the nationÊs position as an international centre of origination and trading for Islamic instruments and for wealth management services. Bank Negara, SC and other stakeholders have collaborated to launch the Malaysia International Financial Centre initiative (MIFC) with a view to creating an increasing liberalised environment for Islamic financial activities and tax incentives were provided to attract global players and capital flows to conduct Islamic intermediation activities in MalaysiaÊs Islamic Capital Market.

TYPES OF PROFESSION IN CAPITAL MARKET

Before we close this topic, let us discuss the various types of work or profession that exist in the capital market. As we have discussed earlier from 1.1 to 1.5, behind the scene of a functioning of capital market, we must be aware that we need various types of professionals to support the good functioning of capital market. These professions can be your future job opportunities as well!

1.6


Figure 1.8: The website of Securities Commission Source: http://www.sc.com.my

The first group of people is regulators. The regulator whom is given the authority of watching the functioning of Bursa Malaysia (formerly known as Kuala Lumpur Stock Exchange (KLSE)) is Securities Commission (SC) (Figure 1.8). Companies that are listed on the Bursa are known as Public Listed Companies or PLCs. These companies must comply with the Securities Industry Act (SIA 1983). Companies (PLCs) are required to submit annual financial report to the SC. Other than that, Bank Negara Malaysia (BNM) is given the authority of overseeing the functioning of financial institutions such as commercial banks and merchant banks. The second group of people is the finance and banking professionals. They are bankers, analyst and portfolio managers. Portfolio managers are also known as fund managers. They basically manage the funds on behalf of the asset management companies (AMC) as we have discussed earlier. Supporting this group are analysts. They are known as „research analyst‰, „market analyst‰ or „financial analyst.‰ These analysts provide analysis of companies listed in the Bursa Malaysia to the fund managers, so that fund managers can select good stocks to be included in their portfolios.


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In this topic we have discussed the economics of financial market. We have

shown that there is a need for the existence of various players in the market to enable the market force of demand and supply to come into play.

We have also distinguished the differences between indirect and direct financing and based on that, investors can be also classified along that line.

The major part of discussion deals with financial assets and asset classes that are available in the market. These asset classes are invested by fund managers to provide returns to unit trust investors.

We have discussed the recent development in the Malaysian capital market. One of prominent development since 2001 is the launch of capital market plan. This is a 10-year strategic plan to develop the Malaysian capital market.

Lastly, we have discussed the various type of careers in the capital market.

Bond portfolio

Capital market plan

Deficit of funds

Direct finance

Economic agent

Financial market

Hot money

Indirect finance

Institutional investor

Portfolio investment

Regulator

Retail nvestor

Suplus of funds

Unit trust funds

1. Give a few examples of economic agent. 2. Draw supply and demand curve of funds for a financial market. Explain. 3. Given two examples of retail investor. 4. There are two ways to classify investors. What are they?


5. What is direct financing? 6. Who are institutional investors? 7. What is hot money? 8. Name the different types of financial markets?

1. Differentiate the meaning of financial instrument and financial asset? 2. Name the various types of financial instrument available in the market? 3. What are the three parties involved in unit trust investment? 4. What are the main legislations used in unit trust investment? 5. What is the objective of Capital Market Master Plan (CMP)? 6. How many phases are there in implementing CMP? 7. Within equity funds, are there any sub-categories? 8. List the various careers in Capital Market.

INTRODUCTION

Welcome to Topic 2 on risk and return! In the earlier topic, we have touched on the concept of risk when discussing different types of unit trust funds. In this topic, we will introduce to you the fundamental concepts of risk and return. These concepts are the building blocks in understanding portfolio management. Hence, Topic 2 is very important if you intend to progress well in the subsequent topics. We will begin by explaining the underlying concept of risk and return and then followed by how to measure return and risk. As we move on, we will also talk about the concepts of correlation and covariance. Finally, we will put together the concept of risk and return together in what is known as mean variance analysis, in the context of portfolio investment. We wish to remind you that the story of risk return is closely related to Topic 3. Hence, please read on until the end of Topic 3 before you put up any question! Measuring financial risk is important as highlighted by the speech of Mr. Alan Greenspan, the former chairman of the United States Federal Reserve Board (1987-2006), a body that oversees the Federal Reserve Bank. Enjoy the reading!

TTooppiicc

2Risk and

Return

2 By the end of this topic, you should be able to:

1. Explain the underlying concept of risk and return;

2. Describe how to measure return and risk;

3. Discuss investorÊs behaviour and utility function;

4. Measure covariance and correlation; and

5. Explain mean-variance analysis in the context of investing in riskysecurities.

LEARNING OUTCOMES

TOPIC 2 RISK AND RETURN 21

Measuring Financial Risk in the Twenty-first Century Remarks by Chairman Alan Greenspan Before a conference sponsored by the Office of the Comptroller of the Currency, Washington, D.C. October 14, 1999 One of the broad issues that you have been discussing today is the nature of financial risk. This evening I will offer my perspective on the fundamental sources of financial risk and the value added of banks and other financial intermediaries. Then, from that perspective, I will delve into some of the pitfalls inherent in risk-management models and the challenges they pose for risk managers. Risk, to state the obvious, is inherent in all business and financial activity. Its evaluation is a key element in all estimates of wealth. We are uncertain that any particular nonfinancial asset will be productive. We're also uncertain about the flow of returns that the asset might engender. In the face of these uncertainties, we endeavor to estimate the most likely long-term earnings path and the potential for actual results to deviate from that path, that is, the asset's risk. History suggests that day-to-day movements in asset values primarily reflect asset-specific uncertainties, but, especially at the portfolio level, changes in values are also driven by perceptions of uncertainties relating to the economy as a whole and to asset values generally. These perceptions of broad uncertainties are embodied in the discount factors that convert the expectations of future earnings to current present values, or wealth. In a market economy, all risks derive from the risks of holding real assets or, equivalently, unleveraged equity claims on those assets. All debt instruments (and, indeed, equities too) are essentially combinations of long and short positions in those real assets. The marvel of financial intermediation is that, although it cannot alter the underlying risk in holding direct claims on real assets, it can redistribute risks in a manner that alters behavior. The redistribution of risk induces more investment in real assets and hence engenders higher standards of living. This occurs because financial intermediation facilitates diversification of risk and its redistribution among people with different attitudes toward risk. Any means that shifts risk from those who choose to withdraw from it to those more willing to take it on permits increased investment without significantly raising the perceived degree of discomfort from risk that the population overall experiences.

Source: http://www.federalreserve.gov/boarddocs/speeches/1999/19991014.htm

TOPIC 2 RISK AND RETURN

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RISK AND RETURN 2.1

By having an understanding of the concept of asset class in Topic 1, it is assumed that investors intend to invest their surplus unit of monies with the expectation to receive returns in future periods. For example, an investor of unit trust fund expects to receive a five percent annual return based on the historical returns of the fund. Due to changes in macroeconomic factors, historical returns may not be the same as current return. This investor may have set five percent annual return as investment objective. However the actual return may vary according to market condition. There could be three possible scenarios:

It is important to understand return is a measurement concept which is related to period of time and economic condition. Hence, a less than favourable return or negative return is related to one particular period, for example a year or a month. In subsequent period, if macroeconomic factors become favourable, for instance, a sudden increase inflow of Foreign Direct Investment (FDI) to Malaysian economy or an increase of quarterly Industrial Production Index (IPI), then the return from investment may become positive.


2.1.1 The Concept of Volatility

Based on the above discussion, it is therefore understandable that returns from investment are volatile. In portfolio investment, risk is measured using the concept of standard deviation of the expected returns, which is a statistical concept that describes the dispersion of returns around the expected returns. For example, if an investment is said to have an expected annual return of five percent with a standard deviation of two percent. Therefore, under the assumption that the returns are normally distributed, it could be interpreted that the return is between three percent to seven percent i.e. the expected return plus or minus one standard of deviation.

2.1.2 Definition and Type of Risk

Henceforth, based on the above, risk is defined as the uncertainty of future outcomes. Often it is stated as the probability having unfavourable outcome to the investors. Generally, there are many types of risks which are related to portfolio investment as illustrated by Figure 2.1.

Currency Risk

Systemic Risk

Operation Risk

Credit Risk

Liquidity Risk

Market Risk

Types of Risk

Figure 2.1: Type of Risks

Now, let us look at Table 2.1 that itemise the details about these six different types of risk.


24

Table 2.1: Types of Risk and its Descriptions

No Types of Risk Explaination Example

1. Market Risk

Related to adverse movements in the value of a security or securities.

When there is an increase in oil prices which would increase the operating cost of transportation, stocks of airlines and logistics companies would decrease in value.

2. Liquidity Risk

Related to the inability of converting the existing securities into cash at reasonable price.

If an investor holds a stock that has extremely low trading volume, then it would be difficult to sell the stock due to inactive market for that stock.

3. Credit Risk Related to the inability of seller or buyer of securities to fulfill the financial obligations in the specified time period.

A bond issuer who is unable to fulfill the interest payment as promised by the contract. This would cause financial loss to bond holders. Therefore, it is important for prospective bond investors to assess the creditworthiness of bond issuer and its total financial commitments.

4. Operation Risk

Related to the inability of information system or trading system to have accurate record or effective internal control for smooth transaction between seller and buyer of securities.

A sudden breakdown in trading system would result in material loss to investors as they could not conduct the selling and buying of securities through the stock exchange.

5. Systemic Risk

Refers to the entire risk of decline in prices faced by all securities traded in the stock market due to some changes in macroeconomic factors or policy shifts.

For example, the imposition of capital control by government may be perceived by foreign fund managers as an unfavourable event resulted in general price decline of majority of securities listed in the stock market.

6. Currency Risk

Related to risk of loss in value due to conversion of returns or investment priced in foreign currency to domestic currency or vice versa, due to unexpected changes in exchange rates.

For example, a unit trust fund which invests part of its funds into foreign securities will face currency risk due to unexpected changes in exchange rates. This risk is unavoidable in cross border investment. Hence, portfolio managers must be aware of such risk especially when repatriating the returns or dividends of foreign securities to home country. This is can be done by hedging the foreign currency returns in advance by using derivatives.


In this topic, we will touch on investment risk and also portfolio risk in subtopic 2.3. Investment risk is a general concept. It can take the meaning of market risk, liquidity risk or credit risk. Portfolio risk refers specifically to the risk of portfolio i.e. the risk when we combine different financial assets or securities. Of course, the main idea of portfolio theory is attempting to reduce portfolio risk by having different combination of financial assets with different correlation coefficients.

SELF-CHECK 2.1

1. During the Asian financial crisis in 1997, assuming that you were an investor in stock market, what kind of risk did your investment suffer?

2. The subprime mortgage problem in the US is expected to pose somerisks to commercial banks. What kind of risk do commerical banksface?

(Hint: search the keyword „subprime mortgage‰ in www.google.com)

MEASURING RETURN 2.2

2.2.1 Rate of Return

How do we measure the Rate of Return?

What we need is a measure of the effect on relative wealth at the end of an investment period. The rate of return links initial ringgit investment and end-of-period wealth. Say that the initial investment is RMI; the final wealth is RMW. Then the investorÊs rate of return, R, is

W I

RI

(2-1)


26

From equation (2-1), if we hold a financial asset for a period of time, and during the period, we receive distribution of dividend (Dt). Then we must write a new equation (2-2) as shown below. This is known as Holding Period Return (HPR) for time period t,

1

1

t t tt

t

P P DR

P

(2-2)

HPR for time period t is the capital gain (or loss) plus distributions (Dt) divided by the beginning- period price (Pt-1). Current price or end-of-period is Pt. The distribution for stocks, it is dividend; for bonds, it is coupon payment. The time interval, t can be a day, week, month, or year. Rates of Return are the fundamental units that analysts and portfolio managers use for making investment decision. There are two characteristics of HPR. Firstly, there is element of time. For example, rate of return is a monthly figure. Secondly, no currency unit is attached to it. The resulting ratio would not have any units because the denominator and numerator cancel one another.

2.2.2 The Certain and Uncertain Outcomes

Let us now look at the scenarios regarding certain and uncertain outcomes.

Scenario 1: Certain Outcomes

The above rate of returns is calculated with the assumption that certain present value of the investments and the rate of return.

However, in the real world, for risky assets we often need to consider the various outcomes and assign probabilities to each one of them.

Scenario 2: Uncertain Outcomes (Real World)


Risk and Returns: An Example Suppose the existing price (P0) of XYZ firm is RM30 per share; the best estimates of the future price are:

Probability End-of-Period Price Return 0.1 $25 16.70% 0.2 $28 6.70% 0.4 $30 0 0.2 $35 + 16.70% 0.1 $45 50%

2.2.3 Expected Return

From the above example, we know we need some statistics to summarise the range of possible outcomes. We need the Measures of location describe the most likely outcome in a range of events. The most often used measure of location is the mean or expectation. The mean is defined as:

1

( ) PrN

i ii

E X

X (2-3)

Pr is the probability of random events, X is the possible Event outcomes. The mean weights each event by its probability, then sums all events. For XYZ firm, the expected end of period price is: = 0.1(25)+ 0.2(28)+ 0.4(30)+ 0.2(35)+ 0.1(45) = $31.60E P

The mean (expected) return is the expected price less the current price divided by the current price. Alternatively, we can use the previous approach and apply it to this case

= 0.1(-16.7%) + 0.2(-6.70%) + 0.4(0%)+ 0.2(16.70%)+ 0.1(50%) = 5.30%E R


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MEASURING RISK 2.3

It is important for us to be able to quantify or measure risk. If we can measure and price risk correctly, then we may observe the following:

(i) Investors value risky assets;

(ii) There will be better allocation of resources in the economy;

(iii) Investors are better at allocating their savings to various types of risky securities; and

(iv) Managers better-off allocating shareholdersÊ (and creditorsÊ) funds among scarce capital resources.

2.3.1 Investment Risk

Supposed that we invest RM1000 in XYZ firm, we expect to have an end-of-period wealth of RM1053. However, you should ask yourself an important question: what is the risk being taken? There is variance. The variance is the statistic most frequently used to measure risk (this is the dispersion of the distribution). Variance is defined as the expectation of the squared differences from the mean:

2 2

2 2

2 2

2 2

Var(X) E[{X E(X)} ] E[(X ) ]

E[X 2X ]

E(X ) 2E(X)

E(X )

Remember to take the probabilities of the events occurring, that is:

(2-4) 2

1

( ) Pr ( ( )N

i ii

Var X X E X


Applying this concept to our example of XYZ firm, we will obtain the following:

2 2 2

2 2

2 2 2 2 2

= 0.1 25 - 31.60 + 0.2 2.8 - 31.60 + 0.4 30 - 31.60

+0.2 35 - 31.60 + 0.1 45 - 31.60

= 0.1 6.6 + 0.2 3.6 + 0.4 1.6 + 0.2 3.4 + 0.1 13.4

= 0.1 43.56 + 0.2 12.96 + 0.4 2.56 + 0.2 11.56 + 0.1 179.56

= 28.24

Var P

Var P

Var P

Var P

This is the variance expressed in RM squared.

ACTIVITY 2.1

1. Why do we need to know the risk and return?

2. Like anything else in life, the problem of uncertainty exists. Do you make use of probability concept to find the most likely solution to our problem?

2.3.2 Standard Deviation

Variance is one measure of risk.

Investors, though, do not usually think in terms of Ringgit squared. Hence we shall be using a standard deviation, which is a square root of the variance.

In our previous example, this gives us

5.31P Var P RM (2-5)

If returns distributions are normal, we can use the expected return and standard deviation to describe the entire probability distribution. In this case, the standard deviation is a measure of (downside) risk.


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2.3.3 Frequency of Means and Standard Deviation

If you have a mean and a standard deviation on a monthly basis you can express them on an annual basis by multiplying them with 12 and, respectively: 12Annual Monthly (2-6) 12Annual Monthly (2-7) Examples

An average return of 1% per month can be expressed as an average return of 12% per year;

A monthly standard deviation of 6% corresponds to an annual standard deviation of 21%.

INVESTOR’S BEHAVIOUR AND UTILITY FUNCTION

2.4

Underlying the concept of portfolio theory, investors are assumed to be risk averse. It is said that investors demand returns to compensate for their risk taking activity, of which is known as risk premium. Hence, investors assume risk with anticipation to obtain returns, of which part of the returns is risk premium. From economics point of view, the trade-off between risk and return of investors is measured by utility function in Figure 2.2. As shown in Figure 2.2, there are three indifference curves of U１, U２ and U３. We can observe that U３is more preferred than U２. Likewise, U２is more preferred than U１.


Figure 2.2: Utility function

2.4.1 The Concept of Utility

A risk averse individual is one who prefers less risk for the same expected return. If you give such an investor a choice between RMA for sure, or a risky gamble in which the expected payoff is RMA, a risk averse investor will go for the sure payoff. Individuals are generally risk averse when large fractions of their wealth is at risk. This is important because it introduces us to the relationship between an individualÊs wealth and utility.

2.4.2 Why the Knowledge of Utility Function is Important?

Knowledge of the investorÊs utility function enables him/her to choose between securities. In a single measure we have the investorÊs attitudes to risk and return at each level of wealth. If the investors do not have knowledge of the utility function, it is difficult for them to make decisions between different securities with different expected returns and different risks.


32

There are several factors that influence oneÊs utility function. Factors such as:

(i) Different degrees of unwillingness to bear risk; or

(ii) How much the investment could affect the investorÊs total wealth. For example, a potential loss of RM1,000 would probably worry a millionaire less than someone with earnings of RM100 per week. We need to put some structure on the concept of risk aversion. In this way we will better understand the dynamics in the investment process. Although investors are presumed risk averse, each investor will face different trade-off decisions between different risk and expected returns.

The indifference curve represents a set of risk and expected return combinations that provide the investor with the same amount of utility. They indicate an investorÊs preference for risk and return.

Drawn on a two-dimension where the horizontal axis gives you risk and the vertical axis provides you expected return. When we use quadratic utility functions, we can nicely express our utility functions; one example is the following:

0.005U E R A 2= ‐ (2-8) Hence, the investor just considers risk and return. In other words, you require a higher expected return, the higher the risk of the investment. Based on equation (2-8), where U is the utility value and A is an index of investorÊs risk aversion, then

If A < 0 the investor is risk-loving. If A > 0, then the investor is risk averse.


Figure 2.3: Indifference curves for a risk-averse investor

As shown in Figure 2.3, investors are risk-averse. If they are highly risk-averse, then their indifference curve will look like Figure 2.4. However, if they are low risk-averse investors, then their indifference curve will look like Figure 2.5.

Figure 2.4: Indifference curves for a highly risk-averse investor


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Figure 2.5: Indifference curves for a low risk-averse investor

COVARIANCE AND CORRELATION 2.5

In this section, we will look at the covariance and correlation.

2.5.1 Covariance

When we consider a combination of two or more securities, we have to start thinking about the covariance, which is a measure of the co-movements between the different securities. Covariance will give you a measure on how returns of different securities move in relation to each other. This will become extremely important when you consider portfolios of assets.

Corr(ABC,XYZ) = 0.61

Corr(XYZ,KLM) = 0.27

Figure 2.6: Covariance


As shown in Figure 2.6, we can observe that the top series (ABC) is moving in the same direction and similar magnitude as the central series (XYZ). Hence, it is found that the correlation between the two series is 0.61. As for the bottom series (KLM), it does not move in similar manner with XYZ. It is found that the correlation between the two series is 0.27. We can say they are lowly correlated. Let us assume we have two variables, X and Y. Then the covariance between X and Y is given by:

Cov(X,Y) = E[{X E(X)}{Y E(Y)}] (2-9) = E[{XY XE(Y) E(X)Y + E(X)E(Y)}] = E(XY) E(X) E(Y) When X and Y are independent then we find that Cov(X,Y) = 0. We can state the above (2-8) <<or (2-9)>> in the below manner

N

RRRR

Covyyxx

xy

]][[

(2-10)

where:

Covxy = Covariance between x and y

Rx = Return of security x

Ry = Return of security y

xR = Expected return of security x

yR = Expected return of security y

N = Number of observations


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2.5.2 Relationship between Variance and Covariance

One important result is the following: Var(X + Y) = Var(X) + Var(Y) + 2Cov(X,Y) (2-11) If X and Y are independent then:

Var(X μ Y) = Var(X) + Var(Y)

Var(aX μ bY) = a2Var(X) + b2Var(Y), where a and b are constants.

2.5.3 Correlation

There is a need to examine the relationship between two or more financial variables. Two useful methods are scatter plots and correlation analysis. A scatter plot is a graph that shows the relationship in two dimensions. Example of the relationship between long-term money growth and long-term inflation in seven industrialised countries. Figure 2.7 shows a fairly strong linear relationship with a positive slope.

Figure 2.7: Scatter Plot

Correlation analysis expresses the same relationship using a single number. It measures the direction and the extent of linear association. The correlation coefficient is a number between -1 and 1. If there is no relationship between the two financial series, the correlation coefficient is zero or a very low figure. As the strength of the relationship between the two financial series increases so does the correlation coefficient. A perfect fit gives a coefficient of 1.0. Thus the higher the correlation coefficient, the higher co-movement between the two series.


To calculate correlation coefficient, first, we need another measure of linear association: covariance. The correlation coefficient is the covariance of two variables divided by the product of their sample standard deviation.

( , )

xy

x y

Cov X Yr

s s (2-12)

Where

Like covariance, correlation coefficient is a measure of linear association. The advantage of being a single number, with no unit of measurement. The only limitation that it is not always reliable if nonlinear relationship between two variables or outliers exist. However, bear in mind that correlation does not imply causation. It only measures the strength or linear relationship of two variables.

MEAN-VARIANCE ANALYSIS

Putting together what we have learnt from the above on risk and return on something known as mean-variance analysis. As shown in Figure 2.8, we view investors as measuring the expected utility of choices among risky assets by using the mean and variance of the different combinations of these assets. For a portfolio, the risk and return are measured by the mean and variance of weighted average of the assets held in the portfolio.

2.6

xyr = Coefficient of correlation between x and y.

xyCov = Covariance between x and y.

xs = Standard deviation of x.

ys = Standard deviation of y


38

Figure 2.8: Mean-variance analysis

Investors want to have high returns, but they also want the returns to be as certain as possible. In other words, the investor wants to maximise expected return and minimise risk. These two objectives must be balanced against each other when making the investment decision. Hence the shaded area in Figure 2.8 shows all possible mean and variance pairs that an investor can attain by holding risky assets.

The underlying concept of risk and return by presenting the possible

scenarios of favourable, fair and unfavourable outcomes.

About all types of risk faced by investors.

On how to measure return. We have introduced rate of return, Holding Period Return (HPR) and expected return.

Risk of which is measured by variance and also standard deviation and also the conversion of risk from monthly to annual values.

The utility function of investors and reasons why the knowledge of utility function is important.

Covariance of different financial series have been discussed, and followed by correlation coefficient.

Put altogether the concepts into mean-variance analysis, investors have one investment goal of finding the optimal combination of different assets by looking. Mean of the securities returns and also their risk.


Certain outcomes Credit risk Currency risk Expected return Liquidity risk

Market risk Operation risk Rate of return Systemic risk Uncertain outcomes

1. What are the definitions of risk? 2. How many types of risk are there? 3. What is the main idea of portfolio theory? 4. Differentiate investment risk and portfolio risk? 5. In view of the existence of uncertainties, how do we measure return? 6. What are the benefits to investors if they can measure and price risk

correctly? 7. What is the measure of downside risk? 8. For risk-averse investors, what is their demand for risk-taking activities?

End of Period Returns Probability Return

30 0.10 3.00

40 0.30 12.00

50 0.40 20.00

60 0.10 6.00

70 0.10 7.00

30 0.10 3.00


40

1. Based on the above, calculate expected return?

2. Based on the above, calculate the investment risk?

3. Based on the above, calculate the downside risk (standard deviation)?

4. What is covariance? If A and B have positive covariance, what does it mean? If A and B have negative covariance, what does it mean?

5. How variance is related to covariance?

6. How covariance is related to correlation coefficient?

Year Rx Ry

1 10 17

2 12 13

3 16 10

4 18 8

7. Based on the above, calculate the covariance between security X and Y?

8. Based on the above, calculate the correlation coefficient of X and Y?

INTRODUCTION

Welcome to Topic 3. After we have studied the basics of risk and return as well as correlation and covariance, we will now expand these ideas to better understand portfolio theory. This topic introduces students to the fundamental concepts and terminologies that are used in portfolio theory. These concepts are important for understanding portfolio construction and management. In this topic, we will begin by learning the underlying concept of portfolio formation and the idea of diversification. We will also see the importance of correlation and covariance in portfolio diversification. Here, the differences between systematic risk and non-systematic risk are also explained. Figure 3.1 explaining Modern Portfolio Theory of MPT.

TTooppiicc Portfolio

Theory and

Diversification

33

6. Distinguish the differences between diversifiable risk and non-diversifiable risk.

5. Analyse the concept of minimum variance portfolio; and

LEARNING OUTCOMES By the end of this topic, you should be able to:

1. Explain the concept of portfolio formation;

2. Discuss the idea of diversification;

3. Calculate and formulate portfolio return and portfolio risk;

4. Explain the importance of correlation and covariance in portfolio diversification;

TOPIC 3 PORTFOLIO THEORY AND DIVERSIFICATION

42

Modern Portfolio Theory (MPT)

A theory on how risk averse investors can construct portfolios to optimise or maximise expected return based on a given level of market risk, emphasising that risk is an inherent part of higher reward. Also called "portfolio theory" or "portfolio management theory."

According to the theory, it's possible to construct an "efficient frontier" of optimal portfolios offering the maximum possible expected return for a given level of risk. This theory was pioneered by Harry Markowitz in his paper "Portfolio Selection," published in 1952 by the Journal of Finance. There are four basic steps involved in portfolio construction:

(a) Security valuation

(b) Asset allocation

(c) Portfolio optimisation

(d) Performance measurement

Figure 3.1: Modern portfolio theory Source :http://www.investopedia.com/terms/m/modernportfoliotheory.asp

INTRODUCTION TO PORTFOLIO THEORY 3.1

In this topic, we would like to discuss the concepts related to portfolio theory. In simple terms, a portfolio is made from a combination of securities. We can combine different stocks to make a portfolio, or we can combine stocks and bonds to make a portfolio. In other words, we can combine different asset classes (as introduced in topic 1) to make a portfolio. Having said that, we need to consider the effects of risk and return when combining different securities. Why we are interested in forming a portfolio? This is because combining these asset classes into a portfolio may be a good idea in reducing risk. Recall the mean-variance analysis we have discussed in sub topic 2.6, for each security, investors compare the expected return from a range of probable outcomes with the risk of security. Hence, investors need only to consider expected returns and standard deviations when choosing securities for their investment portfolios. There are two possible choices:

TOPIC 3 PORTFOLIO THEORY AND DIVERSIFICATION 43

(i) Investors can either choose securities that offer highest return given level of risk; or

(ii) They can choose the lowest risk for a given level of returns.

DIVERSIFICATION 3.2

Whether the combination of different asset classes into a portfolio will reduce the risk or not is a question that needs to be answered. Generally, when we combine different stocks into a portfolio, we are likely to reduce the combined risk or portfolio risk. The risk of a portfolio is measured by its standard deviation. How can we explain this matter? For example, letÊs say a person invests his monies in two stocks, one in a plantation sector and another one in construction sector for a two-year period. How can the concept of diversification work in portfolio investment? In a hypothetical case, letÊs say, in that period, the plantation sector is performing extremely well because palm oil is found to be useful as bio-fuel. At the same time during that period, as construction material is getting expensive, and in the environment of high interest rates, construction activities are slow. Hence, the good returns from the investment in the plantation sector will be able to offset the not-so-good returns from construction sector. So the investor ends up with a fair return as he diversifies his investment in two sectors. From economics, we know that there is such thing as a business cycle (refer to Topic 9) in an economy. There are certain years where the economy is performing reasonably well and there are certain years where the economy is performing not so well. And then, there are certain industries that perform well, and there are also certain industries that are not performing so well due to internal or external factors, or some macroeconomic factors. An example is the Asian financial crisis in 1997 where the economy was not doing well. The principles of diversification also work in such a scenario, if one person invests his monies in a developed country like Japan, as well as in a developing country like Malaysia during the Asian financial crisis. This investor will end up with a fair return if he diversifies his investment in two countries. We will soon learn that diversification plays an important role in designing efficient portfolios. We will explain the concept of diversification in a more rigorous manner using a mathematical approach. We will use the concept of correlation we have learned in Topic 2 to do so. This will be explained in subtopic 3.5.


44

Before that, we will learn how to calculate portfolio return and portfolio risk in subtopic 3.3 and 3.4 respectively.

We also practice the concept of diversification in our day-to-day activities? Remember the old adage „do not put all your eggs in one basket?‰ Think of one or two examples that apply this idea.

ACTIVITY 3.1

PORTFOLIO RETURN 3.3

The expected return of a portfolio is given by the weighted average of the expected returns obtained from the individual stocks (held in the portfolio)

(3-1) )()(1

i

ni

iip REwRE

Where w is the weight that each stock has in the portfolio, with the total weight being equal to 1.

(3-2) 11

ni

iiw

In the case of a two-asset portfolio: 1 1 1 21PE R w E R w E R (3-3) where

)( pRE = Expected return of the portfolio

)( 1RE = Expected return of stock 1

)( 2RE = Expected return of stock 2

1w = Weight of Investment in stock 1

11 w = Weight of Investment in stock 2 two


3.3.1 Example

LetÊs consider two securities for investment. Aman Berhad and Sentosa Berhad From the historical record, we know that Security E[R] SD[R] Aman 15% 18.6% Sentosa 21% 28.0% If you have decided to invest 60 percent of your portfolio in Aman and 40 percent in Sentosa Berhad, then what is the portfolio return? The answer is

0.60 15 0.40 21 17.40%pE R Recall that from Topic 2, the expected return of a portfolio equals to the weighted average of the individual securityÊs returns.

PORTFOLIO RISK 3.4

The risk of a portfolio is measured by its standard deviation or the variance. LetÊs say we have a portfolio with two stocks, the variance of portfolio is

2 2 2 2 2( ) 21 1 2 2 1 2 12

VAR R w w w wp p

(3-4)

Where 1w = Weight of Investment in stock 1

2w2

= Weight of Investment in stock 2

12

= Variance of Investment in stock 1

2 = Variance of Investment in stock

12 = Covariance between stock 1 and 2 We can also express the above using the correlation coefficient, 1,2 , between the two stocks: Remember the formula (2-12) from topic 2,

2 2 2 2 2( ) 21 1 2 2 1 2 12 1 2

Var R w w w wp p

(3-5)


46

CORRELATION AND RETURN: TWO ASSET CASE

3.5

Following our earlier discussion from Topic 2 on the concept of correlation, we extend the idea to two assets. As shown in Figure 3.2, 3.3 and 3.4. In Figure 3.2, it can be observed that if stock A and B are perfectly and positively correlated, then the returns of A and B are positively and linearly related. In Figure 3.3, if stock A and B are perfectly and negatively correlated, then returns of A and B are inversely related. If stock A and B are uncorrelated, then we can observe that there is no clear pattern of relationships between A and B as shown in Figure 3.4.

Figure 3.2: Perfectly positively correlated securities

Figure 3.3: Perfectly negatively correlated securities


Figure 3.4: Uncorrelated securities

INVESTMENT OPPORTUNITIES SET FOR TWO SECURITIES

3.6

In a simple case of two-asset portfolio, the expected return is a weighted average of the expected returns of each asset in the portfolio:

E(rP) = w1E(r1) + (1 w1)E(r2) where E(rP) is the expected return of the portfolio, and w1 and (1 w1) = w2 are the percentage of portfolio value invested in each asset. E(r1) and E(r2) are the expected returns on asset 1 and asset 2, respectively. The variance of the portfolio can be written as:

2 2 2 2 21 1 2 2 1 2 1 22 ,P w w w w Cov r r

or

2 2 2 2 21 1 2 2 1 2 1 2 1,22P w w w w

where 2

P is the variance of the portfolio; 12 and 2

2 are the variance of returns of asset 1 and asset 2, respectively; Cov(r1,r2) is the covariance of returns between asset 1 and asset 2; 1 and 2 are the standard deviation of returns of assets 1 and 2; and 1,2 is the correlation of returns between asset 1 and asset 2.

1 21,2

1 2

Cov r r


48

Now you can see that the riskiness of the portfolio depends on the following three factors:

(a) The weighting of each asset in the portfolio (wi).

(b) The riskiness of each individual asset in the portfolio (i). (c) The correlation of returns between assets in the portfolio (i,j) for i j. Of course, when any of the weightings of assets in the portfolio changes, the corresponding variance of the portfolio will change accordingly. Holding other things constant, when the standard deviation of each asset in the portfolio varies, the variance of the portfolio will also change. Furthermore, the variance of the portfolio not only depends upon the weights and standard deviation of each individual asset in the portfolio, but also relies on the pair-wise correlation of returns between assets in the portfolio. For instance, if the correlation of returns between two assets is very high, then diversification will not lower the variance of the portfolio. On the other hand, if the correlation of returns between two assets is very low, then diversification will indeed lower the variance of the portfolio. If the correlation of returns between two assets is equal to one (i.e., i,j = 1), which means that asset iÊs return increases (decreases) by 10%, and asset jÊs return also increases (decreases) by 10%, then the correlation of returns between asset i and asset j are perfectly positively correlated. If the correlation of returns between two assets is equal to zero (i.e., i,j = 0), this means that the movement of asset iÊs returns has nothing to do with asset jÊs returns. If this is the case, then the correlation of returns between these two assets indicates that they are independent of each other. Finally, if the correlation of returns between two assets is equal to negative one (i.e., i,j = –1), this means that when asset iÊs return increases (decreases) by 10%, the return of asset j will decrease (increase) by 10%. In this case the correlation of returns between asset i and asset j shows that they are perfectly negatively correlated. Let me show you an example based on actual data from the Hong Kong stock market. I have to use historical data (ex-post analysis) since I am not able to get the expected returns on Hong Kong stocks (ex-ante analysis). If I could get the expected returns data on the Hong Kong stock market, I probably could have retired by now! The following table comprises information on the stocks of the Hong Kong and Shanghai Banking Corporation (HSBC) Holdings and Swire Pacific A (Swire) during the period of January 2, 2002 to May 31, 2002.


Stock Daily average return (r) Standard deviation ()

HSBC 0.041% 1.16%

Swire 0.030% 2.09%

HSBC,Swire = 0.38 Data source: Datastream For simplicityÊs sake, letÊs assume that there is an equally weighted portfolio (i.e., wHSBC = 0.5, and wSwire = 0.5). The return of the portfolio:

Pr 0.5 0.041 0.5 0.030 0.036%

The variance of the portfolio:

2 2 2 22

p

2p

0.5 1.16 0.5 2.09 2 0.5 0.5 1.16 2.09 0.38

0.3364 1.0920 0.4606 1.889

The standard deviation of the portfolio:

1.889 1.374P

Now we can obtain the return on the equally weighted portfolio (0.036%) as well as the standard deviation of the portfolio (1.374%). You should be aware that if the weights of both stocks are changed, then the portfolioÊs return and variance will also change accordingly. As I showed you earlier, the riskiness of the portfolio depends on three factors. Suppose we keep the first two factors constant (i.e., wi and i) and assume that the correlation of returns between HSBC and Swire (HSBC,Swire) varies. Case 1:

If HSBC,Swire = 1 (i.e., perfectly positively correlated) 2

p = (0.5)2(1.16)2 + (0.5)2(2.09)2 + 2(0.5)(0.5)(1.16)(2.09)(1) 2

p = 0.3364 + 1.0920 + 1.2122 = 2.641 This result shows that the portfolio variance is much higher than the previous one when the actual �HSBC,Swire = 0.38. Thus diversification does not reduce the


50

portfolio variance relative to a portfolio that is completely invested in one asset in this case. Case 2:

If HSBC,Swire = 0 (i.e., no correlation) 2

p = (0.5)2(1.16)2 + (0.5)2(2.09)2 + 2(0.5)(0.5)(1.16)(2.09)(0)

2p = 0.3364 + 1.0920 = 1.428

This result illustrates that the portfolio variance is almost reduced by half as compared to the case when �HSBC,Swire = 1. In other words, if we combine stocks with returns that are less than perfectly positively correlated in the portfolio, then the portfolioÊs variance will be reduced significantly. This illustrates the concept of diversification. Case 3:

If HSBC,Swire = -1 (i.e., perfectly negatively correlated) 2

p = (0.5)2(1.16)2 + (0.5)2(2.09)2 + 2(0.5)(0.5)(1.16)(2.09)(-1)

2p = 0.3364 + 1.0920 1.2122 = 0.216

When the two assets are perfectly negatively correlated, the variance of the portfolio is reduced significantly and approaches zero. If, say, we suppose 2HSBC = 2Swire = 2, then 2

p = 0.522 + 0.522 + [2(0.5)(0.5) 2 ( 1)] 2

p = 0.252 + 0.252 + ( 0.52) = 0 These two assets create a perfect hedge. This demonstrates that diversification can be thought of as a hedge of risks.

MINIMUM VARIANCE PORTFOLIOS 3.7

In the numerical example stated in the previous section, the question we would like to address is how low can portfolio variance be? The answer is quite simple as long as the lowest possible value of correlation coefficient is 1 (1,2 = 1), representing the case of perfectly negatively correlated assets. The variance of the portfolio:

2p = w2

121 + w2

222 + 2w1w2121,2


can be simplified to 2

p = (w11 w22)2 and the portfolio standard deviation is

P = Absolute value (w11 w22)2 When 1,2 = –1, a perfectly hedged position can be obtained by selecting the portfolio weightings to solve the following equation: w11 w22 = 0

The solution of the above equation is

1 1 1 2 2 1

21

1 2

1 0 set 1w w w

w

w

Example: LetÊs think back to the numerical example of HSBC and Swire that I presented earlier. We can calculate the proportions of HSBC and Swire in order to obtain a zero variance portfolio. Let 1 be HSBC and 2 be Swire:

HSBC

SWIRE

2.090.643

1.16 2.091 0.643 0.357

w

w

Now we know the exact proportions of wHSBC and wSwire in a perfect hedge portfolio if and only if HSBC,Swire = –1 (i.e., perfectly negatively correlated). 2

p = (0.643)2(1.16)2 + (0.357)2(2.09)2 + 2(0.643)(0.357)(1.16)(2.09)(-1) 2

p = 0.556 + 0.557 1.113 = 0 The minimum variance portfolio provides us with an idea about the maximum diversification benefit we can achieve by combining two different assets. In other words, we can obtain a zero variance (risk-free) portfolio, provided that the correlation of returns between two assets is -1 (i.e., they are perfectly negatively correlated). However, you might obtain a positive return portfolio with a zero variance portfolio. Therefore, it is important to calculate the pair-wise correlation of returns together with the appropriate weights of each asset in order to obtain a zero variance portfolio. Practically speaking, if you want to create a zero variance portfolio, you need to identify the assets with a correlation of returns equal to -1, and then calculate the appropriate weights of each asset employing the following formula:


52

21

1 2

w

and

2 11w w If you can gain access to databases of stock prices or foreign exchange rates, then it would be interesting to create a zero variance portfolio by using you yourself as an activity. Look at Figure 3.5, by combining both assets 1 and 2, we can create a new portfolio with minimum variance relative to asset 1 and 2. Now, letÊs expand the idea of 2 assets in 30 assets. If we have invested in 30 assets, the combination of different assets in different portfolios will give us a new frontier known as minimum variance frontier as shown in Figure 3.6. The frontier looks like a belt. The point where it is nearer to y-axis is the minimum variance portfolio as shown in the figure.

Figure 3.5: Minimum variance portfolio


Figure 3.6: Minimum variance frontier

Learn to sketch the above diagram. Point to where exactly is:

(a) Minimum variance portfolio,

(b) Minimum variance frontier,

(c) Risk-free asset,

(d) Efficient frontier,

(e) The area of preference by investors.

SELF-CHECK 3.1

DIVERSIFIABLE AND NON-DIVERSIFIABLE RISK

3.8

The total risk of a portfolio (2p) consists of two components, namely,

diversifiable risk and non-diversifiable risk. The following readings provide a very clear picture of the concepts of diversifiable and non-diversifiable risks. In summary, diversifiable risk is a firm-specific risk. For instance, if you know that a firm will encounter serious financial problems shortly, you as an investor will definitely sell the stock of that firm in order to minimise the risk. Diversifiable risk is unique to a specific firm, so it is also called unique risk, firm-specific risk or non-systematic risk. The central idea is that we can avoid this unique risk by means of diversification. If you hold a well-diversified portfolio, you will probably only be faced with non-diversifiable risk. As its name implies,


54

non-diversifiable risk is that the risk cannot be diversified or avoided by means of diversification. Thus non-diversifiable risk is also known as market risk or systematic risk. No single investor can avoid market risk; the same is also true for fund managers or institutional investors. Recent studies have shown that if you hold a portfolio that consists of 20 stocks (across different industries), then your portfolio will be considered a well-diversified portfolio. In other words, all you then need to care about is the non-diversifiable or market risk.

Figure 3.7: Diversifiable and non-diversifiable risks

In short, unique risks are many of the risks faced by an individual company are peculiar to its activity, its management, etc. Take for example, company winning an overseas contract, there are complaints filed on the products produced by the company and there is pending governmental investigation. This risk can be eliminated by diversification as shown in Figure 3.8. On the other hand, businesses face economy-wide risks or market risks! These risks will threaten each company. Example, there is sudden increase in the exchange rate of US dollar against local currency, there is hike in the lending rate in the economy due to policy of the central bank to fight inflation, etc. This risk cannot be avoided, regardless of the amount of diversification.


Figure 3.8: Unique risk and market risk

SELF-CHECK 3.2

1. Why is it called unique risk?

2. Why it is said that market risk cannot be diversified away?

We have discussed the importance and benefits of diversification from the

perspective of portfolio investment. We have also learned how to calculate portfolio return and portfolio risk. The correlation between two assets influences the portfolio risk. Hence, the

first step before forming a portfolio is to find out the correlation between the two assets.

Diversification depends on correlation between stocks. We have defined what is a minimum variance portfolio and its implication to

investors.


56

Diversifiable risk is known unique risk, firm-specific risk or non-systematic risk.

Non-diversifiable risk is known market risk or systematic risk. Diversification has limits it cannot eliminate market risk.

Correlation Covariance Diversification Firm-specific risk Minimum variance frontier Minimum variance portfolio

Non-systematic risk Portfolio return Portfolio risk Portfolio theory Systematic risk Unique risk

1. Disucss the importance of an efficient portfolio from the perspective of investing.

2. Elaborate the way how to calculate return and standard deviation of a

portfolio. How is it different from a single asset? 3. Discuss the importance of correlation with respect to asset returns. Provide

three scenarios where two asets are postively correlated, negative correlated and uncorrelated.

4. Discuss the effect of diversification of risk on the risk of portfolio as

compared to the risk of individual assets inside the portfolio. 5. Discuss the concept of diversifiable risk with respect to porfolio investment. 6. Discuss the concept of nondiversifiable risk with respect to porfolio

investment. 7. Discuss the benefits of international diversification from the perspective of

individual investor who like to increase the return and reduce the risk of his portfolio.


8. Discuss how diversification can be achieved by investing abroad and investing domestically.

Given the monthly rates of return for ABC Berhad and XYZ Berhad for Question 1 to 5.

Month ABC Berhad XYZ Berhad

1 -0.04 0.07

2 0.06 -0.02

3 -0.07 -0.10

4 0.12 0.15

5 -0.02 -0.06

6 0.05 0.02

1. Calculate the average monthly rate of return iR , for each stock. 2. Calculate the standard deviation of returns for each stock. 3. Calculate the covariance between the rates of return. 4. Calculate the correlation coefficient between the rates of return. 5. Based on the correlation coefficient of ABC and XYZ, can these two stocks

offer diversification effect if we put them in our portfolio?

Given two assets with the following information for Question 6 to 8: 15.0)( 1 RE E ( )1 =0.10 5.01 w

20.0)( 2 RE E( )2 =0.20 5.01 w 6. Calculate the mean and standard deviation of the portfolio if =0.40 2,1r

7. Calculate the mean and standard deviation of the portfolio if = - 0.60 2,1r

8. Plot the two portfolios on a risk-return graph and discuss the results.

Efficient

Frontier and

Asset

Allocation

INTRODUCTION

The most important topic covered in this topic is the modern theory of portfolio management. It has now been more than 50 years since the Markowitz portfolio was introduced. The Markowitz portfolio theory is a set of methods to select an optimal or the best portfolio. The landmark paper on „Portfolio selection‰ that was published in the Journal of Finance enabled Markowitz to receive the Nobel Prize in Economics in 1990. The other task of this unit is learning to derive the capital market line (CML). The CML shows the risk-return trade-off for all financial assets and portfolios. To derive the CML, we will define the efficient frontier as a graph that represents all portfolios that yield the highest level of return for a given level of risk. A rational risk-averse investor will choose portfolios on the efficient frontier. The capital

TTooppiicc

44

3. Apply asset allocation strategies in forming optimal portfolios; and

4. Evaluate the usefulness of market indices.


1. Explain the concept of efficient frontier and Markowitz portfolio theory;

2. Discuss the concept of capital allocation line (CAL) and capital market line (CML);

TOPIC 4 EFFICIENT FRONTIER AND ASSET ALLOCATION 59

market line is the linear combination between a risk-free asset and a risky portfolio that is tangent to the efficient frontier. We will introduce the construction and use of market indices. Broadly speaking, a market index is a numerical value that measures the performance of the market and also serves as a benchmark for portfolios and mutual funds.

THE EFFICIENT FRONTIER AND MARKOWITZ PORTFOLIO THEORY

4.1

Up to now you have learned how to reduce risk by forming a two-stock portfolio. However, in the real world, we need to consider portfolios that consist of more than two stocks. The Markowitz portfolio theory allows us to examine cases in which the portfolio consists of more than two stocks. In other words, you can think of the Markowitz portfolio theory as the generalisation of the portfolio theory youÊve studied so far. The Markowitz portfolio theory is a set of methods used to select the optimal or best portfolio. According to this theory, an investor calculates and then compares the rewards and risks of alternative portfolios. As you know, an investor who is risk averse prefers portfolios with higher returns and with lower risks. The Markowitz portfolio theory has been used extensively to choose the optimal portfolio in a complex investment environment. The origin of the theory is vested in the consumer optimisation theory from microeconomics. Markowitz published the landmark paper on „Portfolio selection‰ in the Journal of Finance more than 50 years ago. This paper and other works on portfolio theory enabled Markowitz to win the Nobel Prize in Economics in 1990. You should first read the paper in the Journal of Finance in order to grasp its insights on the Markowitz portfolio theory. The article is non-technical and you would enjoy reading it. In the remainder of this section, we will first review the construction of the Markowitz portfolio and take you through an example of a three-asset portfolio case. Next, we will see examples of how to construct the efficient frontier. Finally, we will derive the capital allocation line (CAL) in a portfolio that consists of one risk-free asset and one risky asset.

TOPIC 4 EFFICIENT FRONTIER AND ASSET ALLOCATION

60

4.1.1 Portfolio Construction with More than Two Assets in the Portfolio

The Markowitz portfolio theory is just an extension of a two-asset portfolio case to an n-asset case portfolio. The expected return and variance of the n-assets portfolio is as follows:

1

( ) ( )n

P i ii

E r w E

r

2

1 1

( , )n n

P i j i ji j

w w Cov r r

or

2

1 1

n n

P i j iji j

w w

An example of a three-asset portfolio case (n=3)

Using the example ; itÊs set for two securities, and here one more stock is added to the portfolio. The additional stock is based on the actual data from Citic Pacific (CP) for the period from January 2, 2007 to May 31, 2007.

Stock Daily average return (r) Standard deviation () HSBC 0.02% 0.74% Swire 0.07% 1.56% CP 0.20% 1.91%

HSBC,Swire = 0.43

HSBC,CP = 0.43 Swire,CP = 0.46


Again, assuming an equally weighted portfolio, the return and the standard deviation of the portfolio are as follows: Let HSBC be subscript 1, Swire be subscript 2, and CP be subscript 3.

rP = w1r1 + w2r2 + w3r3

rP = 0.33(0.02) + 0.33(0.07) + 0.33(0.20) = 0.096%

2P = w2

121 + w2

222 + w2

323+ 2w1w2121,2 + 2w1w3131,3 +

2w2w3232,3 2

P = (0.33)2(0.74)2 + (0.33)2(1.56)2 + (0.33)2(1.91)2 + 2(0.33)(0.33)(0.74)(1.56)(0.43) +

2(0.33)(0.33)(0.74)(1.91)(0.43) +

2(0.33)(0.33)(1.56)(1.91)(0.46)

2P = 0.060 + 0.265 + 0.397 + 0.108 + 0.013 + 0.30 = 1.143

P = 1.143 =1.069% By the same token, you can calculate the portfolio return and variance for a portfolio that consists of more than three assets by extending the formula of calculating the portfolio return as well as the portfolio variance. In Table 7A of your Bodie textbook, a spreadsheet model shows how to calculate returns and standard deviations for stock indices from seven countries. Thus you can use Excel to do the same calculations. I would like to summarise the procedures of estimating a portfolioÊs return and variance as follows:

Step 1: Download the appropriate data from a reliable database such as Datastream. Datastream contains all the stock prices for the global markets.

Step 2: You can calculate the individual stock return on a daily, weekly, monthly, quarterly or annual basis using the following formula (for simplicityÊs sake, we ignore the dividend part of the return formula):

1t

1ttt

PPP

r

where Pt = the market price of an individual stock at time t.

Step 3: Calculate the average return of each stock during the sample period or holding period.

Step 4: Once you obtain the average return of each stock in your portfolio, you need to determine the weight or proportion of each stock in your portfolio.


62

Step 5: Estimate the pair-wise correlation or covariance coefficient of the returns data.

Step 6: Now you can calculate both the portfolioÊs return and its variance (standard deviation) in Excel.

4.1.2 Quantifying the Efficient Frontier

An efficient portfolio is one that gives the maximum return for a given level of risk. The efficient frontier, on the other hand, is a collection of portfolios that has the maximum rate of return for every given level of risk, or the minimum risk for every potential rate of return. In other words, only the efficient frontier contains all the optimal portfolios. „Optimal portfolios‰ implies the portfolios that yield the highest rate of return for every given level of risk. I will start to develop the construction of the efficient frontier by considering the case of a two-asset portfolio again. Recall, from our previous discussion, the expected return and variance of a two-asset portfolio as follows:

E(rP) = w1E(r1) + (1 w1)E(r2)

2P = w2

121 + w2

222 + 2w1w2121,2

Now suppose that we have two assets, A and B. The assetsÊ expected return and standard deviations are:

Asset A Asset B Expected return 20% 10% Standard deviation 10% 6%

LetÊs first assume that the returns between two assets are perfectly positively correlated (i.e.,A,B = 1). Next I am going to vary the weights of the two assets and then present the results in the graph. First, letÊs assume wA= 1 (i.e., all the wealth is invested in asset A). The return and standard deviation of the portfolio are:

E(rP) = 1(20%) + 0(10%) = 20%

P = [(1)2(10%)2 + (0)2(6%)2 + (2)(1)(0)(10%)(6%)(1)]1/2 = 10% As you can see, the expected return and standard deviation of the portfolio are the same as for individual asset A since all wealth is invested in asset A. I am now going to construct the portfolio again, now assuming that wA and wB are both 50% (i.e., an equally weighted portfolio). In this case, the expected return on the portfolio is 15% and the standard deviation of the portfolio is 8%.


I now add the case in which wA = 0 and wB = 1. In this case, the expected return and the standard deviation are the same for individual asset B. I can graph these three computations as three points on the graph, and show what happens to expected returns and standard deviation as the portfolio weights vary across the assets. As the correlation between asset A and asset BÊs returns = 1 (A,B = 1), when I connect the three points together, they form a straight line, as shown in Figure 4.1.

Figure 4.1: Portfolio return and standard deviation when �A,B = 1

However, when �A,B is not equal to 1, then the relationship is not going to be linear. Let us recalculate the same three points (wA = 0, wA = 0.5, and wA = 1), but with a different assumption of the correlation coefficient. Suppose that the correlation coefficient (A,B) is equal to 0.75. In this case the returns on both assets are positively correlated, but not perfectly correlated. For the two extreme cases in which all wealth is either invested in asset A or asset B, the expected returns and standard deviation of the portfolio are the expected returns and standard deviation for that asset (we have shown this earlier). When wA = wB = 0.5 (i.e., an equally weighted portfolio), the expected returns and standard deviation under different assumptions of A,B are:


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Correlation

coefficient (A,B) wA = 1 wA = wB = 0.5 wA = 0

1.0 E(rP) = 20% P = 10%

E(rP) = 15% P = 8%

E(rP) = 10% P = 6%

0.75 E(rP) = 20% P = 10%

E(rP) = 15% P = 7.52%

E(rP) = 10% P = 6%

0.5 E(rP) = 20% P = 10%

E(rP) = 15% P = 7%

E(rP) = 10% P = 6%

0.25 E(rP) = 20% P = 10%

E(rP) = 15% P = 6.44%

E(rP) = 10% P = 6%

0 E(rP) = 20% P = 10%

E(rP) = 15% P = 5.83%

E(rP) = 10% P = 6%

0.5 E(rP) = 20% P = 10%

E(rP) = 15% P = 4.35%

E(rP) = 10% P = 6%

1.0 E(rP) = 20% P = 10%

E(rP) = 15% P = 2%

E(rP) = 10% P = 6%

As indicated in the above table, when the correlation coefficient decreases, the portfolioÊs risk decreases as long as some wealth is invested in each asset. As the correlation of assets in the portfolio decreases, we can reduce the risk of the portfolio. We need to pay attention to ensure that the line relating risk and return was straight when A,B = 1. When A,B = 0.75%, risk is reduced, so the line bends to the left (i.e., becomes concave), as shown in Figure 4.2.

Figure 4.2: PortfolioÊs return and standard deviation when A,B = 0.75

As shown in Figure 4.3, when the correlation coefficient drops further, the line becomes even more curved (i.e., more concave).


Figure 4.3: PortfolioÊs return and standard deviation when A,B = 0.5 What you have learned so far is that we can diminish risk by investing in assets that are less than perfectly correlated. We can diversify our portfolio by owning an amount of each financial asset. We can graph a large number of assets in risk-return space. This graph looks like the top part of an umbrella. The outer curve solid line represents the combination of assets that are efficient. This is known as the efficient frontier (Figure 4.4). These are the efficient portfolios that yield the highest-level returns given the level of risk (or the lowest level of risk given the level of returns).

Figure 4.4: The efficient frontier

Once the efficient frontier has been set, it not only indicates whether our portfolio is efficient, but also tells us how to adjust the components of our portfolio in order to achieve the highest return with the same risk (the standard deviation of return). However, although youÊve now been taught how to quantify the efficient frontier, you might think that it is very complicated and difficult for you to do so, especially if a portfolio comprises a lot of stocks or securities, because this involves a lot of calculations. Please donÊt worry -

． we have computers! There are

a lot of computer applications on the market that can help us develop the


66

efficient frontier for optimising our investment portfolio. Some websites even offer free services for optimising portfolios for higher expected return! In the following activity you will see how easy it can be for you to check whether your portfolio is efficient or not!

Although there are some websites which can help us to do portfolio optimisation

What I am going to introduce to you is an Excel template from Excel Business Tools. Please visit the following Web address:

<http://www.excelbusinesstools.com/portopt.htm>

After going to the above Web address, you can click ÂTryÊ to download the Excel template of portfolio optimisation for free. Assume that you have the following investment portfolio:

Please open the Excel template from the Web address above. You will see that there is a sample of five US stocks in the template. Please delete these data and download the previous 32-month stock returns of the above five stocks from Yahoo Finance, at:

<http://Malaysia.finance.yahoo.com/stock/index.php>.

After that, reset the „Min Constraint‰ and „Max Constraint‰ of each stock to 0% and 100%, respectively. Please also change the current units of each stock according to the number of shares shown above. Finally, you can click „Optimise Portfolio‰ to see how efficient your portfolio is.

ACTIVITY 4.1

CAPITAL ALLOCATION VERSUS ASSET ALLOCATION

4.2

In a broader sense, capital allocation is the choice of investing funds in both risky and risk-free assets. For instance, if you had RM1 million, how much would you put into risk-free assets such as time deposits in a reputable bank, and how much would you put into risky assets such as stocks, bonds, foreign exchanges, options and futures, etc.? Asset allocation comprises the investment decision making over the choices of different risky assets that I mentioned earlier. You should read the following textbook selections as outline in the course guide in order to learn more about the concept of capital allocation as well as asset allocation.


Now that youÊve read the text, you probably know how to calculate the weights of a complete portfolio of both risk-free and risky investments.

4.2.1 The Capital Allocation Line (CAL)

The capital allocation line (CAL) is derived from the investment of a complete portfolio that consists of one risky portfolio and a risk-free asset. You should consult the following readings, after which I will summarise the concept of CAL and provide you with numerical examples of the construction of the CAL. Let us make a summary of the concept of CAL as follows: LetÊs say the risk-free asset has a return rf (since the return is certain and there is no expectation sign attached to it). The risky portfolio, however, has an expected return E(rp) and variance 2

P, and let y and (1 y) be the risky and risk-free weights. Here I use y instead of w to represent the weights for differentiation of a conventional risky portfolio to a complete portfolio. Then the expected return of a complete portfolio (E(rCP)) holding positions in risk-free and risky assets is:

E(rCP) = y E(rp) + (1 y)rf

Re-arranging the equation yields:

E(rCP) = rf + y[E(rp) rf]

The variance of the complete portfolio (2CP) is

2CP = y22P + (1 – y)22

rf + 2y(1 – y)P,rfPrf

where

2rf is the variance of risk-free asset, which is equal to zero

P,rf is the correlation coefficient between the risky portfolio and the risk-free asset, which is equal to zero.

P is the standard deviation of the risky portfolio. rf is the standard deviation of the risk-free asset, which is equal to zero.

In the equation of 2CP, the second and third terms are zero; it then reduces to

2CP = y22P, and the standard deviation is simply yP.

In Malaysia, the one-month or three-month Kuala Lumpur inter-bank offer rate (KLIBOR) is a proxy for the return of the risk-free asset. In the US, the 90-day treasury bill rate (TB) is a proxy for the return of the risk-free asset.


68

Suppose the one-month KLIBOR is 3% and the expected return and standard deviation of a portfolio consisting of Malaysian stocks are 15% and 8%, respectively. Then the return and standard deviation of the complete portfolio are as follows:

E(rCP) = 3% + y[15% 3%]

CP = y(8%) The actual outcomes depend on the value of y (i.e., the weight of risky stock portfolios). Suppose y takes the values of 0, 0.5, and 1 and we obtain the following table.

y Expected return Standard deviation

0 3% 0

0.5 9% 4%

1 15% 8%

The above table indicates that if y = 0, then the expected return is exactly the same as the rate of return of the one-month KLIBOR (risk-free asset), and the standard deviation is zero. If y = 1, then the expected return and standard deviation are the same as the risky stock portfolio. If y = 0.5, then this is the linear combination between the risky portfolio and the risk-free asset. This information can be plotted in the following graph (Figure 4.5).

Figure 4.5: The capital allocation line (CAL)

The straight line is known as the capital allocation line (CAL), and it represents the risk-return combination that investors must encounter.


SELF-CHECK 4.1

The following table is an extension of the table in the topic above. Fill in the blanks and plot the capital allocation line (CAL).

y Expected return Standard deviation

0 3% 0

0.5 9% 4%

1 15% 8%

1.5 ? ?

2 ? ?

ACTIVITY 4.2

How can you invest more than what you have in the portfolio P,(i.e., Y > 1)?

4.2.2 Reward-to-risk Ratio

You should now see that the slope of the CAL is the reward-to-risk ratio:

P

fP r)r(ES

This is also known as the Sharpe Index, and it represents the risk-adjusted excess rate of return. The definition of excess rate of return is [E(rP) - rf], which is the numerator of the reward-to-risk ratio. The Sharpe Index is a performance measure of portfolios and mutual funds. The higher the value of S, the more preferable it is to investors or mutual funds managers, since it implies a higher risk-adjusted excess rate of return. In order to have a higher value of S, we tend to maximise the excess rate of return and to minimise the risk of the risky portfolio.


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THE CAPITAL MARKET LINE (CML) 4.3

The derivation of the capital allocation line (CAL) is based on the assumption of an active portfolio strategy. The derivation of the capital market line (CML), however, is based on the assumption of a passive portfolio strategy. Instead of constructing our own portfolio, the derivation of the CML employs a market portfolio as the benchmark. In this section, I will first show you how to derive a CML by using the market portfolio as the benchmark, and then I will talk about the CML and the separation theorem. You should now refer to the textbook sections to gain a better understanding of the CML and the separation theorem.

4.3.1 The Derivation of the CML

As you have learned, the efficient frontier contains the only efficient portfolios. I will therefore construct a portfolio with the risk-free asset and one of the efficient portfolios. This CML is drawn from the risk-free rate of return to a point just tangent to the efficient frontier as shown in Figure 4.6.

Figure 4.6: The tangency of CML to efficient frontier

Note that the CML is tangent to the efficient frontier at point M. Point M is known as the market portfolio, which has to include all assets if investors are risk averse. An investor who is risk averse chooses portfolio A such that the investor allocates part of his/her funds to the risk-free asset, and the remaining funds to the market portfolio. On the other hand, if the investor chooses portfolio B, then that investor would borrow money at the risk-free rate, and invest all of his/her funds - including the borrowed funds - in the risky portfolio, M.


We can derive the CML within the context of a two-asset case portfolio. The two assets in the portfolio are the risk-free asset with the rate of return (rf) and the market portfolio with the expected rate of return E(rM). Let w be the proportion of the portfolio invested in the risk-free asset and (1 w) be the proportion invested in market portfolio. The expected return of the portfolio will be:

E(rP) = wrf + (1 w)E(rM)

where rM is the rate of return on the market portfolio.

P = [w22rf + (1 – w)22

M + 2w(1 – w)rf,rMrfM]1/2

where

2M is the variance of return on the market portfolio

M is the standard deviation of return on the market portfolio

rf,rM is the correlation coefficient between the rate of return of the risk-free asset and the market portfolio.

In the above equation, since 2

rf, rf, and rf,rM are all zero, the above equation reduces to:

P = (1 – w) M

From the standard deviation equation we can solve for w:

w = 1 (P/M)

We can also solve for 1 w:

1 w = P/M

We can then substitute for (w) and (1 w) in the expected return equation. This substitution reveals:

E(rP) = [1 (P/M)]rf + (P/M)E(rM)

Simplifying the equation gives:

E(rP) = rf + [E(rM) rf] (P/M)

The above is the equation for the CML.


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SELF-CHECK 4.2

1. What is the slope of the CML?

2. What kind of portfolios will never lie on the CML?

4.3.2 The Capital Market Line and the Separation Theorem

The separation theorem implies that portfolio choice can be separated into two independent tasks. The first task is to determine the optimal portfolio purely based on existing information from the market portfolio. This is rather passive investment decision making. That is, if an investment analyst has data on the market portfolio then he or she can achieve the optimal portfolio, as can other investment analysts using the same data. This is exactly the point M on the capital market line in Figure 4.6, which is tangent to the efficient frontier. The second task is the personal choice of the best mix of the risky portfolio and the risk-free asset. This means that the choice of any of the points moving along the capital allocation line depends upon the risk preferences of individual investors. We will talk more about the relationship between risk tolerance and asset allocation in the next section.

OPTIMAL COMPLETE PORTFOLIOS 4.4

In this section, I am going to introduce to you the relationship between risk tolerance and asset allocation. In particular, weÊll consider how the changes in investorsÊ preferences eventually alter their asset allocation decisions. In other words, we will combine both indifference curves as well as the capital allocation line (CAL) to show you how the optimal portfolio is derived. In addition, I would like to show you how to determine optimal composition in the portfolio if we have more than one risky asset in that portfolio. Finally, I will show you how to construct and use market indices.

4.4.1 Risk Tolerance and Asset Allocation

The textbook provides a very good numerical example to show you how to superimpose an investorÊs indifference curves onto the capital allocation line. You should consult the following reading to enhance your understanding of the relationship between risk tolerance and asset allocation.


If we superimpose an investorÊs indifference curves with the capital allocation line (CAL), we can obtain that investorÊs optimal portfolio. By superimposing the two graphs, we can see how tolerance for risk impacts an investorÊs choice of portfolio. Recall from our earlier discussion that this portfolio comprises the risk-free asset and the portfolio of risky assets. In Figure 4.7, we have two investorsÊ indifference maps.

Figure 4.7: The lending and borrowing portfolios

The first investor has a lending portfolio (i.e., has a lower tolerance for risk). This investor chooses to invest part of his wealth in the risk-free asset and part of his wealth in the risky portfolio. The lending portfolio is tangent at point L. This is the point at which the highest indifference curve just touches the CAL. The second investor has a borrowing portfolio (i.e., has a higher tolerance for risk). This investor chooses to invest all her wealth in the risky portfolio. In addition, this investor also borrows money from financial institutions at a set borrowing rate, and has a leveraged portfolio. Here we implicitly assume that the lending rate is the same as the borrowing rate, and is exactly the same as the risk-free rate (i.e., rL = rB = rf). The tangency point of the indifference curve and the CAL is at point B. Point B therefore yields the highest level of satisfaction for the investor who has a high tolerance for risk. As you can see, both the lending and borrowing portfolios have invested in the same risky portfolio. However, the investor who holds the lending portfolio is more risk averse and invests in both the risk-free asset and the risky portfolio. The investor who holds the borrowing portfolio is less risk averse and invests all her wealth in the risky portfolio.


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4.4.2 Optimal Composition (Weightings) in a Portfolio

Your textbook illustrates the simple case for optimal weightings in a portfolio of one risk-free asset and two risky assets. You are advised to read the following section from your textbook; you should work carefully through the numerical example provided, and be sure you should know how to calculate the optimal weightings for a portfolio of one risk-free asset and two risky assets. Activity 2.9 in the textbook then guides you in obtaining the optimal weightings in a portfolio for a two risky asset portfolio case; if you can handle Activity 2.9 easily, then you should have no problem understanding the construction of an optimal portfolio. However, if your portfolio has more than two risky assets, then you will likely want to make use of computer software to figure out the optimal weightings of your portfolio.

What will the CAL look like if the lending rate and borrowing rate arenot the same? In reality, the borrowing rate is, of course, greater thanthe lending rate (i.e., rB > rL).

ACTIVITY 4.3

Suppose you have the following data on two risky assets:

Asset 1 Asset 2 Expected return 12% 8% Standard deviation 10% 5%

The correlation coefficient of return between Asset 1 and Asset 2 is 0.40 and the return on the risk-free asset is 4%.

1. Find the optimal weights for w1 and w2.

2. What is the expected return for a portfolio consisting of these two assets?

3. What is the standard deviation of the portfolio?

4. What is the slope of CAL or the reward-to-risk ratio?

5. If an investor has a coefficient of risk aversion A=20, what will be the proportion invested in the two risky asset portfolio? What will be the proportion invested in the risk-free asset?

ACTIVITY 4.4


CONSTRUCTION AND USE OF MARKET INDICES

In the construction of the capital market line (CML), we need to have the information on the market portfolio (M). As youÊve learned, a stock market index can serve as a proxy for this market portfolio. A stock market index is a number that indicates the relative level of prices or value of securities in a market on a particular day compared with a base-day figure, which is usually 100 or 1000. There are three main types of index, namely price-weighted indices, value-weighted indices and equally weighted indices. You should learn more by working through the following readings on the construction of stock indices in the US as well as in Malaysia. The two commonly quoted stock market indices in the US are the Dow Jones Industrial Average (DJIA) and the Standard and Poor 500 (S&P500) indices. In Malaysia, the Kuala Lumpur Composite Index (KLCI) is the most important stock market index. The main objective of constructing market indices is to measure the performance of the relevant markets. By comparing the values of a market index over time, we can see how a market is performing over different periods. Technical analysts also use market indices to forecast the up and down trends of markets. They argue that these patterns of market index movements tend to repeat themselves. This kind of analysis requires a way to measure market performance. Besides measuring market performance, however, returns on market indices may be used as benchmarks to evaluate the performance of particular portfolios and mutual funds. Finally, market indices may be used to make comparisons on the performance and riskiness of various international markets, thereby providing information that can be used for international investments. We can try to find out, for example, which market has out-performed others. In fact, there are lots of financial futures instruments attached to market indices, such as the Hang Seng Index futures (Hong Kong), the Dow Jones Industrial Average Index futures (US), and the Nikkei 225 futures (Japan). See Figure 4.8 for an example.

4.5


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Figure 4.8: KLCI and other indices

Source: http://www.klse.com.my/website/bm/ Satisfaction and lower utility means a lower level of satisfaction. We generally assume that investors are risk-averse. This is one of the major assumptions for the construction of MarkowitzÊs portfolio selection. The level of risk aversion can be measured with indifference curves. An indifference curve, which is sometimes known as an indifference map, measures the mean and variance of portfolios that an investor would be equally happy with. A risk-averse investor will prefer higher indifference curves in the risk and return space. The concept of risk-aversion and utility theory were the essential elements needed to discuss the idea of diversification. A risk-averse investor tries his best to minimise risk. Diversification is a means of reducing risk in investment decision-making. Practically speaking, diversification is the process of adding assets to a portfolio in order to minimise the portfolioÊs diversifiable risk, and hence the portfolioÊs total risk. In this unit, you were shown many numerical examples of how to reduce risk by means of a well-diversified portfolio. The difference between diversifiable and non-diversifiable risks was discussed. According to many empirical studies, if


investors hold a portfolio that consists of at least 20 stocks, then the portfolio is considered to be well-diversified. A well-diversified portfolio implies that all you have to be concerned with is non-diversifiable, or systematic, risk.

We have discussed the importance of efficient frontier and Markowitz

portfolio theory. We have also learned the concept of capital allocation line and its application. The derivation of capital market line and its importance in portfolio

management have been highlighted. We have discussed the asset allocation strategies in forming optimal

portfolios. The construction of market indices and their usefulness have also been

discussed.

Asset allocation Asset allocation Strategies Benchmarks Capital allocation Capital allocation Line (CAL) Capital Market Line (CML) Dow Jones Industrial Average (DJIA) Efficient frontier KLIBOR Kuala Lumpur Composite Index (KLCI)

Market indices

Markowitz portfolio theory Optimal complete portfolio Optimal allocation Reward-to-risk ratio Risk tolerance Separation theorem Sharpe index Standard and poor 500 (S&P500) Two-asset portfolio


78

1. Explain why more risk-averse investors have a steeper indifference curve. 2. Portfolio X, consisting of stocks and T-notes, has an expected return and

risk equal to 10% and 14% respectively. Your coefficient of risk aversion is 5. The T-bill rate equals 4%. What is your allocation of investment between T-bills and portfolio X? If Portfolio X is made up of 70% bonds and 30% stocks, what are your investment proportions in T-bills, bonds and stocks?

3. You are given the following information:

Expected return Standard deviation

T-bills 4% 0%

Bond A 12% 40%

Stock B 20% 60%

The correlation coefficient between bond A and stock B is 0.3.

(a) Calculate the weight, risk and expected return of the optimal risky portfolio formed by bond and stock.

(b) Find the slope of the CAL. 4. S&P500 index has an expected return of 12% and a standard deviation of

20%. The T-bill rate is 4%. Calculate the slope of the CML. 5. Would you choose a passive strategy by investing in S&P500 index fund or

would you invest in portfolio A?

Expected return Standard deviation

T-bills 4% 0

S&P500 index 12% 20%

Portfolio A 15% 25% 6. Which of the following investments violates MarkowitzÊs efficient frontier?

Investment Expected return Standard deviation

A 8% 12%

B 10% 16%

C 30% 40%

D 9% 20%

E 15% 25%


7. Suppose you are given the following information:

Portfolio Expected return Standard deviation

T-bills 4% 0%

A 10% 11%

B 18% 16%

C 23% 18%

D 24% 20%

E 25% 25%

(a) Using the above information, plot the CAL.

(b) Which is the optimal risky portfolio? Why? 8. You have the following data on two risky assets:

Asset 1 Asset 2

Expected return 12% 8%

Standard deviation 10% 5%

The correlation coefficient of returns between Asset 1 and Asset 2 is 0.40 and the return on risk-free rate is 4%.

(a) Find the optimal weights for w1 and w2.

(b) What is the expected return for a portfolio consisting of these two assets?

(c) What is the standard deviation of the portfolio?

(d) What is the slope of CAL or the reward-to-risk ratio?

1. How efficient frontier is related to the attainable set of all possible portfolios?

2. How efficient frontier can be used with an investorÊs utility function to find

the optimal portfolio? 3. Differrentiate among the diverfiable, non-diversifiable and total risk of a

portfolio? 4. What does the term „relevant risk‰ refer to and how is it measured?


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5. How can one measure the beta of a portfolio when we know the beta for each of the assets included in it?

6. Discuss the feasible or attainable set of all possible portfolios with relation

to efficient frontier. 7. Summarise the idea of modern portfolio theory (MPT) based on the

concepts of correlation, beta and diversifiable risk. 8. Discuss how to apply the concept of modern portfolio theory (MPT) from

the perspective of individual investor.

INTRODUCTION

Investors want to know the „fair‰ value or „equilibrium‰ price of an asset. Once they find out the appropriate, i.e. „fair‰, price of an asset, they will compare it with the market price. If the market price is higher than the „fair‰ price, then the asset is said to be over-priced. By the same token, if the market price is lower than the „fair‰ price, then the asset is said to be under-priced. For decades, academics in the fields of finance and economics have tried to develop a model that accurately predicts the „fair‰ value of an asset. In this topic you are introduced to several asset-pricing models that can help us predict or explain the „fair‰or „equilibrium‰ returns on securities. The capital asset pricing model (CAPM) serves exactly this purpose, i.e. of predicting the „fair‰ value of an asset, so this is the first model we will discuss. The CAPM is an extension of MarkowitzÊs portfolio selection, which does not tell us the „fair‰ value of an asset. Professor William Sharpe initiated the CAPM in 1964. The main theme of Professor SharpeÊs CAPM is to predict the return

TTooppiicc

55

Capital Asset

Pricing

Model


1. Explain Capital Asset Pricing Model (CAPM) and its assumptions;

2. Compute Security Market Line (SML);

3. Apply SML for investment decision making;

4. Analyse empirical evidence of CAPM;

5. Appraise the implications CAPM for investors; and

6. Evaluate the limitations of CAPM.

TOPIC 5 CAPITAL ASSET PRICING MODEL

82

relationship of an individual asset. The model simply tells us that if some assumptions are held, the CAPM can enable us to estimate the „fair‰ return on securities. It provides substantial information about how to estimate the equilibrium expected rates of return on individual assets as well as on a portfolio. The security market line (SML) could simply be the CAPM graphed in a diagram. The SML also depicts the positive linear relationship between risk and return. If the beta value is greater than 1 (remember that beta is a measure of the systematic or market risk), then we should expect that the rate of return of that stock will be higher than the market portfolioÊs return. Thus, the greater the beta value, the higher the rate of return on that asset. Again, this reflects the trade-off between risk and return.

CAPITAL ASSET PRICING MODEL (CAPM)

The CAPM is a simple asset-pricing model that helps us to determine the „fair‰ values of assets. The integral element of the CAPM is the estimation of the beta coefficient; that is, determining the CAPMÊs beta coefficient can help investors select which securities to invest in. For example, if the beta value of a particular asset is very high, say greater than 1, then we know that this particular stock has a higher risk than the market portfolio. CAPM is a simple model that requires certain strong assumptions to be held. If these assumptions are not held, then the CAPM collapses. You should also note that empirical tests of the CAPM show that the CAPM fails to predict and explain the „fair‰ value of assets. The main reason for this failure is that some of assumptions of the CAPM are not held in reality. Nevertheless, the CAPM is an easy model to learn, and the construction of the CAPM is not sophisticated, so it provides useful information on the risk characteristics of securities. However, Markowitz portfolio selection is based on the information about expected returns and the co-variances of the stocks concerned. However, using historical information to construct a well-diversified portfolio will not make a fortune for us. Only if we can measure the expected returns on stocks can we make profits from our investments! In reality, the expected returns on stocks are, of course, very hard to measure. One thing that would be very useful, but which we donÊt yet have, of course, is a model that accurately predicts what the expected returns on stocks should be. The capital asset pricing model (the CAPM) is an equilibrium model that represents the relationship between the expected rate of return and the return co-variances for all assets. As you will learn later, this equilibrium is the most important assumption of the CAPM. „Equilibrium‰ is an economic term that characterises a situation where no investor wants to do anything differently.

5.1

TOPIC 5 CAPITAL ASSET PRICING MODEL 83

LetÊs look at this example: if, for instance, you think the equilibrium price of TENAGA stock at this moment is RM10 per share, and the market price of TENAGA is exactly RM10 per share, then you may not want to trade (buy or sell) TENAGA stock at this moment. In other words, you would say that the stock of TENAGA is fairly priced. However, if the market price of TENAGA stock were below the equilibrium price, say RM9 per share, then TENAGA stock would be said to be under-priced. If you know the equilibrium price of TENAGA is RM10, then you have the incentive to buy TENAGA stock at RM10 per share, since you will earn a profit of RM1 per share if the market price of TENAGA goes back to RM10 per share (i.e., the equilibrium price). When investors realise that TENAGA stock is under-priced, then the overall buying pressure will push the price up. After the market adjusts, the price of TENAGA stock might eventually go back to RM10 per share (i.e., the equilibrium price). On the other hand, if the market price of TENAGA were RM12 per share, the market price would be above the equilibrium price. Thus, TENAGA stock is said to be over-priced. Investors have the incentive to sell over-priced stock. The selling pressure would eventually take the price back to the equilibrium price, i.e. RM10 per share. In the real world, the equilibrium price will of course not be constant; it may change in accordance with MalaysiaÊs economic fundamentals, or the internal developments of TENAGA, the company. Instead of using price, therefore, the CAPM expresses its results in terms of returns to predict or forecast the equilibrium expected return of all assets. Professor William Sharpe developed the foundations of the CAPM in a 1964 article. The contributions of Professor Sharpe earned him the Nobel Prize in Economics in 1990. Practically speaking, the CAPM is very useful for predicting the equilibrium expected return on assets. Fund managers do, in fact, use this model to select stocks in their portfolios. In the process of capital budgeting, financial managers use the CAPM to evaluate the risk of new projects.

5.1.1 The Assumptions of the CAPM

Before you learn more about the CAPM, you have to understand its assumptions. This model must make a number of assumptions to formally derive the CAPM relationship. Some of these assumptions can be relaxed without too much effect on the results. In the later section on the extensions to the CAPM, we will discuss


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the effects on the model when some of its assumptions are relaxed. Of course, relaxing its assumptions makes the CAPM more amenable to practical usage. It is important to stress that the CAPM is a theory about the real world; it is not necessarily a description of the real world. In order to evaluate the usefulness and applicability of the CAPM we must thus try to determine how much the theory corresponds to the real world. You can refer to the textbooks mentioned to learn more about the assumptions of the CAPM. You should now have a good grasp of the basic assumptions of the CAPM. Let me make some critical remarks here regarding some of these assumptions.

(a) Investors can borrow and lend any amount at a fixed, risk-free rate. The implication of this assumption is that the rate of borrowing and rate of lending are equal to the risk-free rate, in short (rB = rL = rf). However, in the real world, the rate of borrowing is higher than the rate of lending (rB > rL). The difference between the rate of borrowing and the rate of lending is the spread that is regarded as the profit to the financial institutions (rB rL = spread). In Malaysia, the Base Lending Rate (BLR) is much higher than the savings and time deposit rates. Therefore, the difference between the BLR and the time deposit rate is the spread that it provides profits for financial institutions. By definition, the risk-free rate is the interest rate that provides an appropriate default-free (riskless, guaranteed) investment. In the US, the Treasury Bill Interest Rate is the proxy for the risk-free rate. In Malaysia, Kuala Lumpur Interbank Offer Rate (KLIBOR) is the proxy for the risk-free rate.

(b) Investors pay no taxes on returns and no transaction costs (commissions and stamp duties. Investors have to pay commission to brokers, as well as stamp duties to the government of Malaysia. Recently, the commissions charge has been significantly reduced because of the introduction of e-trading of stocks. In the US, the institutional arrangement is quite different: investors in the US have to pay both capital gains taxes and dividend income taxes for buying and selling stocks.

(c) Homogeneous expectation. This assumption states that all investors have the same expectations regarding the performance of the stock market. For instance, during a period of deflation and economic recession, the model assumes that all investors will have the same feeling, i.e. that the stock price of HSBC will decline. Practically speaking, this is not necessarily the case; different investors may have different opinions about the price distribution of a certain asset. Some investors may think that it is a good time to buy banking stocks during a time of deflation and economic recession. Thus, in the real world, investors have different expectations. This so-called heterogeneous expectation is quite common in investment decision-making.


The simplifying assumptions underlying the CAPM were relaxed one at a time. Each time, the implications of the model were slightly obscured. I will show you in the subsequent section how the CAPM is altered if the assumptions are relaxed one at a time. If all assumptions are relaxed simultaneously, however, the results of the CAPM cannot even be determined. However, the fact that such analysis is not derivable under realistic assumptions does not mean it has no value. The CAPM still rationalises the complex behavior that is observed in the financial markets.

In the real world, we do not expect all individual investors to behave rationally. Of course, we expect most investors to be rational. Still, there are some investors who behave irrationally. For instance, a risk loving investor might invest all of her wealth in a single stock.

MARKET PORTFOLIO AND MARKET RISK PREMIUM

The market portfolio is an integral part of the CAPM. By definition, the market portfolio is a portfolio of all risky securities held in proportion to their market value. This means that the return on the market portfolio is given by the following:

N

M i ii i

r v r

where

i

total dollar valueof security iv

total dollar valueof all risky securities

rM is the return on market portfolio

ri is the return of security i In practice, the „market portfolio‰ usually refers to national market indices, such as the S&P500 for the US, the Financial Times 100 for the UK, the Nikkei 225 for Japan, the All Ordinaries for Australia, the Hang Seng Index (HSI) for Hong Kong and KLCI for Malaysia. These national market indices can be found in

5.2

That all investors are rational is an implicit assumption of bothefficient diversification and the CAPM. Do you think this assumptionis realistic? Why or why not?

ACTIVITY 5.1


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financial time series databases such as Data Stream International. Fund managers use these national market indices as the benchmarks for their locally or globally diversified portfolios. Once we have the information on the market portfolio, we can easily estimate the market portfolio risk premium. YouÊre introduced to this in the next reading. Investors now face two different investment instruments: namely, the risk-free rate investment and investment in the risky market portfolio. If investors allocate their wealth in these two investments, then the risk-free rate is considered as the opportunity cost of holding the risky market portfolio. The opportunity cost is defined as an implicit cost that equals the difference between what was actually earned and what could have been earned in the highest-paid alternative use of the capital. For instance, suppose a risk-averse investor has RM1 million to invest. LetÊs say he allocates RM0.5 million to the risk-free rate investment and the other RM0.5 million to the risky market portfolio. However, if another investor is less risk-averse, she could invest the entire RM1 million in the risky market portfolio. This investor will earn a higher rate of return because she bears more risk. The market risk premium is simply defined as the difference between the return on the market portfolio and the return on the risk-free investment:

Market portfolio risk premium = E(rM) rf

The market portfolio risk premium is also known as the excess expected return on the market portfolio. If the risk-free rate is getting smaller, then the excess expected return on the market portfolio, or the market portfolio risk premium, will be higher according to the definition of the market portfolio risk premium. For example, if the annual expected return for the KLCI is 5%, and the annual rate of the 1-month KLIBOR (the proxy for the risk-free rate) is 2%, then the market portfolio risk premium is simply 5% 2% = 3%. The market portfolio risk premium will not be constant over time; the market portfolio risk premium is a time-varying parameter, which means that the market portfolio risk premium will change from time to time. Both the expected return on the market portfolio and the KLIBOR will change over time to reflect the changing economic fundamentals in Malaysia.

5.2.1 The Excess Return on Individual Stocks

Similar to the excess market portfolio return, the excess expected return on an individual stock is defined as the difference between the expected return on that individual stock and the risk-free rate (i.e., excess expected return = E(ri) rf). The excess expected return on an individual stock could also be considered as the risk premium of that individual stock. If the opportunity cost of holding risky


stocks is higher (i.e., the higher the level of the risk-free rate), then the risk premium for an individual stock is smaller if the expected return on individual stock is held constant. On the other hand, if the opportunity cost of holding risky stocks is lower, then the risk premium for an individual stock is greater than if the expected return on individual stock is held constant. Both the expected return on an individual stock and the risk-free rate will change in response to economic fundamentals. Thus, the risk premiums of individual stocks will also change over time.

5.2.2 The Expected Return on Individual Stocks

You need to know how the return on an individual stock is determined under the framework of the CAPM. In the following reading youÊll learn more about the theoretical background of the CAPM. After the reading, I will make some comments that emphasize the application of the model. So far we have discussed two important risk premiums, namely the market risk premium [E(rM) rf ] and the individual stock risk premium [E(ri) rf]. The main objective of the CAPM is to explain the relationship between these two risk premiums. The relationship can be written in the following fashion:

E(ri) rf = i[E(rM) – rf]

If we switch the term for the risk-free on the left-hand side to the right-hand side, then we obtain the following:

E(ri) = rf + i[E(rM) – rf]

This is the well-known relationship characteristic of the CAPM that shows that the expected return on an individual stock is equal to the sum of the risk-free rate plus the beta (i) times the expected market risk premium. The beta (i) coefficient is the measure of the systematic risk of a stock, i.e. the tendency of a stockÊs returns to respond to swings in the market portfolio. We will discuss the beta coefficient and the estimation of beta in subsequent sections. The intuition of the CAPM is quite precise. The expected return on individual stock is equal to the opportunity cost of holding risky assets (i.e., rf) plus the reward of bearing more risk, which is the second term of the CAPM (i.e., i[E(rM) – rf]). For example, if the annual rate of the 1-month KLIBOR (the proxy for the risk-free rate in Malaysia) is 2%, the expected growth on the KLCI is 5%, and the beta coefficient of HSBC stock is 1.2, then the expected return on HBSC is as follows:

E(rHSBC) = 2% + 1.2(5% - 2%)

5.6% = 2% + 1.2(5% - 2%)


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Since the CAPM is an equilibrium model, the equilibrium expected return on HSBC is 5.6%, which is higher than the return on the KLCI. Now, suppose the beta coefficient of HSBC is 0.9 instead of 1.2. Then the equilibrium expected return on HSBC is:

4.7% = 2% + 0.9(5% - 2%)

The result tells us that if the beta coefficient of HSBC or the measure of the systematic risk of HSBC is lower, the equilibrium expected return for HSBC becomes lower. The new equilibrium expected return for HSBC (4.7%) is lower than the return on the KLCI. In practice, it is very easy to calculate any individual stockÊs equilibrium expected return. The only information we need to know is the risk-free rate, the expected return on the market portfolio, and the beta coefficient. The risk-free rate and the return on the market portfolio (ex-post) can be found in financial newspapers. We only have to estimate the beta coefficient. Once weÊve obtained the value of the beta coefficient, we can easily determine the equilibrium expected return. Fund managers use the information on stocksÊ betas to make investment decisions from time to time. For instance, the security analyst from a fund house might estimate the value of beta for a number of individual stocks. Then the fund managers use this information, i.e. the estimated betas, to form their portfolios. An aggressive portfolio will comprise stocks with high betas. Normally speaking, stocks with beta values greater than 1 are considered to be aggressive investments. Conversely, a defensive portfolio will comprise stocks with low betas, i.e. with values less than 1. A fund manager can also form a mixed portfolio, which consists of stocks with both high and low beta values. This is why the beta values are significant for fund managers making investment decisions related to portfolio selection. As I will show you later, the calculation of beta is rather handy and requires only a few bits of information.

5.2.3 The Ex-ante and Ex-post Versions of the CAPM

There are two versions of the CAPM, namely the ex-ante version and the ex-post version.

Ex-ante version: E(ri) = rf + i[E(rM) – rf] Ex-post version: ri = rf + i[rM – rf]

The ex-ante version is based on information about the future market risk premium, and the ex-post version is based on historical data related to the market risk premium.


THE SECURITY MARKET LINE (SML)

The CAPM analyses the linear relationship between an individual stock and the market risk premium. We can actually plot this linear relationship into a graph. This graphical presentation makes it easier for us to visualise the CAPM. When the CAPM is depicted graphically, it is known as the security market line (SML). Plotting the CAPM, we find that the SML will, in fact, be a straight line which is similar to the capital market line (CML). The SML indicates the equilibrium expected rate, or sometimes we refer to the required rate of return the investor should earn in the stock market for each level of systematic risk (i.e., the beta). I will now show you how to graph the SML and discuss the implications of the SML thereafter.

5.3.1 Graphing the SML

The CAPM can be plotted by simply calculating the equilibrium expected return, or the required rate of return for a series of betas when holding the risk-free rate and the return on market portfolio constant. Referring back to our previous example with HSBC using the ex-post version of the CAPM:

rHSBC = 2% + HSBC(5% - 2%)

The following table shows the required rate of return for a number of betas when we apply the above CAPM to HSBC:

Beta of HSBC Require rate of return 0 2%

0.5 3.5% 1 5%

1.5 6.5% 2 8%

5.3

LetÊs say youÊve used historical data to obtain the following information:

Market risk premium = 10%

The required rate of return of an individual stock = 16%

The beta coefficient of the individual stock = 1.2

Assuming the CAPM holds, what is the risk-free rate (rf) in this case?

SELF-CHECK 5.1


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Plotting these values on a graph (with the beta on the horizontal axis and the required rate of return on the vertical axis), we have a straight line that is known as the SML (Figure 5.1). The SML clearly shows that as the beta (i.e. the systematic risk) increases, so does the required rate of return. Any point along the SML is considered as the equilibrium rate of return.

Figure 5.1: The security market line (SML)

5.3.2 The Investment Decision-making Process

According to the CAPM, the SML reflects the equilibrium condition of a stockÊs required rate of return and that of the market return. However, the securityÊs actual return may not be on the SML. For instance, points U and O are not on the SML in Figure 5.2. As shown in Figure 5.2, point U lies above the SML and point O is below the SML. When the actual return of a stock is above the SML, it is considered to be an under-priced stock. In other words, the expected return of stock U is higher than that predicted by the CAPM. Therefore, when investors identify stock U as an under-priced stock, there will be pressure in the marketplace for buying it. As a result, the price of stock U will be bid up and the expected return on stock U will be lower. Please bear in mind that when the price of a security is bid up, its return becomes lower since return at time t is defined as follows:

rt = (selling price buying price)/buying price

When the buying price is bid up because of buying pressure in the marketplace, then the return at time t will be lower because the denominator is getting larger. Eventually, point U will move towards the SML and an equilibrium condition will be re-established.


By the same token, stock O is an over-priced stock, since its expected return is lower than that of the equilibrium return. When investors see that stock O is over-priced, then there will be pressure in the market for selling stock O. As a result, the price of stock O will drop, and the required rate of return on stock O will be higher when the equilibrium condition is re-established. Thus, when there is a disequilibrium situation in the market place, the market forces of supply and demand will push prices toward the equilibrium position suggested by the CAPM.

Figure 5.2: A disequilibrium situation

The SML will not stay at the same position all the time it will move up and down in accordance with economic fundamentals. In the real world, fund managers tend to use the SML as an indicator to manage stocks in their portfolios. Nowadays, thanks to widespread ease of access to financial databases, we can easily estimate betas and plot the SML. The SML therefore serves as a preliminary procedure for identifying under-priced and over-priced securities. There are real limitations on using the CAPM/SML to predict return patterns for securities. We cannot totally rely on the CAPM/SML to make our investment decisions. You should understand right now, however, that the CAPM is not the only tool that we can use to predict the returns on stocks. There are, of course, other tools such as the multifactor model and arbitrage pricing theory (APT) models, and using them is preferable to simply employing the CAPM on its own. One of the major shortcomings of the CAPM is that we assume beta is stable over time. In fact, the beta value of any stock will keep on changing. For example, letÊs say you obtain a beta during a bull market period. Then, all of a sudden, the market experiences a downturn. If you still keep on using the same beta to make


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predictions, then the outcome will definitely be unfavourable. In this case, you need to have a dynamic CAPM to handle the problem. The dynamic CAPM allows the beta to be changed over time. In this case, the predictions that result will be more reliable.

SYSTEMATIC RISK

You know by now that the beta coefficient is a measure of systematic risk or non-diversifiable risk. It is your task in this topic to learn how to estimate the beta coefficient of a stock. Once we obtain the value of the beta coefficient, we can then use this beta value and plug it into the CAPM equation in order to obtain the appropriate equilibrium expected return for an individual stock.

5.4

Use all the information you have obtained from Activity 3.3 and plotthe security market line (SML). If the actual market return of the stockis 18%, what is your investment decision?

SELF-CHECK 5.2

ACTIVITY 5.2

LetÊs say you are considering investing in two stocks, Stock X and Stock Y. After doing your research, youÊve come up with some information on these stocks, as given below:

Stock Beta Standard deviation of annual return X 0.35 20.50% Y 1.85 20.00%

After you show the information above to your classmate he points out that you have made some mistakes in your analysis. He further explains that, as the beta of Stock Y is much greater than that of Stock X, it is impossible for these two stocks to have similar total risk (standard deviation of annual return). Do you think his argument is correct? Why or why not?


5.4.1 The Estimation of the Beta Coefficient

To gain deeper insight into systematic risk, letÊs consider the estimation of the beta coefficient from an ordinary least squares regression:

rit rft = i + i(rMt rf) + it

where

rit rft is the excess rate of return on individual stock i at time t.

rMt rf is the excess rate of return on market portfolio or the market risk premium at time t.

i is the alpha coefficient in the regression at time t.

i is the beta coefficient in the regression, the measure of systematic risk at time t.

it it is the error terms of the regression at time t. In the above characteristics line regression, which is also known as the Market Model regression, the alpha is the intercept in the regression, and the beta is the slope of the regression. Remember, this is not the CAPM equation. This is a regression that allows us to estimate the security beta coefficient. The CAPM equation suggests that the higher the beta value, the higher the equilibrium expected return. Note that this is the only type of risk that is rewarded in the CAPM. The beta risk is referred to as systematic, non-diversifiable, or market risk. This risk is rewarded with expected returns. The other type of risk, which we mentioned in earlier topics, is known as unsystematic risk, or diversifiable risk. This type of risk is represented by the error terms in the above states time-series regression. To sum up, the term�i(rMt rf) represents the systematic risk or non-diversifiable risk, and the it represents the error terms, which are also known as residual terms in the regression, and which represent unsystematic risk or diversifiable risk. The security characteristics line is the line of the best fit for the scatter plot that represents simultaneous excess returns on an individual stock and the market portfolio. This was illustrated in Figure 5.3


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Figure 5.3: The characteristic regression line for stock i

As you can see, this is just the fitted value from a regression line. As you learned earlier, the beta will be the regression slope and the alpha will be the intercept. The error in the regression, the epsilon, is the distance from the line (predicted) to each point on the graph (actual). The CAPM implies that the alpha is zero. So we can interpret, in the context of the CAPM, the alpha as being the difference between the expected excess return on the individual stock and the actual excess return. Therefore, in an equilibrium situation, the expected excess return on the individual stock is same as the predicted excess return in the market. The alpha value should be zero. If a disequilibrium exists in which the expected excess return on the individual stock is not the same as the actual excess return, the value of alpha should be non-zero. Now, let me summarise the procedures for estimating the coefficients of alpha and beta as follows:

(a) Obtain the historical data on the individual stock (HSBC), the market portfolio (the KLCI) and the risk-free return (the 1-month KLIBOR).

(b) Calculate the excess return on the individual stock and the excess return on the market portfolio (i.e., market risk premium).

(c) Uses Microsoft Excel to run the regression (i.e., a two-variable regression, where the excess return on the individual stock is the dependent variable and the market risk premium is the independent variable).

(d) Obtain the values of alpha and beta from the regression line.


(e) You can also calculate the error terms or residual terms using the actual data minus the values predicted from the regression line.

This is the most simple and standard way to obtain the values of alpha and beta for an individual stock. There is, however, another even more direct way to obtain the value of beta for an individual stock, as depicted in the following equation:

i = Cov(ri,rM)/Var(rM)

where

Cov(ri,rM) is the covariance between returns of individual stock and the market portfolio.

Var(rM) is the variance of the market portfolio.

The covariance between returns on the individual stock and the market portfolio can also be written in the following equation:

Cov(ri,rM) =ri,rMrirM Note also that ri,rM is the correlation coefficient of returns between the individual stock and the market portfolio, which you have learned about in topic 2 in the context of portfolio risk. ri is the standard deviation of the individual stock and rM is the standard deviation of the market portfolio. In other words, once we know the covariance of returns between the individual stock and the market portfolio and the variance of the market portfolio, we can easily obtain the beta value right away. Finally, note that the beta of the market portfolio is 1:

M = Cov(rM,rM)/Var(rM) = Var(rM)/Var(rM) = 1

The market portfolio (M) serves as a benchmark for investment decision-making. This provides a reference point against which the risks of other securities can be measured. The average risk (or beta) of all securities is the beta of the market portfolio, which is one. Stocks that have a beta greater than one have above average risk, tending to move more than the market portfolio. On the other hand, stocks with betas less than one are of below average risk and tend to move less than the market portfolio. If we invest in a stock with a beta value greater than 1, this is known as an aggressive investment (i.e., weÊll encounter risk that is higher than the average risk). Conversely, if we invest in a stock with a beta value of less than 1, this is considered a defensive investment (i.e., weÊll encounter risk that is lower than the average risk).


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In the real world, whether a fund manager wants to invest in aggressive securities or portfolios merely depends upon the risk preference of the fund manager as well as the nature of the fund. For example, if the fund is a pension fund, then the fund manager will likely have to invest in less aggressive securities or portfolios. In other words, the pension fund manager has to invest in securities with low beta values. On the other hand, if the nature of the fund is a growth fund, then the fund manager has to invest in stocks with high beta values. The same is true for an individual investor. If the individual investor is rather risk averse, then that individual investor should invest in stocks with low beta values. Needless to say, if an individual is less risk averse, then that individual investor will want to invest in stocks with high beta values. Now you can really appreciate why beta is so important for investment decision making. The state of the economy is another element that enters into investment decision making that uses beta value as the benchmark. During economic booms, investors and fund managers would like to invest in stocks or portfolios with high beta values in order to take advantage of the free ride of the economyÊs growth. Generally speaking, during the periods of economic boom, firms have better earning performance, and this will immediately be reflected in share prices. Investors pay more attention to capital gains (i.e., the appreciation of share prices) during booms. Clearly, stocks with high beta values will provide more capital gains to investors. Conversely, during recessions investors generally want to invest in stocks with low beta values. For example, the stocks of public utilities usually have low beta values. Investors want to invest in such stocks during recessions in order to avoid capital losses (i.e., depreciation of share prices) and at the same time to get higher dividend yields.

EXTENSIONS OF THE CAPM

So far we have focused on the use of the CAPM for an individual stock. We need to be able to construct the CAPM to cover a portfolio comprising a series of risky securities. This is so-called portfolio CAPM. In addition, in this topic we look into the stability problem of beta - in other words, whether beta is constant over time. Finally, we examine what happens to the CAPM if some of its assumptions are relaxed.

5.5.1 The CAPM for a Portfolio

Instead of having an individual stock, letÊs say we now have a portfolio that consists of risky securities. The CAPM for a portfolio can be set out as follows:

rP = rf + P(rM – rf)

5.5


where

rP is the equilibrium rate of return of a portfolio

P is the portfolio beta, which is defined:

i

n

iip w

1

and

wi is the weights of individual stocks in the portfolio The beta of the portfolio is the weighted average of the individual stock betas where the weights are the portfolio weights. Thus we can think of constructing a portfolio with whatever beta we want. All the information we need is the betas of the underlying stocks. For instance, if I wanted to construct a portfolio with zero systematic or non-diversifiable risk, then I could choose an appropriate combination of stocks and weights that delivers a portfolio beta of zero. Once we obtain the information on P, we can easily calculate the equilibrium or the required rate of return of the portfolio. At this point you should understand that the CAPM not only applies to individual stocks, but also to portfolios that comprise a series of risky assets. Practically speaking, then, portfolio managers can employ the CAPM to help manage their portfolios. The portfolio beta (P) provides information on the risk profile of the entire portfolio and is useful in portfolio managersÊ investment decision-making.

LetÊs say a well-diversified portfolio is composed of the following five stocks:

Stocks Prices Shares held Beta () A $10 1,000 0.8 B $20 1,500 0.9 C $5 5,000 1.2 D $35 2,000 1.3 E $50 1,500 1.5

LetÊs also say that the capital asset pricing model (CAPM) holds, the expected return on the market portfolio is 12%, the market portfolioÊs standard deviation is 8%, and the risk-free rate is 4%. What is the expected return on this five-stock portfolio?

SELF-CHECK 5.4


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5.5.2 The Beta Stability Problem

You should now be aware that beta is a measure of systematic or non-diversifiable risk. However, there is one question concerning the stability problem of beta that we must raise here: is beta constant over time? I am sorry to tell you that the answer is that beta is not constant over time. In other words, beta is a time-varying parameter so its value will change at different time periods. If the beta coefficient is not constant over time, then the CAPM will fail to predict the equilibrium expected return or the required rate of return for an individual stock as well as for a portfolio of stocks. This means a more advanced version of the CAPM should be used to counter the stability problem of beta. However, pursuing this is not within the scope of this course.

THE RELAXATION OF CAPM ASSUMPTIONS

It is important to stress that the CAPM is a theory about the real world. It is not necessarily a description of the real world. In order to evaluate the usefulness and applicability of the CAPM, we must therefore try to determine how well the theory actually corresponds to the real world. One way of doing this is to relax some of its assumptions and thereby allow the CAPM to be more flexible and correspond to the real world: (a) We can relax the assumption that the borrowing rate is equal to the lending

rate, and assume instead that the borrowing rate is higher than the lending rate (i.e., rB > rL). As we have mentioned before, in the real world the borrowing rate is indeed higher than the lending rate, and the spread between borrowing rate and lending rate is the operating cost as well as the profit of financial institutions. If separate borrowing and lending rates are assumed, then two different CAPMs emerge:

E(ri) = rB + i(rM – rB) and

E(rj) = rL + j(rM – rL)

The corresponding SMLs are depicted in Figure 5.4.

5.6


Figure 5.4: The SML for a borrowing rate that does not align

perfectly with the SML for the lending rate (b) If transaction costs such as brokerage commissions and search cost are

taken into account, then these realities can be modelled as „bands‰ on the sides of SML, as shown in Figure 5.5.

Figure 5.5: The SML with bands on the sides when

transaction costs are taken into account There may be only a few percentage points of spread between the top and

bottom transaction cost bands. Within this band, it is not profitable for investors to trade securities, because the transaction costs would consume


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the potential profit that would induce such trading. Consequently, the market will never attain the equilibrium situation indicated in the solid line of SML, even if there are no changes in the other assumptions.

(c) Incorporate taxes into the CAPM model. Many countries in the world have

legislated capital gains taxes as well as dividend income taxes for buying and selling stocks. In the US an investor is subject to both capital gains tax and dividend income tax when trading stocks. However, there are no such taxes in Hong Kong except for the stamp duties that are levied on the trading of stocks. With the existence of taxes taken into account, every investor would see a slightly different CAPM in terms of after-tax returns, since those returns would depend upon their particular tax situations. As a result, a static equilibrium condition will never emerge, even if other assumptions are maintained.

(d) Eliminating the assumption of homogeneous expectations will eventually

allow investors to use different expected returns as well as the covariance of returns to construct the efficient frontier. The efficient frontier and the CAPM are composed of „fuzzy‰ curves and lines. The static equilibrium situation again could never emerge, even if other assumptions are held constant.

I believe that you are now very familiar with the CAPM. Before you go on to the next section, I just want to ask you one more question. What useful implications does the CAPM have for investors, in spite of its shortcomings? For investors, the CAPMÊs implications can be summarised as follows:

(a) If you are a diversified investor, all you need to be concerned with is the systematic risk you bear. Total risk or the volatility of any individual security in your portfolio is irrelevant.

(b) Is your desired level of risk consistent with your portfolioÊs beta or systematic risk? Is the risk level of your portfolio what you intended? If not, you can simply adjust your portfolio beta by changing the component securities in your portfolio to match your desired level of risk.

(c) Based on existing finance literature, although it is strongly doubtful whether beta is a useful measure of expected return, beta is still a very useful measure of market-related volatility.


We have discussed the importance of Capital Asset Pricing Model (CAPM)

and its assumptions. We have also learned how to derive Security Market Line (SML). It is important to learn how to apply Security Market Line (SML) for

investment decision making. The empirical evidence of CAPM has been shown using example a stock,

KLCI and KLIBOR. The implication of CAPM to investors has also been discussed. However, there are limitations of CAPM, and therefore we must move

forward to other asset pricing models (to be discussed in next topic)

Attainable frontier Base Lending Rate (BLR) Beta Capital asset pricing model Equilibrium price Excess return Expected returns Fair value Feasible frontier Market portfolio

Market risk premium Markowitz portfolio selection Modern portfolio theory Over-priced stock Relative risk Required return Risk-free rate. Security market line Systematic risk Under-priced stock

1. Discuss the relevant risks that are measured by beta? 2. Using Kuala Lumpur Composite Index (KLCI) as example. Explain what is

market return and how beta is related to it? 3. Discuss the relationship between market return and interpretation of beta

for a stock listed in the exchange?


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4. Discuss the range of values typically exhibited by beta. 5. Discuss the role of beta in the Capital Asset Pricing Model (CAPM). 6. Discuss the relationship between security market line (SML) and the

Capital Asset Pricing Model (CAPM)? 7. Discuss the role of CAPM as a predictive model and its importance to

investors. 8. What does the coefficient of determination (R-squared) for the regression

equation used to derive a beta coefficient indicate?

1. Given that the risk-free rate (Rf) is 10 percent and the market return (RM) is 14 percent. Compute the required return

Stock Beta E(R)

ABC 0.85

XYZ 1.25

2. You are given the betas for securities A, B and C as follows:

Security Beta

A 1.40

B 0.80

C -0.90

(a) Calculate the change in return for each security if the market experiences an increase in the rate of return of 13.2% over the next period.

(b) Calculate the change in return for each security if the market experiences a decrease in the rate of return of 10.8% over the next period.

(c) Discuss the relative risk of each security based on (a) and (b).


3. Use Capital Asset Pricing Model (CAPM) to find the required return for each of the following securities.

Security Rf (%) Market Return(%) Beta

A 5 8 1.30

B 8 13 0.90

C 9 12 -0.20

D 10 15 1.00

E 6 10 0.60

Given that the risk-free is 7% , market return is 12% and the following asset classes which you are interested to invest in (for Questions 4 to 6):

Asset Classes Beta

A 1.50

B 1.00

C 0.75

D 0

E 2.00 4. Which asset class is the most risky and least risky? 5. Using CAPM, calculate the required return on each of these asset classes. 6. Draw the security market line (SML), based on answers from no. 5.

You are given a number of portfolios with their returns and risk (for Questions 7 to 8):

Portfolio Return(%) Risk(%)

A 9 8

B 3 3

C 14 10

D 12 14

E 7 11

F 11 6

G 10 12

H 16 16

I 5 7

J 8 4


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7. (a) Plot the feasible or attainable set represented by these data on a set of portfolio risk on x-axis and portfolio return on y-axis.

(b) Draw the efficient frontier on the graph in 7(a). 8. (a) Which portfolio lies on the efficient frontier and explain the reason

why is these portfolios dominate the others in the feasible or attainable set ?

(b) How would an investorÊs utility function or risk-indifference curves

be used together with the efficient frontier in finding the optimal portfolios?

INTRODUCTION

Having covered the single-indexed model in Topic 5 and CAPM-based asset pricing model in Topic 6, moving ahead, this topic introduces students to the alternative model of explaining asset prices. All the previous models in earlier topics are the equilibrium models which are based on mean-variance analysis. The topic starts with the introduction to the concept of Arbitrage Pricing Theory (APT). This will then be followed by discussion on factor sensitivities where the unexpected changes in the macroeconomic factors that affect the returns, are captured by the sensitivities of the respective factors. Subsequently, the empirical issues in implementing APT are discussed. This is followed by discussion on the usage of APT. The last section in this topic draws comparison between CAPM and APT.

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The Arbitrage

Pricing Model

APTLEARNING OUTCOMES

By the end of this topic, you should be able to:

1. Explain the concept of Arbitrage Pricing Model (APT);

2. Assess factor sensitivities in APT;

3. Analyse empirical issues of APT;

4. Discuss the usage of APT; and

5. Distinguish between CAPM and APT.

TOPIC 6 THE ARBITRAGE PRICING MODEL APT

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ARBITRAGE PRICING THEORY

Arbitrage Pricing Theory (APT) was introduced by Ross (1993, 1994) as a new approach to explain the pricing of financial assets. It is based on the law of one price i.e. two items that are similar must be sold at the same price. There are two assumptions:

(a) The existence of homogeneous expectation among investors; and

(b) The existence of the process generating security returns. Based on the (ii) assumption, security returns is said to be linearly related to a set of indices as shown in equation 7.1. ijijiiii eIbIbIbaR ...2211 (7.1)

Where:

All indices are assumed to be unconnected with each other. Equation 7.1 represents a return-generating process that expresses the return of any security as a linear function of a series of indices. Using the above framework, a model can be constructed to explain stock returns. Roll and Ross (1995) uses four macroeconomic factors to their model to explain stock returns as shown in equation 7.2. ER = fR + INF1 + IP2 + RP3 + I4 + e (7.2)

6.1

ia = the expected level of return for stock i if all indices have a value of zero

jI = the value of the jth index that affects the return on stock i

ijb = the sensitivity of stock iÊs return to the jth index

ie = a random error term with mean equal to zero and variance equal to 2ei


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Where:

Equation 7.2 assumes that stock returns are affected by four macroeconomic factors, therefore it can also be known as a four-factor model. The unexpected changes in the macroeconomic factors that affect returns are captured by the sensitivities of the respective factors.

FACTOR SENSITIVITIES IN APT

Figure 7.1: A positive relationship between factor returns and stock returns

6.2

ER = The expected return to security or portfolio i.

fR = Risk free rate

i = The sensitivity of security i to movements in factor INF = Unexpected inflation IP = Unexpected changes in the level of industrial production RP = Unexpected shifts in bond risk premium I = Unexpected changes in the term structure of interest rates. e = Unsystematic return


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Figure 7.2: A negative relationship between factor returns and stock returns

As shown in Figure 7.1, there is a positive relationship between unexpected movements in the factor and the securities returns. The steepness of the slope reflects the sensitivity of a stock to the changes in the factor. A steeper slope reflects more factor sensitivity involved than a flatter slope. Figure 7.2 shows a negative slope. This indicates an inverse relationship between factor returns and securities returns.

6.2.1 Passive Management

As a multi-index model, APT can assist in improving passive management. If you recall in passive management, fund managers practically limit their intervention in the pre-set or target portfolios once they are set. Therefore, a multi-index model can be used in designing a passive portfolio or tracking an index. In the above instance, a multi-index model can be built to closely follow an index. For example, a Malaysian fund manager can use a multi-index model with all industrial indices as the factors to track Kuala Lumpur Composite Index (KLCI).

6.2.2 Active Management

As an active management tool, APT can be used to determine stocks that are under-valued or over-valued.


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For an example, an analyst can first forecast the return of a stock. The APT is used to estimate the sensitivity of the stock to the factors to calculate the required return for the stock (after subtracting risk free rate from the expected return) as shown in equation 7.3. ER - fR = INF1 + IP2 + RP3 + I4 + e (7.3) If the estimated or forecasted return is above the required return given by the stock sensitivity and the value of factors, the particular stock is purchased.

6.2.3 Performance Evaluation

As a multi-index model, the APT models are used in the area of portfolio performance evaluation. In the example given in equation 7.3, it can be seen that under APT, the expected performance of any portfolio is a function of the portfolioÊs sensitivity to inflation, the level of industrial production, bond risk premium and interest rates. Hence, in evaluating the performance, these influences on the return-generating process must be taken into account.

COMPARISON BETWEEN CAPM AND APT

CAPM is a special case of the APT when there is only one factor involved and that factor is the return to the market portfolio. In this instance, CAPM is equivalent to APT. APT is used in passive management, active management and portfolio evaluation. Generally, APT differs from CAPM in a few aspects:

(a) APT recognises that there are other factors than market index that can affect on securities returns.

(b) APT is a more general model as it has many factors as compared to CAPM with only one factor.

(c) APT has fewer assumptions than CAPM.

(d) The focus of APT is not on market portfolio, but rather on portfolios which are sensitive to other macroeconomic factors such as inflation or industrial production.

6.3


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More importantly, the APT does not require the following assumptions:

(a) Investors have quadratic utility functions.

(b) Security returns are normally distributed.

(c) The market portfolio contains all securities and is mean variance efficient.

This topic introduced you to both the theoretical and practical aspects of

asset-pricing models. Generally speaking, asset-pricing models enable us to predict assetsÊ returns. If investors can predict the returns on assets, then they can make their investment decisions based on these predictions.

The index model, which is an extension of the CAPM, requires fewer assumptions.

The CAPM is, in fact, a special case of a single index or factor model. A single index model can be easily estimated by a simple regression. The slope of the regression is the risk measure for a particular factor.

Multifactor models provide better predictive power than single index or factor models. The factors included could be macroeconomic variables or firm-specific variables.

The arbitrage pricing theory (APT) is a model that asserts that, given that certain securities are exposed to common factors and are on the same level of risk, the returns on these securities should be identical. If the returns on such securities are not identical, then arbitrage opportunities exist.

Practically speaking, both the CAPM and APT cannot pass empirical tests. Tests of the CAPM indicate that the model fails to explain or predict the return behaviour of securities. On the other hand, one can hardly perform empirical tests on the APT.

Behavioural finance is a new branch of financial economics that has been added to the mix. Behavioural finance considers how various psychological traits affect individuals or groups when.

As a fund manager, which are the macroeconomic factors that likely toimpact the performance of stock portfolios given rising price in thegoods market?

ACTIVITY 6.1


111

Arbitrage Pricing Theory (APT) Expected return Expected utility

Macroeconomic variables Multifactor model Risk factors

1. Explain what is an Arbitrage Pricing Theory (APT) model.

2. What are the assumptions of Arbitrage Pricing Model?

3. What does the steepness of the slope of factor sensitivity in an APT model reflect?

4. State the general form of an APT model.

5. What are the empirical issues of APT Model?

6. Name the usages of APT Model.

7. How APT differs from CAPM?

1. Give examples of macroeconomic factors used in APT models.

2. Why inflation is a factor to be concerned by investors?

3. Passive management is also synonymous with what?

4. What kind of unit trust fund that mostly employ passive management strategy?

5. Give examples of microeconomic variables as risk factors in the context of APT.

6. What is a multifactor model in the context of APT?

7. Name the three assumptions that APT model does not require to have.

8. Given a APT model with risk free rate of 6%; sensitivities to factor 1 and 2 are 0.5 and 2; risk factor 1 and 2 is 0.02 and 0.01. What is the expected return from the security?

INTRODUCTION

Previously, we have studied the Capital Asset Pricing Model (CAPM) in Topic 6. From there, we have learnt how the returns of securities are measured against market benchmark like Kuala Lumpur Composite Index (KLCI) or EMAS Index. Hence, from Topic 6, we know that there are many market participants that would like to sell and buy securities or stocks in the financial markets. Will the price of stocks be influenced by the number of market participants? In this topic, we are going to discuss the concept of Efficient Market Hypothesis (EMH). This is an important concept on explaining how the flow of information will affect the price of stocks with the assumption that there are many market participants. EMH has become one of the cornerstones of modern finance theory ever since it was introduced in 1970. It has attracted researchers to conduct empirical works on many stock markets. On the practical aspect, it has helped to explain the formation of price in stock market. The speed of price formation can also be seen

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Markets

Hypothesis

77

4. Assess the implication of EMH to investment strategies; and

5. Review market rationality in relation to EMH.


1. Explain the concept of efficient markets;

2. Describe the three main degrees of efficiency;

3. Discuss the empirical tests of Efficient Markets Hypothesis (EMH);

TOPIC 7 EFFICIENT MARKETS HYPOTHESIS 113

as one aspect of stock market development. In well developed stock markets like the US and Japanese markets, where the flow of information is faster, the changes of stock price is sensitive to any social, political or economic news. For example, the moment the news of worse than expected economic data is released to the market, we can see that the US dollar will lose its value. We can also observe certain stocks which are related to the economic sectors will suffer losses. This phenomenon show that EMH works in these advance markets. Having said the importance of EMH, we will also discuss market rationality in the last part of this topic. The recent research on behavioral finance is a new phenomenon. The new area attempts to explain what cannot be explained by EMH. In a glance, for this topic, we will firstly look at what is market efficiency. Secondly, we will discuss on what are the different degrees of market efficiency. Thirdly, we will learn about how we know that the market is efficient. Here we will learn some empirical test to confirm or reject the hypothesis. Fourthly, we will discuss the implication of EMH on activities of investing in stock market. Finally, we will discuss the issue of market rationality.

EFFICIENT MARKETS 7.1

Efficient Markets Hypothesis (EMH) is one of the dominant ideas developed in 1960s by Eugene Fama.

From investorsÊ point of view, under the assumption EMH, it can also be said stocks are always traded at their fair value in stock exchanges, and investors are unable to purchase undervalued stocks or sell overvalued stocks.

In finance, efficient capital market refers to a stock market where security prices fully reflect all available information. In other words, it is difficult for investors to beat the market because the prices have reflected all relevant information.

Fair value is the amount at which an asset could be exchanged or a liability settled, between knowledgeable, willing parties in armÊs length transaction.

Also, under EMH, it is also impossible for investors or fund managers to outperform the overall market through stock selection or market timing. The implication is that, the only way investors can obtain higher returns is by

TOPIC 7 EFFICIENT MARKETS HYPOTHESIS

114

purchasing riskier investment. We have discussed this risk-return trade-off in Topic 2. EMH is based on expected return theory. It can be denoted by jttitjtitj pREpE )]|(1[)|( ,, (7.1) Where

E is the expected value operator;

jtp is the price of security j at time t;

itj , is random variable at time t;

itjR ,

t

is the one-period percentage return;

is a general symbol for information set.

The conditional expectation notation in equation (6.1) implies that whatever expected return model is assumed to apply, the information set in is fully utilised in determining equilibrium expected returns. In other words, the formation of i.e. the price of security j at time t is fully reflective of

information set .

t

jtp

t How we interpret the above mathematical notation in normal day-to-day trading in the stock market? In a hypothetical example, if an oil and gas company discovers some new oil fields, the stock price at time t will be fully reflective of this new piece of information.

7.1.1 The Effect of Efficiency

The nature of information does not have to be limited to financial news and research. Any information about political, economic and social events, combined with how investors perceive such information, whether they are true or false, will be reflected in the stock price. According to EMH, as prices respond only to the information available in the market, and, because all market participants are privy to the same information, no one will have the ability to out-profit anyone else in the market. In other words, if the market is truly efficient, no investor will have the ability to out perform the market.


The above paragraph is certainly a bad news for investors who want to out-beat the market. But in the real world, is our stock market really efficient? We will examine the question whether the market is truly efficient in Sub topic 7.5. Right now, let us proceed to subtopic 8.2 to read about the degrees of efficiency.

1. Do you think stock market is truly efficient?

2. What are factors that will contribute to the efficiency of stock market?

ACTIVITY 7.1

DEGREES OF EFFICIENCY 7.2

According to Efficient Market Hypothesis (EMH), there are three types of market efficiency as reflected by the degree to which it can be applied to as illustrated Figure 7.1:

Figure 7.1: Degrees of efficiency

Table 7.1 describes each of the degrees of efficiency.


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Table 7.1: Degrees of Efficiency and Descriptions

No Degrees of Efficiency Descriptions

Weak Efficiency This type of EMH claims that all past prices are reflected in todayÊs stock price. Therefore no excess returns can be earned by using investment strategies based on historical share prices or other financial data.

i

Semi-strong Efficiency This form of EMH implies that all public information is calculated into a stockÊs current share price. Share prices adjust instantaneously to all public information, so that no excess returns can be earned by trading on that information.

ii

Strong Efficiency This is the strongest form which states that all information in a market, whether they are private or public information, will be reflected in the stock price. No one can have excess returns in such markets, even insiderÊs information cannot give investors any advantage.

iii

1. As a developing country, Malaysian stock market is at whatdegree of efficiency?

2. Do you think EMH is realistic? (Hint: Think of this question before you read sutopic 7.4)

SELF-CHECK 7.1


EMPIRICAL TESTS OF EMH 7.3

7.3.1 The Test for Weak Efficiency

There are different empirical test for EMH for different degrees of efficiency. To test for weak form efficiency, it is sufficient to use statistical investigation on time series data of prices. News is generally assumed to occur randomly, so share prices changes must also be random. To test for weak form efficiency, we can use runs test, Von NeumannÂs ratio test and Ljung-Box Q Test. Let us now elaborate runs test. Based on Table 7.2, we have 31 daily stock prices of stock XYZ. Consider a price series in column two. The first step is to define the natural log price changes as vt in column three:

.21 ,....,, nppp

1lnln ttt ppv

In Microsoft Excel, we can use ln(Pt/Pt-1) since log A log B is equivalent to log (A/B). In column four, we will state a positive sign for positive value of Vt, and a negative sign for negative value of Vt.


118

Table 7.2: Runs Test


In column five, we can count the blocks of positive change, negative change and no change. In our example, number of blocks for positive change or m1 is 17, number of blocks for negative change or m2 is 11. The number of blocks for no change is 2. The total number of blocks for all the three groups or R is 15. We sum up the total of m2, m3 as 414 and 6252 respectively. Since we lose one data point when we calculate the return of this stock price, the number of observations, n is only 30. And we can calculate the Expected value of R and Variance of R with the following formula:

23

11

30 1 414 / 30

17.2

i

miE R n

n

3 3 32 3 3 3

1 1 1

2

3 2

1 2

1

414 414 30 30 31 2 30 6252 30 / 30 29

5.91172

i i imi mi n n n mi n

Var Rn n

Using the below hypothesis,

H0: The stock returns are independent.

H1: The stock returns are not independent. Then, we calculate the test statistics,

1/2

0.50,1

15 0.5 17.2 / 5.91172

0.69918

R E RZ N

Var R

If the R <= E(R), we add 0.5. If R>= E(R), we minus 0.5 Rejection region is Reject H0 if Z< - Z0.05 @ Z < -1.645 Decision : Do not reject H0 at =0.05 because -0.69918 > -1.645. Conclusion: The stock returns are random (independent)


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7.3.2 The Test for Semi-Strong and Strong Efficiency

To test for semi-strong form of efficiency, the adjustments to previously unknown news must be reasonably size and must be instantaneous. To test for this, consistent upward or downward adjustments after the initial change must be looked for. We can use event studies, determination of event date and calculation of abnormal returns (AR) and cumulative abnormal returns (CAR). To test strong form, there are tests which attempt to find out whether those who have access to insider information have managed to earn excess returns. Event studies can be used to study strong form degree of efficiency. However, the ability to prove that those economic agents have access to insider information is an important factor before empirical work can be carried out. Based on some studies on unit trust funds in the United Kingdom, it were concluded investment analysts are not able to have superior returns based on their private information. Hence, we can say that strong form hypothesis is valid with regards to private information.

IMPLICATION OF EMH TO INVESTMENT STRATEGIES

7.4

In order for a market to become efficient, investors must perceive that a market is inefficient and possible to beat. Ironically, investment strategies intended to take advantage of inefficiencies are actually the fuel that keeps the market efficient. A market has to be large and liquid. Information has to be widely available in terms of accessibility and cost, and released to investors at more or less he same time. Transaction costs have to be cheaper than the expected profits of an investment strategy. Investors must also have enough funds to take advantage of inefficiency until, according to the EMH, it disappears again. It is important for the investors to believe that there are always positive possibilities to outperform market. Sufficient conditions for capital market efficiency are:

(a) There are no transaction costs in trading securities;

(b) All available information is costless to all market participants; and

(c) All participants agree on the implications of current information for the stock price.


If these conditions are met, in such market, the current price of a security obviously fully reflects all available information. In reality, are these conditions really met in the stock market? In real practice to have costless information available to all participants is not what something we can observe. In addition, the not all participants may agree on the implications of current information for the stock price. Recall the example of oil and gas company previously in subtopic 7.1, not all participants in the stock market would agree that the stock price of this company must go up. Some participants may think the discovery of new oil fields may yield better gain to the company in the immediate future, but not instanteneous. Hence, not all investors may immediately invest in this stock upon knowing the news.

MARKET RATIONALITY 7.5

In the real world, the market cannot be absolutely efficient and totally inefficient. It is more likely to see that the markets are a mixture of both. Some of information is not able to be reflected immediately into the market. However, in the age of information technology (IT), more and more people have greater access to information via cable tv and internet, hence greater efficiency in terms of speed. However, there is a downside of this excess information. Some times, this information or news may not be true. Hence, IT can be said to cause less efficiency if the quality of the information is questionable, investors are hesitate to buy and sell stocks based on suspicious information.

7.5.1 Behavioural Finance and Market Anomalies

The first argument against EMH is behavioural finance. This field of study argues that people are not nearly as rational as stated by traditional finance theory. The idea of psychology drives stock market movement as evidenced by internet bubble and that subsequent dot come crash in the US. The second argument against the EMH is market anomalies. Figure 7.2 illustrates various market anomalies.


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Market Anomalies

January effect

Turn of the month effect

Monday effect

Figure 7.2: Market anomalies January effect states that stocks in general have high historically generated abnormally high returns during the month of January. Turn of the month effect states that stocks consistently show higher returns on the last day and first four days of the months. Monday effect shows that Monday tends to be the worst day to invest in the stock market. Both of these phenomenon (behavioural finance and market anomalies) pose a challenge to EMH.

There are three degrees of efficiencies:

(a) Strong form;

(b) Semi-strong; and

(c) Weak form.

1. Why there is Monday effect?

2. In Malaysia, we tend to have Chinese New Year effect? Search from the internet.

3. Do you think behavioural finance works against EMH?

SELF-CHECK 7.2


There are various empirical tests for different degrees of market efficiency. One of the empirical test is known as runs test of which is used to test weak form efficiency.

The impact of EMH to investment strategies and the need to have sufficient condition where EMH can operate;

In the real world scenario EMH may not operate smoothly if there is an absence of the sufficient conditions.

The challenges to EMH are :

behavioral finance - attempts to explain market irrationality as evidenced during the dot com bubble.

market anomalies such as Monday effect, January effect, etc.

Overall EMH explains the flow of information with respect to stock market investments.

Abnormal Returns (AR) Behavioral finance Cumulative Abnormal Returns (CAR) Degrees of efficiency Effficient Market Hypothesis (EMH) Event studies Fair value Information set January effect Ljung-box Q Test

Market anomalies

Market efficiency Monday effect

Runs test

Semi-strong form efficiency Strong form effficiency Turn of the month effect Von NeumannÊs ratio test Weak form efficiency

1. Why do think advanced financial markets like the US and Japan have

greater market efficiency? 2. Explain the expected return theory used in equation (6.1). 3. Explain what is strong efficiency from the perspective of EMH? 4. What is fair value?


124

5. What is ironical aspect of thinking that the market is inefficient in the first place?

6. Explain the differences between weak form and semi-strong form of

efficiency? 7. What are the sufficient conditions for capital market efficiency? 8. Discuss the existence of sufficient conditions in stock market?

1. What are the empirical tests for weak form of efficiency? 2. What are the empirical tests for semi-strong efficiency? 3. State the null and alternative hypothesis for testing weak form of efficiency. 4. What does behavioral finance argue? 5. What are sufficient conditions for capital market efficiency? 6. In reality, are sufficient conditions really met in the stock market? 7. „⁄.Hence, we can say that strong form hypothesis is valid with regards to

private information⁄.‰ Explain. 8. Name the various types of market anomalies. Explain each of them.

INTRODUCTION We have studied the basic portfolio theory and market models from Topic 1 to 7. In this topic, we would like to go one step further to study what is known as fundamental analysis and security selection. This topic is important because it touches on the practical aspect of how fund managers select or make their investment decision. Making investment decision is a complex process. It has to be looked from many angles before final decision is made. We will begin the topic by look into what is the meaning of fundamental analysis. We will relate this analysis with the process of investment decision, various types of analysis such as domestic and global economy analysis, business cycle analysis and industrial sector analysis. Subsequently we look into company analysis. Again, before we start this topic, we will like to introduce Mr Warren Buffet - the world greatest investor (Figure 8.1). He is one of the famous investors who has started the idea of value investing. He is certainly famous for his stock picking skills. Enjoy the reading!

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Fundamental Analysis and Security Selection

LEARNING OUTCOMES By the end of this topic, you should be able to:1. Discuss the meaning of fundamental analysis; 2. Analyse the economic environment of investment; 3. Evaluate the impact of business cycle to a company; 4. Conduct industry analysis; 5. Assess company based on principles of valuation; and 6. Value common stocks using dividend discount models and the

earnings model.

TOPIC 8 FUNDAMENTAL ANALYSIS AND SECURITY SELECTION

126

Investing Value - Business Profile Investing value profile of a famous businessman, investment guru or financial expert.

Warren Buffett - Considered to be one of the most successful stock market investors of all time, and one of the richest men in the world.

Warren BuffettÊs determination and creativity has made him the success story he is today. He is chairman of an investment company which has more than $2 billion in holdings and is also the 2nd richest man in the world.

Warren Edward Buffett was born in 1930 in Omaha, Nebraska. At an early age warren displayed an aptitude for money and business along with an amazing ability to calculate numbers off the top of his head. He was an enthusiastic paper boy for the Washington Post, often covering more than one paper route at the same time. WarrenÊs interest in money and finance started showing early, and by the age of 11 he was playing the stock market.

Warren purchased three shares of Cities Service at $38 a share for himself and his older sister. Although the stock fell to just over $27 he held his shares until they rebounded to $40, unfortunately selling them before they climbed to $200. The experience taught him one of the basic lessons of investing: patience is a virtue.

In 1947 at the age of 17 he graduated from High School and while he never intended to go to college his father urged him to attend the Wharton Business School. Buffett lasted two years, claiming he knew more than his professors. Warren moved back home and transferred to the University of Nebraska. Even while working full-time, he graduated in only three years with a Bachelor of Science degree, and went on to be rejected by Harvard Business School because he was to young. He completed a masterÊs in economics at Columbia University where he meet Ben Graham a lecturer and famed investor. Warren worked for his father who owed an investment banking company for the next three years during which he meet Susie Thompson and in 1952 they were married and had three children together. Warren didnÊt have a lot of money at this point until he was asked by Ben Graham to join his company as a security analyst, which he did and by 1956 his fortune rose to $140,000.

In 1956 at the age of twenty five, Warren started his own investment company, the Buffett Partnership, using a small amount of his own funds and collecting around $100,000 from partners and family he managed to increase his capital to $300,000 by the years end. One of the companies Warren invested in during his role as managing partner of the Buffett Partnership was a textile company called Berkshire Hathaway.


127

Berkshire Hathaway was eventually liquidated but the name was kept and turned into an investment business. Its main interest was with insurance, which added considerable cash flow for future investments. He liquidated the Buffett partnership in 1969, and spent the remainder of the year liquidating its portfolio.

Warren became chairman of the board and chief executive officer for Berkshire Hathaway in which he remains today. Berkshire Hathaway now owns more than forty companies employing more than 150,000 people.

In 1977 Warren and Susan separated but never divorced, She was also a significant stockholder in Berkshire Hathaway and a board member as well. Susan Buffett died in 2004, and Warren now lives with companion Astrid Menks whom he meets through his wife.

Warren Buffett is also a generous and charitable philanthropist, having started the Buffett Foundation which he donates more than $12 million a year to. On his death he plans to disburse 99% of his wealth to good causes through the Buffett foundation.

In 2005, Forbes magazine estimated Warren Buffett's wealth to be $44 billion.

Copyright © InvestingValue.com - This Warren Buffett Biography may not be redistributed or reproduced online in part or in its entirety.

Warren Buffett News from the Investing Blog.

Berkshire Hathaway Inc. And Warren Buffett - Berkshire Hathaway Inc. has posted a forth quarter profit, level with last years profit even though the company showed profit increases almost across the board.

Warren Buffet stock screen - Warren Buffet is one of the world's best investors, so logically it would make sense to use his investment techniques while investing in stocks.

Figure 8.1: Warrent Buffet profile

Source: http://www.investingvalue.com/investment leaders/warren-buffett/index.htm

FUNDAMENTAL ANALYSIS

We start this topic by looking into fundamental analysis. Before we look into any investment process, we must first examine the economic environment, then the industrial sector we want to invest, and finally the company of which the stock we want to invest into. As shown in Figure 8.2, the sequence of looking at the

8.1


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economy first, then industrial sector and finally company is known as top-down approach. In a snapshot, we can see that a company operates inside an industry, and the industry operates in an economy. Hence, if the economy is in its upswing in business cycle, then there is likelihood that company will have growth in sales volume, translating into higher profit figure. Hence, it is important for any investor to monitor the macroeconomic environment. The process of looking into these three levels of analysis i.e. economy, industrial and company is known as fundamental analysis. We start this topic by looking into fundamental analysis. In Figure 8.2, in a snapshot, we can see that a company operates inside an industry, and the industry operates in an economy. Hence, if the economy is in its upswing in business cycle, then there is likelihood that company will have growth in sales volume, translating into higher profit figure. Hence, it is important for any investor to monitor the macroeconomic environment.

Figure 8.2: Fundamental analysis However, there is another aspect of looking at Figure 8.2, we can start by looking at potential companies we want to invest, then the industry, and finally the economy. This is known bottom-up approach. This approach is more suitable if there are profitable companies with good prospect to invest in. This company can be the market leader in its own right, either through high product differentiation or low cost strategy.

8.1.1 The Top-down Approach to Analysis

One of the common practice by analysts is what we can call a „top-down‰ approach. The top-down approach is typically used not just because it is common


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practice. Empirical evidence indicates that the economic environment has significant effects on firm earnings. The unemployment rate, production level, factory usage and other economic indicators have correlations with aggregate stock prices. A top-down approach implies that security analysts must focus their attention on the overall macroeconomic environments and be aware when the monetary authorities change monetary policy by increasing or decreasing the target interest rate. For instance, security analysts should make a prediction when Alan Greenspan, the Chairman of Federal Reserve in the US, will increase or decrease the Federal funds rate. Such changes in the Federal funds rate have a direct impact on the global stock markets. The next level of analysis is related to the impacts of increases or decreases in the interest rate on the banking industry in Malaysia. This, as you have learned, is known as industry analysis. The final step in the analysis is to determine which bank will be affected most by the changes in monetary policy in the US. This is the company analysis stage in the context of top-down approach analysis. The following figure depicts this simple process:

Macroeconomic Analysis

Industry Analysis

Company Analysis

Figure 8.3: Analysis conducted using the top-down approach The top-down approach finally comes down to picking the right, i.e. most valuable, stock. This involves the valuation of a company. In addition to the model we are going to introduce, of course there are many other models based on free cash flow, operating cash flow, price/cash, price/sales, etc. You will learn some of the details in the next reading. We start by considering the dividend discount model and then the earning models.


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ECONOMIC ANALYSIS There are three aspects we are going to talk about in this section. Firstly, we will discuss components of Aggregate Expenditure. Secondly, we look into the key economic variables and economic indicators. Lastly, we will put all the above in business cycle analysis. We will apply the concept of business cycle analysis again in industrial analysis in subtopic 8.3.

8.2.1 Aggregate Expenditure

The key idea behind of economic analysis is aggregate expenditure (AE).

In simple terms,

AE = C + I + G + X - M where net exports are exports minus imports. Hence, by looking at the above equation, we have to understand the performance of an economy depends on the performance of the four components. Key questions we ask about an economy are:

Are the consumers spending?

If they are not spending, what the possible reasons?

Are the firms making new investment in plant and machinery?

8.2

1. Look through the business section in a local newspaper, look for any economic news that may have impact on your investment?

2. What do you think about the business sentiment in Malaysia?

Is the economy in its upswing along the business cycle?

ACTIVITY 8.1

(Aggregate Expenditure) = Consumption + Investment + Government + Net Exports Purchases


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Is the government putting monies into new projects?

Is the export growing as compared to last quarter?

When we look at individual consumption, we must understand what triggers consumers to spend money. Suffice to look at the theory of demand to understand the reasons for consumption. The conditions of demand for a product in a market can be summarised as follows:

ConsumerÊs demand is a function of price of the good itself (Pn), prices of other goods (Pn⁄Pn-1), consumerÊs income (Y), taste or preferences (T), age-structure of the population (P), expectation of consumer of future prices of goods (E). For each component of the above function, we can analyse whether consumers will be spending, and hence whether companies will be able to have good sales. First of all, in simple economics, consumer follows the law of demand. If prices of goods fall, demand will increase. Conversely, if prices of goods rise, demand for goods will contract, with other factors remain constant or ceteris paribus. Looking at the age-structure pattern of a population, for example, if the population is made up of young people, then probably the sales of electronic goods, mobile phones or IT products will be good. Another example, if the population is made up of aging people, then the demand for welfare services and health related products will be good. Another important aspect from the above equation is the expectation of future prices of goods. In an environment where there will higher tax for certain goods, consumer will purchase in advance. Another example is the inflation rate, if consumers expect the future prices will increase as the result of inflation, consumer are more likely to make the purchase right now instead of buying the future periods. Likewise, companies will make new investment in plant and machinery if there is future anticipation that people will increase their demand for the new product, for example, new mobile phone. Looking at the new products in the current market such as plasma television, iPod phones, digital cameras, organic foods and environmental friendly building materials, these are some of products that will continue to be in demand in the near future.

D = f (Pn, Pn⁄Pn-1, Y, T, P, E)


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8.2.2 Key Economic Variables and Economic Indicators

We look into key economic variables that are important to the economy. One of the important macroeconomic variables is growth domestic product (GDP). Gross domestic product (GDP) measures the value of output produced within the domestic boundaries of the Malaysia over a given time period. An important point is that our GDP includes the output of foreign owned businesses that are located in Malaysia following foreign direct investment in the Malaysian economy. Another key economic variable is consumer price index (CPI). The Consumer price index (CPI) is a weighted price index which measures the monthly change in the prices of goods and services. The spending patterns on which the index is weighted are revised each year, mainly using information from the Family Expenditure Survey. The expenditure of some of the higher income households, and of pensioner households mainly dependent on state pensions, is excluded. As spending patterns change over time, the weightings used in calculating the CPI are altered. From the concept of CPI, we can measure the inflaction. The definition of inflation is as follows: „⁄.Inflation is best defined as a sustained increase in the general price level leading to a fall in the value of money⁄‰ Inflation is a key variable for macroeconomics management of the Central Bank. By looking at the inflation rate, Central Bank will decide whether to increase or decrease the overnight policy rate (OPR) that will alter the level of economic activities. There are many key variables in the economy. As stated in Table 8.1, there are a number of macroeconomic variables that are categorised into three indices, namely the leading economic index (LEI), coincident economic index (CEI) and lagging economic index (LGEI). As shown in Table 8.1, coincident, leading and lagging indices have six, eight and five components respectively. These economic indicators are jointly developed by the Department of Statistics, Malaysia and Center for International Business Cycle Research (CIBCR) at Columbia University. Coincident indicators inform users on the current state of the economy.


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Table 8.1: The Components of Economic Indicators in Malaysia Leading-Coincident and Lagging Economic Indices

Coincident Index Components

1 Index of Industrial Production2 Real Gross Imports3 Real Salaries and Wages, Manufacturing4 Total Employment, Manufacturing5 Real Sales, Manufacturing6 Real Conributions, EPF

Leading Index Components1 Real Money Supply, M12 KLSE Industrial Index3 Real Total Traded: Eight Major Trading Partners4 CPI for Services, Growth Rate (Inverted)5 Industrial Material Price Index, Growth Rate6 Ratio of Price to Unit Labour Cost, Manufacturing7 Number of Housing Permits Approved8 Number of New Companies Registered

Lagging Index Components1 7-day Call Money, Rate2 Real Excess Lending to Private Sector3 Number of Investment Projects Approved4 Number of Defaulters, EPF (Inverted)5 Number of New Vehicles Registered

Leading indicators inform users on where the economy is heading, particularly for the forecasted period of months ahead. Among the earlier signs that an ongoing expansion may start to decelerate is a sustained decline in the leading growth rate. In contrast, lagging indicators inform users what had happened to the economy, especially on performance of cyclical movements of the leading and coincident indicators.

8.2.3 Business Cycles

The economic environment is subject to fluctuation as shown in Figure 8.2. Using the leading, coincident and lagging economic indices we have discussed earlier together with the value and growth style indices from Morgan Stanley Capital International (MSCI), we can see that the graphs fluctuate from one end to


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another throughout the period from May 1997 to May 2003. We will relate the graphs with the concept of business cycles.

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Figure 8.2: The graphs of MSCI style benchmark and economic indicators Source: www.mscibarra.com

Generally, there is a concept known that business cycles (sometimes known as trade cycles) where the rate of growth of production, incomes and spending fluctuates over a period of time. As the structure of an economy evolves, the length and volatility of each of these cycles tends to change over time. There are different stages of business cycles.


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Figure 8.3: Business cycle Source: www.culturaleconomics.atfreeweb.com/111%20114.

As shown in Figure 8.3, in the passage across time, there different phases such as economic boom (peak), slow down, recession and recovery. Economic Boom occurs when real GDP grows much faster than the trend growth rate. In a boom phase, aggregate demand (AD) is high and typically, businesses respond by increasing production and employment. The main characteristics of a boom are as follows: high aggregate demand, a tightening of the labour market, high demand for imports and a wider trade deficit, strong company profits and investment, a risk of a pick-up in inflation. In addition, companies many increase prices and this can cause cost-push and demand-pull inflation. Then there is economic slowdown. A slowdown occurs when real GDP continues to expand but at a reduced pace. If a country can achieve growth without falling into a recession, this is termed a „soft-landing.‰ Whereas a full recession is coined a „hard-landing.‰ Next, there is economic recession. A recession means an actual fall in real national output and a contraction in employment, incomes and profits. In technical terms a recession is a period of two quarters (i.e. six months) when real GDP declines. During economic recession, government can use fiscal policy like having surplus budget to activate the level of economic activities. The government can also lowers interest rates, increasing consumption and investment. This is monetary policy. By lowering the interest rates, the level of cash in the economy will be increasing, as people will probably like to spend than save as the interest rate is low.


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Next, as time passes by, the general economy is likely to become active again. One of the reasons is that as more and more stocks of goods are being consumed, people will start to demand for new goods and services. Hence, the production of goods will become active again. Once the economy is in recovery phase, people start to consume more goods, firms are keen to invest in plants and machinery, government makes new purchases and the economy is once again moving toward economic boom. In addition to the above, economy is also bound to external shocks or crisis. As stated in Table 8.2, there are many events that are responsible for the economic shocks along the business cycle. They are the Asian financial crisis in 1997-98. It was a crisis that started with the float of Thai currency the Baht which eventually triggered shock wave to countries like Malaysia, Indonesia, South Korea and other Asian countries. There is also dot-com bubble in the end of 2000, which the stocks of many ICT companies lost substantial of their market price. On the other hand, the 911 event in the US brought many repercussions to international travel. Many airlines suffered losses as people were not willing to travel. There was also SARS epidemic that was related to air-borne viruses. Again, people were unwilling to travel due to the outbreak of this epidemic.

Table 8.2: Economic Events that affect the Business Cycle

Period Event

1997-98 Asian financial crisis

2000 Dot-com bubble

2001 911 event

2002 SARS epidemic

INDUSTRY ANALYSIS Industry analysis is the study of industry groupings, which is conducted by examining the competitive position of a particular industry in relation to others, and by identifying firms within an industry that hold particular promise. For instance, during the period of the „hi-tech bubble‰ from the early part of 1999 to mid-2000, hi-tech industry stocks were considered the best investments, and yielded very high returns. However, after the „hi-tech bubble‰ burst in mid-2000, hi-tech industry stocks were considered to be the worst investments.

8.3


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The following reading from your text provides a very good introduction to industry analysis. Generally speaking, investors can obtain valuable insights about an industry by looking for the answers to the following questions:

(a) What economic factors are particularly essential to the industry? Is demand for the industryÊs goods and services related to key economic variables and, if so, what are the prospects for these variables? How important is foreign competition to the health of the industry?

(b) How important are technological advancements? Are there any taking place, and what is the likely impact of a potential breakthrough?

(c) What is the nature of the industry? Is it characterised by monopolistic competition or are there many competitors in the industry?

(d) What are the important financial and operating considerations? Is there an adequate supply of labour, capital, and raw materials? And what are the capital spending plans and the needs of the industry?

(e) What are the governmentÊs policies towards the industry? To what extent is the industry regulated? Is it regulated like public utilities are and, if so, how „friendly‰ are the regulating bodies?

The above five questions can be answered in terms of an industryÊs growth cycle. Generally speaking, there are four stages for the development of a particular industry:

Stage 1: The initial stage of the industry. Investors are not familiar with the new industry. The industry is new and untried so the risk in investing in this new industry is very high, especially the financial leverage risk.

Stage 2: The rapid expansion of the industry. During this stage, product acceptance is spreading and investors can foresee the industryÊs future more clearly. Economic variables have little to do with the industryÊs overall performance during this stage. As a result, investors will be interested in investing almost regardless of the economic condition.

Stage 3: The mature stage. During this stage, most industries do not experience rapid growth for a long period. Most eventually slip into the category of mature growth. However, during this stage, investors must take into account the economic situation.

Stage 4: This is the last stage of the industry. The industry is either stable or in decline. During this stage, the demand for the industryÊs products is diminishing, and firms are leaving the industry since profits are


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shrinking in the decline phase. Furthermore, the investment opportunities are almost nonexistent, so investors seek only dividend income. In reality, few companies reach this stage because they try to introduce product changes and to develop other product lines that will help to continue mature growth. Avoiding this stage is obviously a concern for most investors.

COMPANY ANALYSIS Company analysis is mainly concerned with a firmÊs financial position and potential earning power. Many empirical studies have shown that a companyÊs share price is highly related to the changes in that companyÊs financial position and earnings. To understand what financial statements have to say about a companyÊs financial condition and operating results, it is often necessary to turn to financial ratios. Financial ratio analysis is the study of the relationships among and between various financial statement accounts. Each measure relates to one item on the balance sheet or income statement. All the financial ratios that are mentioned in the above reading are considered to be important elements in determining a companyÊs equity value. The following cross-sectional single index regression model that you learned about in Topic 6 can be used to relate the equity value of a company and any of the financial ratios stated in the above reading.

i i ir a b FR e where:

ri is the return on ith companyÊs equity, i = 1, 2, ⁄.., n (n companies)

is the intercept of the regression

is the slope of the regression and is also known as the sensitive measure to the companyÊs equity

FRi is the ith companyÊs financial ratio, i = 1,2, ⁄⁄, n (n companies)

8.4

Use the biotech industry as an example to answer the above five questions that relate to the growth cycle of an industry.

ACTIVITY 8.2


139

i is the random error disturbance term with zero mean and constant variance i.e., i ~ N(0, 2).

To be more specific, supposing the price-to-earnings (P/E) is the most important ratio that determines the equity value of a firm, the cross-sectional regression can be written as follows:

i iir a b P/E e

We will discuss the relationship between equity value and the (P/E) ratio in greater detail in the following section. Once you understand ratio analysis, you can go through the following example of financial statement analysis in your textbook. This example shows you how to perform financial statement and ratio analyses in a practical fashion.

VALUATION OF COMMON STOCKS USING DIVIDEND DISCOUNT MODELS

In this form of valuation process, the intrinsic value of any investment is equal to the present value of the expected cash flow benefits. In the case of common stock, this converts to the cash dividends each year, plus the future sale price of the stock. Another way to view the cash flow benefits from common stock is to assume that the dividends will be received over an infinite time horizon - an assumption that is appropriate so long as the firm is considered a „going concern.‰ The basic idea is that the value of common stock is simply the discounted value of all the cash flows associated with the common stock. In general, the following formula seems reasonable for making this calculation:

1t

tt0 )k1/(DV

8.5

Why is the price-earnings (P/E) ratio considered to be one of the most important financial ratios that indicate the value of a stock?

SELF-CHECK 8.1


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where:

V0 is the value of a common stock at time t=0

Dt is the estimated dividend to be paid by the common stock at time t

k is the „appropriate‰ disscount rate; k is also known as the required rate of return from the CAPM.

The formula stated above cannot really be used in practice, however, since it is unfeasible to estimate dividends for the infinite future! To make the formula useful, we need to make some assumptions about the growth rate of the dividends. For simplicityÊs sake, we assume that dividends are paid annually, so D0 is the last yearÊs dividends (i.e., paid yesterday) and D1 is the amount of dividends to be paid in one year, and so on.

8.5.1 The Zero Growth Model

In this case, dividends are assumed to remain unchanged forever. Thus, the cash flows paid by the common stock constitute a perpetuity, and we have the following formula:

0 1V D /k Solving the above formula for k*, i.e., the implied discount rate, and using P0 (i.e., the price of common stock at t = 0) to replace V0, we obtain:

0 1 1 0P D /k * and k * D /P

8.5.2 The Constant Growth Model

The constant growth model assumes that dividends grow at a fixed rate, which is denoted by g, forever. In this case, the formula for the value of a common stock is the following:

What kind of stock has a dividend growth rate equal to zero?

ACTIVITY 8.3


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0 1V D / k g and k g

Solving the above formula for k*, the implied discount ra te, and using P0 to replace V0, we obtain:

)gk/(DP 10 and g

PD

k0

1*

Intuitively, the implied discount rate (k*) is the sum of dividend yield (D1/P0), and the dividend growth rate or capital gain yield (g).

8.5.3 The Variable Growth Model

In the case of the constant growth model, we simply assumed that the dividend grows in a constant fashion. This assumption is rather naive, as in reality a dividend can be expected to grow in a non-constant matter over time. In particular, according to the industry growth cycle hypothesis that we mentioned previously, a company is likely to expand during the second stage of its industry life cycle. If this is true, then the dividend may grow in accordance with the firmÊs expansion. Figure 8.4 displays a two-stage dividend growth model for a particular firm. In the first stage, the dividend grows at a rate of 5% over the first five years, and it grows at 9% forever thereafter.

SELF-CHECK 8.2

Suppose the expected annual return on the S&P500 (the market portfolio) is 8%, and the annual risk-free rate is 3.5%. The beta value of IBM (IBM) is 1.2. IBMÊs dividends per share in 2006 were as follows: first quarter US$0.50, second quarter US$0.45, third quarter US$0.55, and fourth quarter US$0.60. Assuming a dividend growth rate of 5%, estimate the value of IBMÊs stock in January 2008.


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Figure 8.4: A two-stage dividend growth model The multi-stage growth model assumes that before time T the dividend growth rates can be changing from year to year in the way you find most appropriate. Then, dividends grow at a constant rate g, i.e., dividends grow at g from T to T + 1, T + 1 to T + 2, and so on. Figure 8.5 shows a multi-stage dividend growth model. In the first stage, the dividend growth rate is 5%, it grows at a rate of 9% in the second stage, and the dividend grows at a rate of 7% forever thereafter.

Figure 8.5: A multi-stage dividend growth model


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In the multi-stage dividend growth model, the formula for valuing a stock is:

)gk()k1(D

)k1(D

VT

1TT

1tt

t0

The above formula indicates that when T = 0, we have the constant growth model.

TAX EXEMPTIONS ON REAL PROPERTY GAINS TAX

The previous discussion was based on a model which states that a share of stock is worth the present value of future dividends expected to be paid on the share. This makes perfect sense. The only way a share of stock can improve the investorÊs ability to consume is for it to pay dividends. A stock is bought for the future consumption opportunities it provides. And this comes only from the dividends it provides. Without the potential for future dividends, a stock is worth nothing. In other valuation models, such as the earnings valuation model, dividends are not explicitly part of the equation. In theory, underlying any ongoing stream of dividends are the earnings of the firm. These earnings belong to the equity shareholders. However, a firm will retain a portion of earnings (not pay them out as dividends) to make additional investments, and it can be argued these earnings should also be valued. To do so, we can use the concept of earnings per share (EPS) to value stock. By definition EPS is total earnings divided by total number of shares outstanding. It is perfectly all right to value the EPS of stock as long as the reinvestment of earnings is also valued. The worth of a share of common stock is equal to the present value of all future expected earnings per share less the present value of all future investments per share. The general earnings valuation model can be expressed as follows:

N

1tt

tN

1tt

t0

)k1(IPS

)k1(EPS

P

and

N

1tt

tt0

)k1(IPSEPS

P

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where:

EPSt = the expected earnings per share in year t

IPSt = the expected investment per share in year t

This equation values the expected future earnings per share stream, which legally belongs to the common stock shareholders. But it also values expected future investments made by the shareholders in order to generate the EPS stream.

8.6.1 The Constant Growth Earnings Valuation Model

The general earnings valuation model introduced in the preceding section can be simplified considerably if future growth is expected to be constant. Again, using g as the expected constant growth rate, the constant growth earnings valuation model can be written as follows:

gkIPSEPS

P tt0

The earnings valuation model is the equivalent of the dividend valuation model. The dividend model relies upon net cash flows received by the investors in the form of dividends. However, the earnings model explicitly takes into consideration both legal ownership of earnings per share and the incremental future reinvestment of earnings.

VALUATION OF COMMON STOCKS USING PRICE/EARNINGS RATIO

The price-earnings (P/E) ratio simply measures the market price of a share of stock divided by earnings per share in that year.

shareper EarningspriceMarket

ratio P/E

The P/E ratio indicates the dollar price being paid for each dollar of a firmÊs earnings. P/E ratios are widely used by practitioners as a measure of the relative prices of different stocks. The stockÊs current market price is easy to determine, since it is reported in the financial press. Earnings per share (EPS), however, are more difficult to determine. The easiest way of determining earnings figures is to use the latest EPS shown on the firmÊs financial statements. In this topic, I will first discuss the valuation of stocks using the P/E ratio and then show you how professional analysts use the P/E ratio.

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Conceptually, the P/E ratio is determined by three factors:

(a) InvestorsÊ required returns

(b) Expected returns on equity

(c) Expected earnings retention rate

The easiest way to demonstrate this is to use the constant dividend growth model that you learned in the previous section:

gkD

P 10

Defining E1 as next yearÊs expected earnings per share, and using the fact that g = (ROE x B) where ROE is the return on equity and B is the retention ratio, the constant growth price model can be rearranged into a P/E ratio model as follows:

)BROE(k)B1(E

P 10

The determinants of the P/E ratio are as follows:

)BROE(kB1

)BROE(kE/)B1(E

E/P 1110

The above equation states that if dividends are expected to grow at a constant growth rate, the P/E ratio is theoretically equal to the stockÊs expected dividend payout ratio (1 B) divided by the difference between the required return and the expected growth rate g = (ROE x B).

8.7.1 How Practitioners Use the P/E Ratio

The P/E ratio provides information on stock capitalisation. A high ratio may be an indication that investors expect high earnings in the future, while a low ratio could indicate that investors do not expect high earnings in the future. The ratio is of primary interest to practitioners and investors because it may provide indications of future changes. A firm can also use the ratio as an estimate for its cost of raising capital through equity (i.e., a low P/E ratio makes the cost higher). The P/E ratio also serves as an index of risk: the higher the P/E ratio, the higher the risk for that particular stock. In 2000, during the Internet bubble, some Internet companies listed on the GEM board had a P/E ratio of over 500! You can definitely see how high the risk of such Internet companiesÊ stock was at that time.


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In this topic we have discussed the concept of fundamental analysis where

we can employ either top-down approach or bottom-up approach. It is important the economic environment of a given economy is screened for any potential threats or shocks.

Companies that thrive in an upswing economy will perform better compared to an economy which is heading towards recession. Subsequently, we should look into the type of industries before we make the investment decision.

Obviously each industry has different characteristics and nature. For instance, due to the increase of the price of crude oil to USD147, the palm-oil industry in general has also benefited with increase CPO price to around USD3000 per tonne.

In this instance, we can observe that there is a concept called productÊs life cycle or growth cycle. We can apply this concept to a new car model, for instance. When a new model such as SUV is introduced, the demand for this new model will increase, and hence it is a growth stage.

Eventually more and more companies are producing this type of model, and the market of the product will mature, and finally decline as new generation of consumers prefer other type of car model.

In economic analysis, besides the microeconomics issue of supply and demand, there exists wider scope of analysis such as business cycle. In this instance, analysts can rely on economic indicators such as CPI and GDP to gauge the market sentiment and future direction of the economy.

In similar development, the three indices published by the department of statistics i.e. Leading economic index (LEI), Coincident economic index (CEI) and Lagging economic index (LGEI) can be used to study the direction of the economy.

In company analysis, we have discussed dividend discount model (DDM). Stock price is determined or valued based on the present value of its future dividends.

Hence, a stock that can provide streams of future cash inflow from future profitable projects will have higher price than other stock assuming similar market capitalisation and risk.

From the projected dividends, we can value the stock using different models such as the dividend discount model (DDM), the Gordon growth model or multi-stage dividend discount model. Subsequently, we have also discussed the valuation of common stocks using earnings model, the usage of P/E ratio and how it can used to check whether a stock is overvalued.


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Bottom-up approach Business cycle Coincident Economic Index (CEI) Company analysis Consumer Price Index(CPI) Crisis Dividend Discount Model (DDM) Earning model Economic analysis Economic boom Economic environment Economic indicators External shocks Fundamental analysis

Gordon growth model

Growth rate Hard-landing Industry analysis IndustryÊs (product) growth cycle IndustryÊs (product) life cycle stages Lagging Economic Index (LGEI) Trend Leading Economic Index (LEI) Multi-stage dividend discount model. P/E ratio Soft-landing Top-down approach. Valuation

1. Discuss the relevance of conducting fundamental analysis in the context of portfolio investment management.

2. Do you think that top-down approach is more suitable than bottom-up

approach? 3. What are the usefulness of economic indicator such as consumer price

index (CPI) from the perspective of asset allocation? 4. One of important roles of economic analysis is to forecast demand of

product. Using an example of product like buidling material, discuss how it relates to fundamental analysis.

5. Describe the four stages of an industryÊs growth cycle. 6. People often misunderstood how share price is determined. With the

knowledge you have learnt from this subject, discuss how do we conduct valuation on a stock.

7. Discuss what is a dividend discount model (DDM).


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8. How is the Gordon Growth Model different from dividend discount model (DDM)?

1. ABCÊs company preferred stock RM100, 8% is selling at RM85. What is

ABCÊs cost of preferred equity? 2. Using the Gordon growth model which assumes that dividends grow at a

constant rate rate forever, what is the value of a stock that pay a dividend of RM1 per share next year, if the expected growth rate of dividends is 6% and the shareholder require a return of 16% from their investment?

3. In another scenario, using the Gordon growth model, what is the value of a

stock that paid a dividend of RM1per share last year, if the shareholder require a return of 16% from their investment and if the expected growth rate of dividends is 6%?

4. Discuss the weakness of Gordon growth model? How this weakness can be

overcome? 5. ABCÊs stock which is priced at RM30 will pay an annual dividend of

RM3.00 next year. If the market analyst believe the stock will have a sustainable growth rate of 11 percent. What is the market discount rate for this stock?

6. ABCÊs stock earnings per share has decreased from RM7 to RM5, its

dividends per share has also decreased from RM2 to RM1.50, and its share price decreased from RM70 to RM60. Given the above information, comment what has happened on the P/E ratio of ABC stock?

7. ABC Berhad is expected to pay RM1.40 dividend in next year. The

dividends are expected tp grow at 8% per year. It has a beta of 0.9. Given the existing risk-free rate of return is at 6% and the expected market return is at 11%. Calculate the value of the stock?

8. ABC Berhad has equity capitalisation of RM450,000 and debt capitialisation

of RM225,000. The company distributed RM35,000 out of its reported earnings of RM75,000 to shareholders. If the company pays taxes at 40%, what is ABCÊs sustainable growth rate?

INTRODUCTION We have gone through many important concepts on fundamental analysis, and in this topic, we are going to look into investment strategies on managing portfolios. We will introduce active portfolio management, and later passive portfolio management. The central theme of this topic is to teach you how to use strategies for equity portfolios and fixed income portfolios. Active portfolio management techniques are extensively used in the fund management industry (Figure 9.1). At the beginning of the topic, you will learn the differences in nature and characteristics between institutional investors and individual investors. The objectives of active portfolio management will then be discussed. The process of investment management from the perspective of both institutional investors as well as individuals will be discussed in detail. We will continue our discussion on passive portfolio management, with details on „passive strategies‰ that can be used.

TTooppiicc

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Managing Portfolios – Active and Passive Strategies


1. Distinguish individual and institutional investors;

2. Explain how to construct a portfolio;

3. Formulate active management strategies for equity and bond portfolios; and

4. Apply passive strategies in equity portfolio management.

TOPIC 9 MANAGING PORTFOLIOS – ACTIVE AND PASSIVE STRATEGIES

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Figure 9.1: Website of An Asset Management Company Source: http://www.evansonasset.com/index.cfm/Page/2.htm

INDIVIDUAL INVESTORS

You and I are individual investors. We have quite a number of „small‰ individual investors trading medium to small size stocks every day. What is your trading objective? „Of course to make money,‰ you may answer. But you can be more specific by saying that you want a 10% annual return or a guaranteed 4% annually for five years. To put it simply, your investment decision can be based on your expected return and risk preference. In Topic 2, we learned about utility theory and risk. You can make your investment according to your risk preference. We are not going to repeat the concept here. However, you may wonder how many individual investors are really acting so rationally and investing in order to maximise their utility. This is a true story for some individual and young investors. They trade on the Internet, and their investment decisions rely on very short-term historical information of prices. Do they have an investment strategy? ItÊs hard to say, but you can see that it is hard to explain the behaviour of individuals in order to understand their objectives. You may say that they want to earn as much as possible and therefore they trade frequently. I have no objection to your statement. However, there are constraints.

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Their limited capital is their major constraint. Another constraint is insufficient information. With the advent of the Internet, individual investors are better informed. However, they are still less informed than institutional investors. Other people more easily influence individual investors, and we can call this herd behaviour. Recall, for example, the IT bubbles a few years ago, when investors were crazy for Dot Com. Stocks. It seemed everyone was making some money from buying high tech stocks, so you felt like a fool if you missed it.

INSTITUTIONAL INVESTORS

What are institutional investors? You may think of some big firms or banks with lots of money. You would be right. How do these big firms differ from individual investors? One of the major differences between institutional and individual investors is that the former manage large amounts of funds. Individual investors have more flexibility in terms of the type of investment they can invest in because the investment policies of institutional investors are often restricted by laws, regulations and rules. Institutional investors include pension funds, mutual funds, insurance funds and banks. The constraints, objectives and investment policies depend on the type of investor, and we will learn about all the aspects in detail in this section.

9.2.1 Pension Funds

Pension funds are funds for retirement planning. The funds receive contributions from individuals, firms and their employees. Two major types are defined benefit and defined contribution. Defined benefit pension plans promise to pay retirees a specific income stream after retirement. The company contributes a certain amount to the fund each year and the company also takes up the risk of paying the future pension to the retirees. Any shortfall (due to poor performance of the fund) should be compensated for in the future. The plan can take a conservative approach or a more aggressive approach, but the return objective is to meet the planÊs actuarial rate as set by actuaries. The actuarial rate of return depends on the firmÊs benefit formula, retirement pattern, worker age, current and future salaries, etc. These factors are all constraints on the plan. The details of calculations are left for professional actuaries. On the other hand, defined contribution pension plans make no promise on return. The benefits depend on the employeeÊs contribution and the return on investment. The contribution plans are tax-exempted. The objectives and constraints for the plan depend on individuals.

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Which kind of plan would you want? It depends on whether you are the boss of a firm or an employee. For the defined contribution plan, the firm has no obligation and risks are borne by the employee. Do you want to contribute to your pension? I cannot answer for you as you may have different views on the risks involved and on the expected returns. You might choose a guaranteed fund while I might choose a balanced fund. Your returns may be better than mine due to the recent poor performance of the stock markets around the world. How about the returns when you and I retire? I might end up getting much more than you. Who knows?

9.2.2 Insurance Firms

I am sure you have directly or indirectly paid into some kind of insurance plan. You might have paid for life or medical insurance. Your employer might have paid for injury/accident insurance for you. We can classify insurance firms into two categories in terms of investment objectives and constraints: life insurance firms or non-life insurance firms. For life insurance firms, cash outflows are generally more predictable based on mortality rate. These firms receive premiums during the lifetime of an insured person until a death benefit is claimed. The basic investment policy is to earn a spread, like banks, which borrow at a lower interest rate (imagine what interest rate banks pay to your deposit account) and lend out at a higher interest rate. A positive spread means a surplus of reserve. The risk categories insurance firms can invest in are limited. If an insurance firm invests too much in high-risk categories of stocks or bonds, an extra fund must be set aside to protect policyholders. For non-life insurance firms, the cash flow is not predictable due to the non-predictability of claims from accidents, lawsuits, disaster, etc. Casualty insurance firms put their insurance reserve in bonds for safety purposes and for provision of a source of income for claims. The capital and surplus funds are invested in equities for growth. Liquidity needs also constrain insurance firmsÊ investment policies. A life insurance policy requires a long-term investment. Owing to the non-predictability of the claim pattern of non-life insurance firms, their investment time horizons are shorter. Tax may be a concern for return as insurance firms pay income and capital gains taxes at the corporate rate.


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9.2.3 Mutual Funds

You may recall that mutual funds are pools of money from different investors. Each mutual fund has its own objective like high growth, high income, capital appreciation, etc. Investors should understand the objectives of a mutual fund before they choose one. Although there are rules and regulations restricting the investment a fund can make, fund managers can choose the investments within restrictions. This means that although you are free to choose, for example, an equity fund, you are not free to choose which particular equities the fund itself actually invests in.

9.2.4 Banks

Many of you have likely worked in banks or know a lot about them. You know that there are banking ordinances governing the operations and requirements of a bank. You can go to <http://www.bnm.gov.my> to look at the banking policy and supervision. Although it contains lots of details, you might start with the Three-Tier Banking System to understand the basics. A bank must attract investors in order to have funds to lend. It is obvious that banks have to generate returns in excess of their costs in order to be successful. In other words, a spread must be earned from lending out. If you were the banks, think about how you could achieve these goals.

OBJECTIVES OF ACTIVE PORTFOLIO MANAGEMENT

Having understood the concept of individual and institutional investors, you will proceed to portfolio construction. There are two styles of constructing a portfolio, namely active portfolio management and passive portfolio management. Active portfolio management involves buying and selling portfolios with the objective of earning positive abnormal profit. An active management investment style attempts to engage in:

(a) Selectivity, that is, identifying securities or portfolios that are winners (and losers); and/or

(b) Timing, that is, identifying when weights in asset classes (stocks, bonds, cash, real estate, gold, foreign stocks, foreign bonds and foreign currencies) should be changed.

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Passive investment management, on the other hand, involves buying and holding a well diversified portfolio, typically with the objective of tracking a particular index fund; with no attempt made to engage in selectivity or timing. In reality, institutional investors are practically engaged in active portfolio management all the time. The ultimate goal of institutional investors is to earn positive abnormal profits for their clients.

APPROACHES TO ACTIVE MANAGEMENT

In this section, I wish to share with you the proper approaches to active management and how to construct a portfolio in the framework of the active portfolio management style. You may be aware that an institutional investor will spend millions of dollars to subscribe to financial databases and hire doctoral graduates in financial engineering to conduct financial analysis in order to earn positive abnormal profits. The concept is very simple: if the institutional investor invests 5 million dollars in subscribing to financial databases, purchasing super-power computers and hiring doctoral graduates in financial engineering in order to earn 6 million dollars of profit, it is still worth it to that institutional investor to do so. On the other hand, individual investors do not have proper resources for them to perform the active portfolio management style. It is no wonder that on average, institutional investors are able to make positive abnormal profits better than individual investors. The following analysis of approaches to active portfolio management is from the perspective of an individual investor, and then we will go on to discuss the approaches to active portfolio management from the perspective of an institutional investor.

9.4.1 Approaches to Active Management from the Perspective of an Individual Investor

(a) Security Selection Security selection is the process by which an investor identifies the optimal portfolio considering all the individual securities at the same time. Observe that to generate an efficient set from all the securities in the market, you need forecasts for the expected returns, standard deviation, and co-variances for all available securities. However, excessive costs would be incurred if the optimal portfolio were determined by taking into account all the individual securities simultaneously.

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(b) Security Selection Coupled with Asset Allocation In the first place, the investor needs to find the optimal combination of securities for each class independently of the other classes. Secondly, given these portfolios for each class, determine the optimal asset allocation (i.e., the best mix of classes of assets). The following two types of asset allocation are sometimes mentioned:

(i) Strategic asset allocation refers to what the investor wants the weights to look like, on average, over the long term.

(ii) Tactical asset allocation refers to what the investor wants the weights to look like now, given the current conditions in the financial markets.

Note that this two-stage procedure simplifies our problem of finding the optimal portfolio by constructing efficient sets of subsets of securities.

(c) Security Selection Coupled with Sector Selection and Asset Allocation Firstly, the optimal combination of securities for each sector is determined independently of the other sector and asset classes. Secondly, given these portfolios for each sector, the optimal mix of sectors for each asset class is determined, which is known as sector selection. Thirdly, given these portfolios for each asset class, the optimal mix of asset classes is determined. The procedure stated above can be used with groups of stocks instead of sectors. A group is a category within an asset class. For instance, value and growth stocks are considered as two groups of stocks.

(d) Market Timing Market timing mainly focuses on forecasting asset classes without security selection (i.e., do not try to identify winners and losers). For instance, assume you invest in three classes of assets: stocks, bonds and currencies. Then based on forecasts for the expected returns and risks of these three classes of assets in the immediate future, you may determine the weights in your portfolio. It follows that for each class, you may want to buy a well-diversified representative portfolio of the securities in that class.

(e) Portfolio Revision Portfolio revision involves changing the current holdings in the portfolio. An investor with an active portfolio management style must conduct cost-benefit analysis. Benefits - intended to improve risk-return profile, expect either higher rate of returns or lower risk, or both.


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Costs - transaction costs:

Commission

Bid-ask spread

Price impact of large trades

Taxes (if not tax-exempt)

Making use of derivatives (i.e., forwards, futures, options and swaps, etc.) allows the investor to change the weight of each class of assets in the investorÊs portfolio at minimal cost.

9.4.2 Approaches to Active Management from the Perspective of an Institutional Investor

The approaches to active management of an institutional investor are more systematic than an individual investor. Generally speaking there are three stages in the active portfolio investment process: namely, the planning, implementation, and monitoring stages. Planning stage The initial planning stage is of utmost importance to an institutional investor. There are five steps involved in this stage.

(a) Investor conditions · From the perspective of institutional investors, their clients are small investors. In this case, they need to know the financial situation of their clients. Whether their clients need to invest in marketable or non-marketable assets depends upon the expected liquidation date. The institutional investor needs to know the financial distress of the clients as well as their tolerance for volatility risk.

(b) Market conditions · The institutional investor needs to know the market conditions both in the long term and the short term, for instance how the macroeconomic variables might change in the short term versus the long

You have a portfolio consisting of local and foreign equities and bond funds. They are maintained at a fixed percentage. Recently, you heard that rebalancing once or twice a year can boost your return by one to three per cent per year. What do think about this strategy?

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term. In addition, the movements of interest rates particularly in the short run are the most important market information for their clients.

(c) Investment/speculative policies · This process involves strategic asset allocation as well as speculation strategy such as tactical asset allocation and security selection. I will discuss the framework of strategic asset allocation in greater detail in the next section.

(d) Statement of investment policy · The statement of investment policy includes the objective of the investment, the strategy or investment policies and the constraints of the investment.

(e) Strategic asset allocation · Based on the investment objective, how could the institutional investor allocate assets for investment more strategically? The strategic asset allocation should match exactly with the investment objective set in advance.

Implementation stage The implementation stage beings by periodically adjusting the asset mix to the optimal mix, which is known as strategic asset allocation. In addition, the selection of the fund manager, the tactical asset allocation and the security selection decision are made at this stage. Figure 9.2 summarises all the processes at the implementation stage.

Discuss the five steps in the planning stage of an institutional investor? Why do you think the strategic asset allocation is important from the perspective of investment?

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Figure 9.2: Portfolio implementation stage Source: Adopted from Radcliffe, R. C. (1989). Investment: Concepts, analysis, strategy,

(3rd ed.). Harper Collins Publishers, p. 799

Monitoring stage There are three processes involved at the monitoring stage. In the first place, the actual portfolio held should be examined to ensure that it is compliant with the statement of investment policy to determine whether any rebalancing of the asset mix is required. Second is the evaluation of investment performance. This consists of an evaluation of returns on the aggregate portfolio, each asset class and the fund managers, and the returns from any speculative strategies used. Thirdly, adjustments to the statement of investment policy and fund managers should be made if deemed necessary. Figure 9.3 summarises the process of the monitoring stage.


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Figure 9.3: Portfolio monitoring stage Source: Adopted from Radcliffe, R. C. (1989). Investment: Concepts, analysis,

strategy, (3rd ed.). Harper Collins Publishers, p. 802 Example The following information in Tables 9.1 and 9.2 was obtained from the 1999 annual report of Fidelity Magellan Fund and Bloomberg. These tables serve as an example to show you how an institutional investor revises the portfolio during the monitoring stage.


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Table 9.1: Investment Changes in the Top Ten Stocks in Magellan

Weight in Magellan

Weight in Magellan

Weight in the S&P 500

Rank in the S&P 500

STOCKS as of 03/31/98

as of 09/30/97

as of 03/05/99

as of 03/05/99

General Electric Co. 3.5% 3.0% 3.3% 2

Microsoft Corp. 2.2% 1.3% 3.7% 1

Merck & Co., Inc. 1.7% 1.2% 1.9% 4

Citicorp 1.5% 1.4% 1.3% 14

Cendant Corp. 1.4% 1.2% 0.1% 160

Wal-Mart Stores, Inc. 1.4% 1.0% 2.0% 3

Home Depot, Inc. 1.4% 1.1% 0.9% 25

Bristol-Myers Squibb Co. 1.3% 1.1% 1.2% 16

Cisco Systems, Inc. 1.1% 0.6% 1.5% 9

Philip Morris Companies, Inc.

1.1% 1.3% 0.9% 24


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Table 9.2: Sector and Asset Allocations Changes in Magellan

SECTORS Weight as of 03/31/98

Weight as of 09/30/97

Technology 15.3% 16.8%

Finance 13.1% 12.3%

Health 11.7% 9.2%

Retail &Wholesale 8.6% 7.2%

Industrial Machinery & Equipment 8.1% 8.2%

ASSETS

Stocks 96.2% 95.9%

Short-term investments 3.8% 4.1%

Foreign investments 8.6% 8.2%

ACTIVE EQUITY PORTFOLIO STRATEGIES MANAGEMENT

What are active management strategies? As the words imply, you have to actively participate in forming the strategies. Active management strategies can be categorised into three areas:

(a) Fundamental analysis.

(b) Technical analysis.

(c) Anomalies and attributes.

9.5

The investment decisions made by most of the institutional investors are based on „qualitative‰ judgements. Can you think of any types of „quantitative‰ investment decision-making techniques that might be implemented?

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9.5.1 Fundamental Analysis

You learned about fundamental analysis: the „top down‰ and „bottom up‰ in Topic 8. You should review those topics if you have forgotten what they are. These are the basic strategies for fundamental analysis in active management. As mentioned in the reading, active managers generally use three generic tactics when attempting to add value to their portfolios relative to the benchmark. They are:

Try to time the equity market by shifting funds into and out of stocks, bonds and T-bills depending on broad market forecasts and estimated risk premium.

Shift funds among different equity sectors and industries (property, finance, high tech., etc.) or among investment styles (large capitalisation, value, growth, etc.) to catch the next „hot‰ concept.

Engage in stock-picking by finding undervalued stocks.

The reading pointed out that asset and sector rotation strategies can be extremely profitable but also very risky. On the other hand, stock-picking strategies can be more reliable but less profitable strategies. Do you agree? Can an individual investor follow the above strategies? It would not be that difficult for you to pick stocks as the Internet can provide a lot of information on individual stocks or you can simply subscribe to some information providers (like Bloomberg, etc.) for financial information. On the other hand, shifting funds among assets or sectors may be more difficult for small investors. Moreover, the transaction costs will be higher than for institutional investors. Institutional investors may also have more information on which assets or sectors have more potential than you do.

9.5.2 Technical Analysis

In active portfolio management, managers form equity portfolios based on historical stock information (like price trends) that is used to decide whether price trends will continue or reverse their direction. In the reading, we had contrarian strategy and continuation strategy. To put it simple, attempting to buy when a stock is near its lowest price and to sell when it is near its highest price is the contrarian strategy. Some studies show that investing in over-reacted stocks provides superior returns. Assuming price trends will continue is the central element of continuation strategy.


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These strategies are not difficult for individual investors to implement; however, you need to have a large database and some computer programs in order to track the stocksÊ performance. Therefore, unless individual investors have plenty of resources or access to past stock prices, they will find it hard to implement the strategy effectively. Some financial websites and newspapers do provide information such as which stocks had the biggest rise/fall of the day and technical analysis facilities; these are some cheap resources for implementing the strategies. As we mentioned in the previous topic, Yahoo Finance allows you to do some technical analysis on stocks you picked. Of course you cannot do it on a larger scale, such as ten stocks at the same time. Figure 9.4 shows an example showing the top ten gainers of the day. You can monitor the performance of the gainers to see whether the information helps.

Figure 9.4: Examples of top ten gainers

Source: http://www.klse.com.my/website/bm/market_information/prices/index.jsp


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9.5.3 Anomalies and Attributes

In the reading, it mentioned anomalies like the January effect and the weekend effect and pointed out that the annual fees of the former strategy are not justified while the latter strategy is not cost effective. The reading suggests the approach of forming portfolios based on the characteristics or attributes of companies is more promising. Again, financial websites do provide that kind of information, e.g. firm sizes, P/E, P/BV and other financial ratios. The key point is that we are analysing many stocks instead of a few individual stocks, and this poses difficulties to individual investors with limited reso

ACTIVE BOND PORTFOLIO MANAGEMENT STRATEGIES

In this section we will talk about bond portfolio management strategies rather than the calculation details. The participation rate of individual investors, especially small investors, in fixed income securities is much less than the participation rate in equities. Therefore, the topics covered here apply mostly to large or institutional investors. According to the reading „Active management strategies‰, for bond portfolio management strategies there are five management strategies available:

Interest rate anticipation

Valuation analysis

Credit analysis

Yield spread analysis

Bond swaps.

WeÊll now take a closer look at each of these strategies in turn.

(a) Interest Rate Anticipation In this strategy, the portfolio manager believes he can predict whether or not the future interest rate level will change the portfolioÊs sensitivity to interest rate changes. If the interest rate is expected to increase, he will reduce the duration, and vice versa. How should the duration be adjusted? Think about this. You should be able to come up with the answer. The duration of a portfolio can be changed by swapping bonds in the portfolio for new bonds. Please refer to the reading for details. The key to

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this strategy is whether you have the ability to forecast the direction of the interest rate. The reading also discusses what will happen if the interest rate moves in the opposition direction.

(b) Valuation Analysis Valuation analysis involves the portfolio manager trying to select undervalued/overvalued bonds based on their intrinsic value, which depends on the characteristics of the bonds. The key to success depends on the understanding and accurate estimation of the important characteristics of a bond. Bond valuation has been covered before, and therefore will not be repeated here.

(c) Credit Analysis As the name tells you, this is about the analysis of the credit of the bond issuer. The key is to correctly project rating changes prior to the announcement by rating agencies. The reading has detailed discussion of the credit analysis of high-yield (junk) bonds and credit analysis models. You should make sure that youÊve read the relevant sections carefully so that you have an overall picture of how this method works; you donÊt need to remember the details of the model.

(d) Yield Spread Analysis Yield spread is the difference in yield between different security issues, usually securities of different credit quality. The analysis assumes normal relationships exist between the yields for bonds in different sectors. The key is to develop knowledge of the normal yield relationship and take necessary action to take advantage of the temporary yield abnormality. In other words, portfolio managers have to position a portfolio to capitalise on expected changes in yield spreads between different sectors of the bond market. You should be able to tell whether spread will widen or decline under good or bad economic conditions.

(e) Bond Swaps These involve swapping (exchanging) one bond for another hoping to improve return. As mentioned in the reading, the market may move against you and cause you to incur loss. You should go through the details of the three bond swaps (pure yield pickup swap, substitution swap and tax swap) in the reading. Make sure you understand the benefits and the potential risks of the swaps. In addition to what we have just learned, you can find additional references about active bond portfolio management strategies in Chapter 17 of Bond


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Markets, Analysis and Strategies, (5th ed.) by Frank J. Fabozzi, Prentice Hall Press. LetÊs end this section by doing the coming activity.

We have now finished our introduction to active equity and bond portfolio management strategies. You may ask questions like, „Which strategies are best?‰ and „Which one works?‰ There are no easy answers, and whether a strategy works or not really depends on the vision of the portfolio managers. That is why we have only one Warren Buffet in the world! However, knowing the strategies helps managers react quickly to different market conditions. To implement the strategies efficiently, a lot of analysis and resources are often needed and this limits what individual investors can do. You should also note that the strategies mentioned are not the only way to manage a portfolio.

PASSIVE STRATEGIES FOR EQUITY PORTFOLIOS

Equity portfolio management can be simply categorised into active or passive management. You are encouraged to review the principles of active portfolio management before moving on to this unit. In this first section, I introduce you to the major passive strategies in equity portfolio management. Instead of giving you any „must-work‰ strategies (which we actually do not have!), this introduction leaves room for your judgement. LetÊs start our discussion of passive strategies by looking at the „buy and hold‰ strategy.

9.7.1 Buy and Hold

Have you ever bought stock? If so, what was your trading strategy? Did you buy stock and then plan to hold on to it for years? Or, did you buy it with the aim of making a quick profit and then end up waiting for years because its price has been dropping since the day you bought it? How about TENAGA stock, for example? Are you still holding it now if you bought it at, say, $20, $10 or even $6 per share?

9.7

ACTIVITY 9.3

What are the potential disadvantages of the pure yield pickup swap in which you are picking a higher coupon bond? What are the risks involved?


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The point is, we cannot assume that a „buy and hold‰ strategy is really so simple. On the one hand, of course, you can randomly buy some assets and then leave your portfolio unattended for years. In so doing, it could be said you are actually using a „buy and hold strategy‰, but this is hardly likely to produce a good return on average in the long run. On the other hand, the buy and hold strategy has some very successful practitioners. Warren Buffet, one of the wealthiest investors in the world, applies a buy and hold strategy · but this does not imply that everyone using a buy and hold strategy will end up a billionaire! In the buy and hold strategy, a portfolio manager typically buys stocks in such a way that her portfolioÊs returns track those of an index over time. To track an indexÊs performance (an indexing strategy), you have to keep track of the change of the index constituent stocks. Occasional rebalancing occurs because dividends are reinvested and stocks merge or drop out of the target index and other stocks are added. Usually this kind of portfolio is not targeted to beat or outperform the index but just to match/track its performance. Of course, an active strategy would try to beat the index. LetÊs now take a closer look at how a passive index portfolio can be constructed. The following three approaches are common ways to form a passive index portfolio under a buy and hold strategy. (a) Full Replication

In this variation on the buy and hold strategy, all securities in an index are purchased in proportion to their weights in that index. For example, in a Bursa Malaysia Composite Index portfolio, you would have to buy the 100 constituent stocks according to their market value. What are the disadvantages of this strategy? High transaction costs and the reinvestment risk of dividends cannot be ignored! A good example is the Tracker Fund which tries to track the performance of the Bursa Malaysia Composite Index.

(b) Sampling

This strategy entails buying only a representative sample of stocks that comprise the benchmark of an index. That is, the difference between sampling and full replication is that sampling considers a sample of stocks that can represent the movement of the index instead of holding all the constituent stocks. Again, what would you do if the portfolio tracks the Bursa Malaysia Composite Index (BMCI)? Yes, buy a few stocks with large market capitalisations. What are they? TENAGA, TELEKOM, Maybank etc. Sampling saves on transaction costs, but it may not closely track the index.


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(c) Programming This strategy uses historical information on price changes and correlations between securities to determine the composition of a portfolio that will minimise the tracing error of the index. The drawback is that it depends on historical prices. For example, adding any stock to a portfolio tracking the BMCI can be a reasonable choice, if the correlation between the returns on the particular stock and BMCI is close. A simple way to calculate such a correlation is by using the correlation function of Excel to determine the correlation coefficient of the two assets within a given period. Of course you should not add stocks with negative correlation. A drawback of this strategy is that without programming team support or good programming knowledge, you may find it hard to conduct in practice.

9.7.2 Dollar-cost Averaging

This is a popular method of passive management. Instead of predicting the times of market highs and market lows, portfolio managers just invest an equal amount of funds each period. With this type of fixed dollar investment, managers buy less when stock prices are high and buy more when stock prices are low. The advantage of using dollar-cost averaging is to prevent investing too much at a bad time.

9.7.3 Constant Beta

Unlike an active strategy, a passive strategy will not try to change a portfolioÊs beta based on economic forecasts. You have learned about beta in previous units. Please revise if youÊve forgotten what a portfolio beta is. The key is to manage cash inflows and outflows without harming the portfolio index tracking ability. Futures contracts are typically used to fulfill such tasks. Before ending this section, you should note that a passive strategy is not a strategy trying to earn maximum returns, which requires experts searching for value stocks continuously. You should now do the following activity.

In this topic, we have discussed the differences between individual investors and institutional investors.

We have also discussed the two types of strategies i.e. active strategies and

passive strategies.


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Active equity portfolio management for equity portfolio involves three areas: fundamental analysis, technical analysis and anomalies and attributes.

Active equity portfolio management for bond portfolio involves interest rate

anticipation, valuation analysis, credit analysis, yield spread analysis and bond swaps.

Passive equity portfolio management involves buy and hold, dollar cost

averaging and constant beta.

Active equity portfolio management Anomalies and attributes Bond portfolio Bond swaps. Buy and hold Constant beta Credit analysis Dollar cost averaging

Fundamental analysis Individual investors Institutional investors Interest rate anticipation Passive equity portfolio management Technical analysis Valuation analysis Yield spread analysis

1. What are the major constraints of individual investors as compared to institutional investors?

2. Has the widespread access of internet reduced the information gap between

individual investors and institutional investors? 3. What is herd behaviour? 4. If herd behaviour persists, what is the likely outcome as observed in the

past? Provide an example. 5. Who are institutional investors? What are their strengths and limitations? 6. There are two types of pension scheme. Explain the differences between

them. 7. What active management investment style attempts to do?


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8. How is it passive investment style different from active management style?

1. From the perspective of an individual investor, what are the approaches to active management?

2. What are the stages for institutional investors when they implement active

portfolio investment strategies? 3. What are the two types of asset allocation strategies usually used by

investors? 4. Discuss the five stages within the initial planning stage of an institutional

investor. 5. Explain the strategy of full replication. 6. What is the strategy of sampling and how it differs from full replication?

What are the pros and cons of this strategy? 7. Discuss the strategy of interest rate anticipation with respect to active

management of bond portfolios? 8. „⁄As one of the strategy of passive management, programming uses

historical information on price changes and correlations between securities to determine the composition of a portfolio that will minimise the tracing error of the index...‰ Discuss the pros and cons of this strategy, and what are the matters that portfolio manager should be aware of?

INTRODUCTION We have finally come to the last topic of this module. In this topic, we are interested in measuring the portfolio investment we have made. Like anything else in life, we want to measure whether our investment has achieved the goals we have set for it. It is important to measure the portfolio performance. Why? Each of us may have different financial goals like providing education fund for our children or saving up monies for retirement when we invest in financial assets. Hence we want to know whether these financial goals can be achieved after a period of time. We start this topic by explaining the importance of performance evaluation. This is followed by the methods of measuring returns and adjusted returns. We also discuss benchmarking and a series of new indices introduced by Bursa Malaysia to Malaysian stock market. Subsequently we discuss Sharpe ratio, TreynorÊs measure, JensenÊs Alpha and the application of these measurements. Lastly, we explain what is meant by market timing and stock selection skills.

TTooppiicc

1100

Evaluation of Portfolio Performance


1. Explain the importance of performance evaluation;

2. Describe the methods of measuring returns and adjusted returns;

3. Discuss the meaning of benchmarking in the context of investment management;

4. Examine what is TreynorÊs measure;

5. Explain the usage of Sharpe Ratio and SensenÊs Alpha; and

6. Appraise security selection and market timing.

TOPIC 10 EVALUATION OF PORTFOLIO PERFORMANCE

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Again, we will start this topic by introducing the excerpt of an article from the Journal of Portfolio Management written by Professor William Sharpe. This article is published in 1994, 25 years after Sharpe ratio was first introduced. Enjoy the reading!

The Sharpe Ratio William F. Sharpe

Stanford University Reprinted fromThe Journal of Portfolio Management, Fall 1994

This copyrighted material has been reprinted with permission from The Journal of Portfolio Management.

Copyright © Institutional Investor, Inc., 488 Madison Avenue, New York, N.Y. 10022,

a Capital Cities/ABC, Inc. Company. Phone (212) 224-3599.

Over 25 years ago, in Sharpe [1966], I introduced a measure for the performance of mutual funds and proposed the term reward-to-variability ratio to describe it (the measure is also described in Sharpe [1975] ). While the measure has gained considerable popularity, the name has not. Other authors have termed the original version the Sharpe Index (Radcliff [1990, p. 286] and Haugen [1993, p. 315]), the Sharpe Measure (Bodie, Kane and Marcus [1993, p. 804], Elton and Gruber [1991, p. 652], and Reilly [1989, p.803]), or the Sharpe Ratio (Morningstar [1993, p. 24]). Generalized versions have also appeared under various names (see. for example, BARRA [1992, p. 21] and Capaul, Rowley and Sharpe [1993, p. 33]). Bowing to increasingly common usage, this article refers to both the original measure and more generalized versions as the Sharpe Ratio. My goal here is to go well beyond the discussion of the original measure in Sharpe [1966] and Sharpe [1975], providing more generality and covering a broader range of applications. THE RATIO Most performance measures are computed using historic data but justified on the basis of predicted relationships. Practical implementations use ex post results while theoretical discussions focus on ex ante values. Implicitly or explicitly, it is assumed that historic results have at least some predictive ability. For some applications, it suffices for future values of a measure to be related monotonically to past values -- that is, if fund X had a higher historic measure than fund Y, it is assumed that it will have a higher future measure. For other applications the relationship must be proportional - - that is, it is assumed that the future measure will equal some constant (typically less than 1.0) times the historic measure.


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To avoid ambiguity, we define here both ex ante and ex post versions of the Sharpe Ratio, beginning with the former. With the exception of this section, however, we focus on the use of the ratio for making decisions, and hence are concerned with the ex ante version. The important issues associated with the relationships (if any) between historic Sharpe Ratios and unbiased forecasts of the ratio are left for other expositions. Throughout, we build on Markowitz' mean-variance paradigm, which assumes that the mean and standard deviation of the distribution of one-period return are sufficient statistics for evaluating the prospects of an investment portfolio. Clearly, comparisons based on the first two moments of a distribution do not take into account possible differences among portfolios in other moments or in distributions of outcomes across states of nature that may be associated with different levels of investor utility. When such considerations are especially important, return mean and variance may not suffice, requiring the use of additional or substitute measures. Such situations are, however, beyond the scope of this article. Our goal is simply to examine the situations in which two measures (mean and variance) can usefully be summarised with one (the Sharpe Ratio). Summary The Sharpe Ratio is designed to measure the expected return per unit of risk for a zero investment strategy. The difference between the returns on two investment assets represents the results of such a strategy. The Sharpe Ratio does not cover cases in which only one investment return is involved. Clearly, any measure that attempts to summarize even an unbiased prediction of performance with a single number requires a substantial set of assumptions for justification. In practice, such assumptions are, at best, likely to hold only approximately. Certainly, the use of unadjusted historic (ex post) Sharpe Ratios as surrogates for unbiased predictions of ex ante ratios is subject to serious question. Despite such caveats, there is much to recommend a measure that at least takes into account both risk and expected return over any alternative that focuses only on the latter. For a number of investment decisions, ex ante Sharpe Ratios can provide important inputs. When choosing one from among a set of funds to provide representation in a particular market sector, it makes sense to favor the one with the greatest predicted Sharpe Ratio, as long as the correlations of the funds with other relevant asset classes are reasonably similar. When allocating funds among several such funds, it makes sense to allocate funds such that the selection (residual) risk levels are proportional to the predicted Sharpe Ratios for the


174

selection (residual) returns. If some of the implied net positions are infeasible or involve excessive transactions costs, of course, the decision rules must be modified. Nonetheless, Sharpe Ratios may still provide useful guidance. Whatever the application, it is essential to remember that the Sharpe Ratio does not take correlations into account. When a choice may affect important correlations with other assets in an investor's portfolio, such information should be used to supplement comparisons based on Sharpe Ratios. All the same, the ratio of expected added return per unit of added risk provides a convenient summary of two important aspects of any strategy involving the difference between the return of a fund and that of a relevant benchmark. The Sharpe Ratio is designed to provide such a measure. Properly used, it can improve the process of managing investments. References

BARRA Newsletter, September/October 1992, May/June 1993, BARRA, Berkeley, Ca.

Bodie, Zvi, Alex Kane and Alan J. Marcus. Investments, 2d edition. Homewood, IL: Richard D. Irwin, 1993.

Capaul, Carlo, Ian Rowley, and William F. Sharpe. "International Value and Growth Stock Returns," Financial Analysts Journal, January/February 1993, pp. 27-36.

Elton, Edwin J., and Martin J. Gruber. Modern Portfolio Theory and Investment Analysis, 4th edition. New York: John Wiley & Sons, 1991.

Grinold, Richard C. "The Fundamental Law of Active Management," Journal of Portfolio Management, Spring 1989, pp. 30-37.

Haugen, Robert A. Modern Investment Theory, 3d edition. Englewood Cliffs, NJ: Prentice-Hall, 1993.

"Morningstar Mutual Funds User's Guide." Chicago: Morningstar Inc., 1993.

Radcliff, Robert C. Investment Concepts, Analysis, Strategy, 3d edition. New York: HarperCollins, 1990.

Reilly, Frank K. Investment Analysis and Portfolio Management, 3d edition. Chicago: The Dryden Press, 1989.

Rudd, Andrew, and Henry K. Clasing. Modern Portfolio Theory, The Principles of Investment Management. Homewood, IL: Dow-Jones Irwin, 1982.


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Sharpe, William F. "Mutual Fund Performance." Journal of Business, January 1966, pp. 119-138.

"Adjusting for Risk in Portfolio Performance Measurement." Journal of Portfolio Management, Winter 1975, pp. 29-34.

"Asset allocation: Management Style and Performance Measurement," Journal of Portfolio Management, Winter 1992, pp. 7-19.

Tobin, James. "Liquidity Preference as Behavior Toward Risk." Review of Economic Studies, February 1958, pp. 65-86.

Treynor, Jack L., and Fischer Black. "How to Use Security Analysis to Improve Portfolio Selection." Journal of Business, January 1973, pp. 66-85

Source: http://www.stanford.edu/~wfsharpe/art/sr/sr.htm (Retrieved 7 August 2007)

THE IMPORTANCE OF PERFORMANCE EVALUATION

Performance data is valuable to chart the progress of your investment. While performance is a key evaluator in identifying a suitable fund, it is not the only factor upon which you should base your decision. It is important to understand that unit trusts do not offer a fixed rate of return: your principal value will fluctuate, and the return on your investment is not guaranteed. The rates of return fluctuate with market conditions, changes of the valuation of the securities a fund invests in, or other factors. For that reason, it is helpful to examine performance over various time periods.

10.1.1 Historical Results

It is important for us to keep in mind that performance is based on historical results and is not intended to project future performance of a fund. Ensure that the fund's objectives as well as the manager's investment style and strategy are aligned with yours. While yesterday's data is no guarantee of future performance, the long-term track record is a useful barometer of the manager's skill and expertise in managing different market cycles. When comparing funds, it is best to focus on long-term performance because financial markets (and the economy) tend to go through cycles that can last for several years. For instance, small-company stocks (and funds) will at times

10.1


176

outperform large-company stocks (and funds). At other times, the large-company stocks/funds will be the star performers. A common mistake investors make is to constantly "chase" the best-performing funds from the recent past. Unfortunately, last year's "hot" sector of the financial market may be replaced this year by a different sector. As historical data is never perfect, the additional information paves the way for investors to make more informed investment decisions. They should also remember that a top or winning fund may not necessarily be the most suitable fund for them. If you are comparing, the performance of several funds, be sure that you are making accurate comparisons: compare funds with the same investment objectives and fund policies before looking at the numbers. The value of investment may rise and fall and investors may/may not get back the amount originally invested. Changes in the currency exchange rates may cause the value of the investment to increase or diminish if you are investing in an offshore fund.

10.1.2 Measuring Fund Performance

A unit trust fund's performance can be measured by its total return. A fund's total return is the change in the value of an investment in the fund, taking into account any change in the fund's unit price during the period and assuming the reinvestment of income and capital gains distributions. Total return is commonly presented in two ways. One is called the fund's cumulative total return, or total rise in the value of a fund's investments over time, assuming that income and capital gains distributions were reinvested. The other is called average annual total return, which is the compounded total return, it would take each year to produce the fund's cumulative total return. Seemingly modest annual returns can be converted, through the power of compounding, into impressive cumulative returns. Measuring funds against a benchmark or market index When evaluating fund performance, a good approach is to compare its total return with the returns of similar funds or with the return of an appropriate market index or benchmark over the same time period. Recall in Topic 1 that we have also discussed index fund. We have said that index fund aims to replicate performance of an index. In our context, Malaysian


177

index fund aims to replicate the Kuala Lumpur Composite Index (KLCI). Hence, an index fund effectively holds a market portfolio. We will explain the issue of benchmark in subtopic 10.3. Comparing within the same risk profile Another issue crises when comparing funds with their peer groups. It is always important to remember that a stock fund or equity fund should be compared with other similar stock funds - ones that invest in the same type of companies. A bond fund should be compared with bond funds that invest in bonds of similar maturities and credit quality (rating). You can usually find the name of the appropriate market index or benchmark on a fund's prospectus or manager's (annual and semi-annual) report.

INSTITUTIONAL INVESTORS

Performance must be investigated over a long period of time: minimum of five years, using monthly returns. Without such a sample size, determining portfolio performance becomes a hazardous task⁄difficult to really assess whether performance was due to good or bad luck or skill (or lack of it). Consider the simple case of an investor neither depositing nor withdrawing money from the fund during a certain time period. How are we going to calculate the rate of return?

10.2

ACTIVITY 10.1

1. Do you think performance is due to the skills of fund managers or good luck?

2. In the market, we have equity funds, index funds, and bond funds what is the appropriate benchmark for these funds?

What to do when different fund managers have managed the

fund over some period?


178

This is the simple case where all we need to know is the fundÊs market value at the beginning of the period and end of the period. In this case, the fundÊs return is calculated this way:

Return=

V VEND BEGINNINGVBEGINNING

(10.1)

In reality, performance measurement is not that simple! The main problem is that the investor may deposit or withdraw cash from the fund. In this case, the market values will be influenced by these cash flows and by only using the previous formula without considering other factors, you will get misleading results.

Example 2: Consider the case of a fund whose market value at the beginning of the period was $200 million. Towards the end of the quarter an investor deposits $10 million in the fund. At the end of the quarter the fundÊs market value is $206 million. When you use the previous formula, disregarding the cash inflow, you find that the return was 3%. But this is incorrect! The increase in market value was not the result of the fund managerÊs skills. The accurate measure of the fundÊs returns over the quarter must take into consideration the $10 million cash inflow. Considering this fact, results in a return of -2% [={($206m -$10m) - $200m}/$200m].

Example 1: Consider a portfolio with a market value of $50 million at the beginning and $56 at the end of the period. The return is 12% [=($56m - $50m)/$50m]


179

The identification of the timing of deposits and withdrawals is crucial in determining the correct returns of a fund. Take into consideration these cash flows to adjust the rate of return. Ignoring these adjustments will lead to misleading conclusions!

10.2.1 Dollar-weighted Returns Method

One method that can be used in order to calculate returns when deposits or withdrawals occur is the Dollar-weighted Returns Method. Similar to the Internal Rate of Return calculation where the beginning-of-period value is set equal to the discounted values of the cash flows and the end-of-period value:

10.2.2 Time-weighted Returns Method

One alternative method is the Time-weighted Returns Method. This methodology uses the fundÊs market value before each cash flow takes place. Continuing from our previous example, assume that the deposit was made in the middle of the quarter. The fundÊs value was $195m before the deposit, so that soon after the $10m deposit its market value went to $205m. Hence the return for the first half would be -2.5% [=($195m-$200m)/$200m] while the return for the second half is 0.5% [=($206m-$205m)/$205m]. These two semi-quarter returns can give us the total quarter returns as follows: [={1+(-0.025)} x {1+(0.005)} - 1]= -2%

10.2.3 Comparison

The dollar-weighted returns are influenced by both the size and the timing of the cash flows. The time-weighted returns do not present this problem. For this reason, the time-weighted return is generally preferred to dollar-weighted in evaluating portfolio performance.

21

206$

1

10$200$

r

m

r

mm


180

BENCHMARKING

In performance analysis you need to make relevant comparisons. The investor has to compare the returns of his/her manager with the returns that would have been obtained had he/she invested in an alternative portfolio with identical risk. In the context of topic, performance evaluation discusses the issue whether the performance was superior or inferior relative to a benchmark, or whether the performance was due to skills or luck. The investor must make use of benchmark portfolios to assess the fund managerÊs performance. These benchmark portfolios must be relevant (similar risk), feasible and known in advance. For example, let us say that you decide to invest in a diversified equity portfolio with average risk. You see that your return was 20%. Is this good or bad? Now let us say that you find out that the KLCI has gone up, for the same period, 14%. Then you can say that your fund, for this period in particular, had a superior return.

10.3.1 New Indices

The Kuala Lumpur Stock Exchange (KLSE) or Bursa Malaysia has introduced a series of indices in 2006. It is a joint effort between KLSE and FTSE.

10.3

1. Why do you think historical data of fund performance can only be used as a guide, and not a guarantee of future performance of that fund?

2. Why time-weighted return is more preferred than dollar-

weighted return?

SELF-CHECK 10.1

Performance must be evaluated on a relative basis; not on absolute basis!


181

The FTSE Bursa Malaysia Index Series is designed to measure the performance of the major capital segments of the Malaysian market. All Malaysian companies listed on the Bursa Malaysia Main Board, Second Board and MESDAQ Market are eligible for inclusion, subject to meeting FTSE's international standards of free float, liquidity and investability. The index series covers all stock sizes within the market and is suitable for the creation of investment products such as ETFs, derivatives and index tracking funds. As shown in Figure 10.1, there are two type of indices. The first group is tradable Indices. The second group is benchmark indices. We will first examine the four tradable indices, and then the five benchmark indices in next section.

Figure 10.1: Family tree of the new indices Source: http://www.bursamalaysia.com/website/bm/

market_information/ftse_bursa_index.html Tradable Indices (a) FTSE Bursa Malaysia Large 30 Index


182

This tradable index comprises the 30 largest companies in the FTSE Bursa Malaysia (FBM) EMAS index by market capitalisation.

(b) FTSE Bursa Malaysia Mid 70 Index Comprises the next 70 companies in the FTSE Bursa Malaysia EMAS Index

by full market capitalisation (c) FTSE Bursa Malaysia 100 Index Comprises the constituents of the FTSE Bursa Malaysia Large 30 and the

FTSE Bursa Malaysia Mid 70 Index (d) FTSE Bursa Malaysia Hijrah Shariah Index The FTSE Bursa Malaysia Hijrah Shariah Index is a tradable index which

comprises the 30 largest companies in the FBM EMAS Index that meets the following triple screening process:

FTSE's global standards of free float, liquidity and investability ;

Yasaar's international Shariah screening methodology; and

Malaysian Securities Commission's Shariah Advisory Council (SAC) screening methodology.

Benchmark Indices (a) FTSE Bursa Malaysia EMAS Index Comprises the constituents of the FTSE BursaMalaysia 100 Index and FTSE

Bursa Malaysia Small Cap Index. (b) FTSE Bursa Malaysia Small Cap Index Comprises those eligible companies within the top 98% of the Bursa

Malaysia Main Board excluding constituents of the FTSE Bursa Malaysia 100 Index.

(c) FTSE Bursa Malaysia Fledgling Index Comprises the remaining 2% of stocks from the Bursa Malaysia Main Board

universe that are too small to be included in the FTSE Bursa Malaysia EMAS Index. No liquidity screening is applied.

(d) FTSE Bursa Malaysia EMAS Shariah Index The FTSE Bursa Malaysia EMAS Shariah Index comprises constituents of

the FBM EMAS index that are Shariah-compliant according to the Securities Commission's SAC screening methodology and FTSE's screens of free float, liquidity and investability. The index has been designed to provide investors with a broad benchmark for Shariah-compliant investment.


183

(e) FTSE Bursa Malaysia Second Board Index The FTSE Bursa Malaysia Second Board Index comprises all eligible

companies listed on the Second Board. No liquidity screening is applied. (f) FTSE Bursa Malaysia MESDAQ Index The FTSE Bursa Malaysia MESDAQ Index comprises all eligible companies

listed on the MESDAQ Market. No liquidity screening is applied. Table 10.1 shows all the details of the new indices lauched in 2006. It is important to take note that existing indices like EMAS, Second Board and Mesdaq are readjusted to become part of the new indices lauched. In line with the Islamic finance, two Shariah Indices as shown in Table 10.2 and 10.3 were also launched.

Table 10.1: FTSE Bursa Malaysia Index Series

Index/Sector Name

Number of Constituents

US Dollar Index

Base Currency

Index

US Dollar

TRI

Base Currency

TRI

Mkt Cap (USD)

Mkt Cap (Base Index)

FTSE Bursa Malaysia 100

Index 100 9327.39 8077.23 9897.29 8570.83 146338.127758 466599.120356

FTSE Bursa Malaysia

Second Board Index

216 6678.50 5783.38 6821.44 5906.90 2305.900424 7352.363501

FTSE Bursa Malaysia Large

30 Index 30 9346.08 8093.42 9944.76 8611.98 116208.966839 370532.290766

FTSE Bursa Malaysia Mid

70 Index 70 9105.32 7884.93 9574.35 8291.10 30129.160919 96066.829590

FTSE Bursa Malaysia

EMAS Index 366 9567.67 8285.31 10140.54 8781.47 167054.955460 532654.725484

FTSE Bursa Malaysia

Fledgling Index242 8501.50 7362.04 8819.08 7636.98 3943.654938 12574.343770

FTSE Bursa Malaysia MESDAQ

Index

121 5595.25 4845.31 5629.23 4874.73 1429.111314 4556.721426

FTSE Bursa Malaysia Small

Cap Index 266 11434.31 9901.76 12017.37 10406.68 20716.827702 66055.605127


184

Table 10.2: FTSE Bursa Malaysia Hijrah Shariah Index

Index/Sector Name


US Dollar Index

Base Currency

Index

US Dollar

TRI

Base Currency

TRI

Mkt Cap (USD)


FTSE Bursa Malaysia Hijrah Shariah Index

30 11183.86 9684.88 11937.15 10337.33 61240.844544 195266.432827

Table 10.3: FTSE Bursa Malaysia EMAS Shariah Index

Index/Sector Name


US Dollar Index

Base Currency

Index

US Dollar

TRI

Base Currency

TRI

Mkt Cap (USD)


FTSE Bursa Malaysia EMAS Shariah Index

269 9945.36 8612.38 10490.60 9084.67 97848.762083 311990.777903

Table 10.4: Correlation Matrix of all Bursa Malaysia Index Series

Source: http://www.bursamalaysia.com/website/bm/market_information /ftse_bursa_index.html

As we have discussed earlier in Topic 2 and 3, correlation among indices is important in portfolio management. As shown in Table 10.4, based on three-year data, FTSE has published the correlation matrix of all the new indices. As mentioned in earlier paragraph, existing indices like EMAS, Second Board and Mesdaq are readjusted to become part of the new indices lauched. In similar


185

manner, the stock listed in Bursa Malaysia are selected regrouped under the new indices based on different criteria. Hence, although the new indices are only launched in 2006, the stocks that become the sample of these different indices have been in existence before 2006. By using the historical data of the listed stocks that forms the new indices, their respective pair-wise correlation can be calculated.

10.3.2 Measuring Portfolio Return

Related to equation (10.1), we would like discuss in detail how we can calculate the one period rate of return, r, for a unit trust fund or mutual fund over a holding period. This is because for unit trust fund, during the holding period, cash inflows into the fund and cash withdrawals from the fund may occured. One period rate of return is

1

1 )(

t

ttttp NAV

CDNAVNAVR (10.2)

where

tNAV = Net Assets Value per unit at the end of the holding period.

1tNAV = NAV per unit at the beginning of the holding period.

tD = Cash disbursements per unit during the holding period.

tC = Capital gains disbursements per unit during the holding period. This one period rate of return on a portfolio is also known as holding period yield. The return is stated in percentage.

10.3.3 Risk Adjusted Return

As stated earlier, we can compare the above return from equation (10.2) against benchmark. However, a word of caution here is that unit trust funds have different risk exposure. Therefore, it is more sensible for the returns to be adjusted for risk before making any comparison. When we mention adjusting for risk, we mean that we looking at reward per unit of risk. As investment in stocks are risky activities, investors must be


186

compensated above risk free rate, hence they must receive risk premium. The higher the ratio of reward per unit of risk, the fund is better in terms of performance. We can use this ratio to rank the unit trust funds. We will learn three methods of risk adjusted performance measurement in subtopic 10.4, 10.5 and 10.6 subsequently.

SHARPE RATIO

One simple way to investigate the fundÊs performance is to consider risk-adjusted return. Remember that the CAPM tells us that the more market risk you take on, the higher should be the return. A widespread measure is the Sharpe ratio:

Sharpe ratio = p

fp RR

(10.3)

Where:

pR = Realised return on the portfolio

fR = Risk free rate of return

p = Standard deviation of portfolio return

The Sharpe Ratio divides average portfolio excess returns by the portfolioÊs risk. In this case, the portfolio risk or the variability of return as measured by the standard deviation of return. This measures the reward to variability ratio.

TREYNOR’S MEASURE

The TreynorÊs measure gives the excess return per unit of risk. It measures reward to volatility. It is the ratio of the reward to the volatility of return as measured by the portfolio beta. However, unlike the Sharpe Ratio, it uses the systematic risk instead of total risk.

TreynorÊs measure = p

fp RR

(10.4)

10.4

10.5


187

Where:

pR = Realised return on the portfolio

fR = Risk free rate of return

p = Portfolio beta

JENSEN’S ALPHA

Like Jack Treynor and William Sharpe, Michael Jensen recognised the CAPMÊs implications for performance measurement. The JensenÊs alpha is the average fundÊs return above the predicted return from the CAPM, given the portfolioÊs Beta and average market return. Using the CAPM model, the expected return of the portfolio can be calculated as follows:

E(Rp) = Rf + p (Rm-Rf) (10.5)

Where: E(Rp) = Expected portfolio return Rf = Risk free rate Rm = Return on marke index

p = Systematic risk of the portfolio The differential return is calculated

Jensen R R R RP P f P M f (10.6)

Where: Rp = Actual return earned on the portfolio

p = Differential return earned

E(Rp) = Expected portfolio return

p represents the difference between actual return and expected return.

10.6


188

If p has a positive value, it indicates the superior return has been earned by the

fund managers due to either selection or timing skills, or both. If p has a zero

value, it indicates neutral performance. This means that the fund managers have done just as well as unmanaged portfolio with buy and hold stocks that are selected randomly. However, if p has a negative value, it means that the fund

managers performed worse than of the market.

10.6.1 Application of Risk-adjusted Returns

Portfolio L Market Portfolio, M

Average Return 35% 28%

Beta 1.20 1.00

Standard Deviation 42% 30%

Non-systematic Risk 18% 0%

Assuming the risk free rate is 6% and market return is 15%, calculate the Sharpe ratio, Treynor measure, JensenÊs Alpha for Portfolio L and M. Solution: Sharpe ratio for Portfolio L = (35-6) / 42 = 0.69 Sharpe ratio for Portfolio M = (28 6 )/ 30 = 0.73 It can be concluded that Portfolio L underperformed Portfolio M. TreynorÊs measure for Portfolio L = (35 6) / 1.20 = 24.17 TreynorÊs measure for Portfolio M = (28 6 )/ 1.00= 22 It can be concluded that Portfolio L has performed better Portfolio M. JensenÊs measure for Portfolio L = 35 [ (6 + 1.20 (28-6) ] = 2.6 It can be concluded that Portfolio L has a positive alpha of 2.6.


189

10.6.2 Criticisms of Risk-adjusted Returns

From empirical point of view, the risk-adjusted returns which have been used have come under attack for the following reasons:

Firstly, the calculation depends on the validity of CAPM;

Secondly, an inappropriate risk-free rate used may result in different measurement; and

Thirdly, the result is unable to differentiate luck from skill statistically.

MARKET TIMING AND STOCK SELECTION

As mentioned in above regarding the skills of fund managers. But what kind of skills are we talking about? In the following section, we will discuss in details what constitute a good market timer.

10.7.1 Market Timing

A good market timer structures a portfolio to have a relatively high beta when the market is expected to rise and low beta when the market is expected to drop. In other words, the market timer wants to do the following strategy: First, hold a high beta portfolio when R R

M f

Second, hold a low beta portfolio when R R

M f

If the fund manager really has good timing abilities (good and accurate forecasts of market movements), then the portfolio will do better than a benchmark

10.7

1. Can you interpret the meaning of a positive alpha of 2.6?

2. What is a systematic risk?

SELF-CHECK 10.2


190

portfolio that has a constant Beta (that is equal to the average Beta of the timerÊs portfolio).

Figure 10.2: Market timing skills and alpha Figure 10.2 indicates that the relationship between the portfolioÊs excess returns and the marketÊs excess return was not linear. The exhibit suggests that the portfolio consisted of high-Beta securities during periods when the market return was high and low-Beta securities when the market dropped. In this case, it appears that the investment manager successfully identified market timing (alpha is positive).

10.7.2 Stock Selection

Figure 10.3 indicates that the relationship between the portfolioÊs excess returns and the marketÊs excess return was linear. This result suggests that the portfolioÊs Beta was, roughly speaking, the same during the entire period under consideration. In this case, it appears that the investment manager successfully identified and invested in some underpriced securities (alpha is positive).


191

Figure 10.3: Stock Selection Skills and Alpha

We have discussed the importance of performance evaluation and how portfolio return is measured. Beside, it also explains the formula that use NAV as a way of measurement.

In benchmarking emphasises that comparison of different funds must be made according to the same risk profile;

A new series of indices has been launched in 2006. It is a joint effort by Bursa Malaysia and FTSE, a company based in the United Kingdom.

(Refer the website: http://www.ftse.com/)

There are three measurements for portfolio. Which are Sharpe ratio, TreynorÊs measure and JensenÊs Alpha.


192

Benchmarkin Benchmark indice Dollar-weighted returns method Indice Institutional investor

JensenÊs alpha Time-weighted returns method TreynorÊs measure Sharpe ratio

1. What are the two important guidelines when comparing funds? 2. If your portfolio has foreign stocks, what particular risk your portfolio has? 3. Why do you think Bursa Malaysia must introduce new indices? 4. In Malaysia, the most frequent used benchmark portfolios are? 5. Why fund managers are particular about correlation of benchmarks? 6. What are the criticisms of risk-adjusted returns? 7. Explain the strategy used by market timer? 8. Explain how stock selection contributes to the Alpha of the portfolio?

Fund Return (percent) Standard deviation (percent) Beta

ABC 12 18 0.7 XYZ 19 25 1.3 KLCI

(Market Index) 15 20 1

1. Assuming the risk free rate is 7 percent, calculate Sharpe ratios for ABC,

XYZ and KLCI. 2. Compare the performance of ABC and XYZ relative to market index based

on answer from no. 1.


193

3. Assuming the risk free rate is 7 percent, calculate TreynorÊs ratio for ABC, XYZ and KLCI.

4. Contrast the performance of ABC and XYZ based on answer from no. 3. 5. What are the differences between the two measurement? 6. If the actual returns realised from ABC and XYZ funds are 12 and 19

percent respectively, given that the market return is 15 percent and beta is 0.7 and 1.3, calculate the expected return for both funds?

7. Calculate the differential return or alpha value for ABC and XYZ funds. 8. Comment on the alpha value of ABC and XYZ funds.

ANSWERS

194

Answers TOPIC 1: INTRODUCTION TO FINANCIAL MARKET

AND SECURITIES Self-Test 1

1. Individual, households, firms and governments

2.

Demand and supply curve of funds for a financial market

Economic agents with surplus of funds will supply the funds. Economic agents with deficit of funds will borrow the funds. There will be an equilibrium of supply and demand at interest i and q amount of funds in the financial market.

3. Individual and household. 4. Investors can be classified into retail and institutional investors. Another

way is fo classify them into local and foreign investors. 5. Institutional investors are commercial banks, investment banks, pension

funds, insurance companies, asset management companies and government linked organisations such as Permodalan Nasional Berhad (PNB) and Khazanah.

6. Hot money is portfolio investments that are short to medium in nature. 7. Different types of financial markets are money market, capital market,

derivative market and foreign exchange market.

Demand Supply

i

Fund

ANSWERS 195

Self-Test 2

1. Financial institutions offer financial instruments to investors. When investors buy or put monies into these instruments, they become the financial assets to the investors.

2. Various types of financial instrument are (i) debt, (ii) cash and cash-

equivalent, (iii) equity (iv) derivatives (v) commodity and (vi) precious metal.

3. They are the asset management companies, independent trustee and unit

holders. 4. They are Securities Commission Act (1993) and Securities Industry Act

(1983). 5. The objective of cmp are:

Address weaknesses in the capital market that were highlighted by the financial sis;

Provide a strategic road map to facilitate future business development; and

Assist in creation on an efficient and competitive capital market. 6. Three. 7. Within equity funds, there are aaggressive growth funds, index funds and

International equity funds. 8. Regulators, fund managers and analyst.

TOPIC 2: RISK AND RETURN

Self-Test 1

1. Risk is defined as the uncertainty of future outcomes. Often it is stated as the probability having unfavorable outcome to the investors.

2. Market risk, Liquidity risk, Credit risk, Operation risk, Systemic risk,

Currency risk

ANSWERS

196

3. The main idea of portfolio theory is attempting to reduce portfolio risk by having different combination of financial assets with different correlation coefficients.

4. Investment risk is a general concept. It can take the meaning of market risk, liquidity risk or credit risk.

Portfolio risk refers specifically to the risk of portfolio i.e. the risk when we

combine different financial assets or securities. 5. In view of uncertainties, the most often used measure of location is the

mean or expectation. The mean is defined as:

N

iii XXE

1

Pr)(

Pr is the probability of random events, X is the possible Event outcomes. The mean weights each event by its probability, then sums all events.

6. If investors and managers can measure and price risk correctly, then:

(a) Investors value risky assets;

(b) There will be better allocation of resources in the economy;

(c) Investors are better at allocating their savings to various types of risky securities;

(d) Managers better-off allocating shareholdersÊ (and creditorsÊ) funds among scarce capital resources.

7. The standard deviation is a measure of (downside) risk. 8. Underlying the concept of portfolio theory, investors are assumed to be risk

averse. It is said that investors demand returns to compensate for their risk taking activity, of which is known as risk premium.

Self-Test 2

1. The expected return is 48 percent based on the excel worksheet below.

Note:

Step (1): Using equation (2-3) in the text, the return in column 3 equals to end of return multiply with probability in each row.

Step (2): Sum up column 3. The total is 48.

ANSWERS 197

End of Period Probability ReturnReturn

30 0.10 3.0040 0.30 12.0050 0.40 20.0060 0.10 6.0070 0.10 7.00

Total: 48.00

2. The variance is 116 percent as shown in the excel worksheet below.

Note:

Step (1): Using equation (2-4) in the text, calculate the deviation in column 4 equals to returns in each row (column 3) minus the mean 48 (bottom of column 3)

Step (2): In column 5, squared all the values from column 4 to get the deviation squared.

Step (3): In column 6, multiply column 5 with column 2 to get the product.

Step (4): Sum up column 6. The total is 116.

End of Period Probability Return Deviation Deviation ProductReturn squared

30 0.10 3.00 -18.00 324.00 32.440 0.30 12.00 -8.00 64.00 19.250 0.40 20.00 2.00 4.00 1.660 0.10 6.00 12.00 144.00 14.470 0.10 7.00 22.00 484.00 48.4

48.00 116 3. Using equation (2-4) in the text, the squared root of 116 is 10.77 percent.; 4. When we consider a combination of two or more securities, we need to

measure the co-movements between the different securities. Covariance is a measure on how returns of different securities move in relation to each other.

If A and B have positive covariance, both will move in the same direction. If A and B have negative covariance, both will move in opposite directions. 5. One important result is the following:

Var(X + Y) = Var(X) + Var(Y) + 2Cov(X,Y) (2-10)

ANSWERS

198

If X and Y are independent then:

Var(X μ Y) = Var(X) + Var(Y)

Var(aX μ bY) = a2Var(X) + b2Var(Y), where a and b are constants. 6. If covariance is divided by the product of the standard deviation of security

x and y will give a standardised measure called coefficient correlation

( , )xy

x y

Cov X Yr

s s

Where

xyr = Coefficient of correlation between x and y.

xyCov = Covariance between x and y.

xs = Standard deviation of x.

ys = Standard deviation of y. 7. Year Rx Deviation Ry Deviation Product

Rx- Ry-1 10 -4 17 5 -202 12 -2 13 1 -23 16 2 10 -2 -44 18 4 8 -4 -16

14 12 -42xR yR

yRxR

[ ][ ]

4210.5

4

x x y y

xy

R R R RCov

N

8.

( , )

10.5

3.65 3.92

0.734

xy

x y

Cov X Yr

s s

ANSWERS 199

TOPIC 3: PORTFOLIO THEORY AND DIVERSIFICATION

Test 1

1. An efficient portfolio is a portfolio offering the highest expected return for a given level of risk or the lowest level of risk for a given level of expected return. In trying to create an efficient portfolio, an investor should be able to put together the best portfolio possible, given his risk disposition and investment opportunities. When confronted with the choice between two equally risky investments offering different returns, the investor would be expected to choose the alternative with the higher return. Likewise, given two investment vehicles offering the same returns but differing in risk, the risk-averse investor would prefer the vehicle with the lower risk.

2. The return of a portfolio is calculated by finding the weighted average of

returns of the portfolioÊs component assets:

1

n

p j jj

r w r

where n =� number of assets, wj weight of individual assets, and rj average returns.

The standard deviation of a portfolio is not the weighted average of component standard deviations; the risk of the portfolio as measured by the standard deviation will be smaller. It is calculated by applying the standard deviation formula to the portfolio assets, rather than just the returns for one asset:

2

1

( ) ( 1)n

p pi

s r r n

3. The correlation between asset returns is important when evaluating the effect of a new asset on the portfolioÊs overall risk. Once the correlation between asset returns is known, the investor can choose those that, when combined, reduce risk.

(a) Returns on different assets moving in the same direction are positively correlated; if they move together exactly, they are perfectly positively correlated.

(b) Negatively correlated returns move in opposite directions. Series that move in exactly opposite directions are perfectly negatively correlated.

ANSWERS

200

(c) Uncorrelated returns have no relationship to each other and have a correlation coefficient of close to zero.

4. Diversification is a process of risk reduction achieved by including in the

portfolio a variety of vehicles having returns that are less than perfectly positively correlated with each other. Diversification of risk in the asset selection process allows the investor to reduce overall risk by combining negatively correlated assets so that the risk of the portfolio is less than the risk of the individual assets in it. Even if assets are not negatively correlated, the lower the positive correlation between them, the lower the resulting risk.

5. Diversifiable (unsystematic) risk is the part of an investmentÊs risk that the

investor can eliminate through diversification. Also called firm-specific risk, this kind of risk can be eliminated by holding a diversified portfolio of assets.

6. Non diversifiable (systematic) risk refers to events or forces such as war,

inflation, or political events and effects all investments. Non diversifiable risk, which cannot be eliminated by holding a diversified portfolio, is considered the only relevant risk. This is because the „smart‰ investor is expected to remove unsystematic risk through diversification. Hence the market will reward an investor for only the systematic risk.

7. International diversification can provide the benefits of higher returns and

reduced risk. However, whether an individual investor ultimately benefits from this kind of diversification depends on factors such as resources, goals, sophistication, and psychology of the investor

8. International diversification can be achieved by investing directly abroad in

foreign currencies securities. International diversification can also be achieved domestically in the Malaysia by investing in mutual funds that invest in foreign markets.

ANSWERS 201

Self-Test 2

Month ABC Berhad (RABC)

XYZ Berhad (RXYZ)

)( ABCABC RER )( XYZXYZ RER

[ )( ABCABC RER ]

x [ )( XYZXYZ RER ]

1 -0.04 0.07 -0.057 0.060 -0.003 2 0.06 -0.02 0.043 -0.030 -0.001 3 -0.07 -0.1 -0.087 -0.110 0.010 4 0.12 0.15 0.103 0.140 0.014 5 -0.02 -0.06 -0.037 -0.070 0.003 6 0.05 0.02 0.033 0.010 0.000

Sum 0.10 0.06 0.0222 1. 0167.06/10.0)( ABCRE (Refer to the last row of column two) 01.06/06.0)( XYZRE (Refer to the last row of column three)

2. 06549.00043.06/0257.0 ABC

08287.0006867.06/04120.0 XYZ 3. Covariance, COV XYZABC , = 1 /6 (0.0222) = 0.0037

4. Correlation, )08287.0)(06549.0(

0037.0, XYZABC = 0.682

5. Since the correlation of these two stocks is positive, they will move in the

same directions. Risk of the portfolio cannot be reduced if they are combined in portfolio. Hence, there will be no diversification effect if we combine them.

ANSWERS

202

6. 15.0)( 1 RE E( )1 = 0.10 5.01 w

20.0)( 2 RE E( )2 = 0.20 5.01 w

175.0)20.0(5.0)15.0(5.0)( portfolioRE

2,1r =0.40

)40.0)(20.0)(10.0)(5.0)(5.0(2)20.0()5.0()10.0()5.0( 2222 p

= 004.001.00025.0

= 0.12845 7. 2,1r = 60.0

)60.0)(20.0)(10.0)(5.0)(5.0(2)20.0()5.0()10.0()5.0( 2222 p

= 006.001.00025.0

= 0.08062

8.

As shown in the above risk-return graph, the negative correlation

coefficient between two assets has enabled the risk to be reduces while maintaining the expected return at the same level.

ANSWERS 203

TOPIC 4: EFFICIENT FRONTIER AND ASSET ALLOCATION

Self-Test 1

1. The more risk-averse you are, the more the expected return you demand for an extra risk.

2. y = (10-4)/(0.01*5*142) = 0.61 Therefore you should invest 61% of your money in portfolio X and 39% in

T-bills.

0.61*70% = 42.7% bonds

0.61*30% = 18.3% stocks

and 39% T-bills 3. (a) Using the equation for an optimal risky portfolio, the weights of

bonds and stocks are found to be 47% and 53 % respectively and E(rp) = 0.47*12% + 0.53*20% = 16% p = 42% (b) Sp = (16 4)/42 = 0.29 4. Slope = (12 4)/20 = 0.4 5. Considering the slope joining risk-free rate and your portfolio choice, we

have:

SlopeS&P500 = (12 4)/20 = 0.4

SlopePortfolio = (15 4)/25 = 0.44

Therefore Portfolio A is better. 6. Investment D. Investment B has a higher return but smaller risk.

ANSWERS

204

7.

Portfolio C is the optimal risky portfolio because it has the highest reward

to variability ratio. 8.

Asset 1 Asset 2

Expected return 12% 8%

Standard deviation 10% 5%

The correlation coefficient of returns between Asset 1 and Asset 2 is 0.40 and the return on risk-free rate is 4%.

The covariance of returns between Asset 1 and Asset 2 (Cov1, 2) = 1,212 = (0.40)(10)(5) = 20

(a) The optimal weights for w1 and w2:

2,1f2f112

f222

f1

2,1f222

f11

]Covr)E(rr)[E(r]r)[E(r]r)[E(r

]Covr)[E(r]r)[E(rw

and w2 = 1 w1 Substituting the data in the above table, the solution is:

20)48412(100)48(25)412(20)48(25)412(

w1

w2 = 1 0.33 = 0.67

ANSWERS 205

(b) The expected return of the portfolio: 0.33(12%) + 0.67(8%) = 3.96% + 5.36% = 9.32%

(c) The standard deviation of the portfolio: 2 = (0.33)2(10)2 + (0.67)2(5)2 + 2(0.33)(0.67)(20) 2 = 10.89 + 11.2225 + 8.844 = 30.9596

off) (rounded 564.59596.30

(d) The slope of CAL or the reward-to-risk ratio:

off) (rounded 956.0564.5

432.9SP

Self-Test 2

1. The efficient frontier is the site of all efficient portfolios (those with the best risk-return tradeoff). All portfolios on the efficient frontier are preferable to the others in the feasible or attainable set.

2. Plotting an investorÊs utility function or risk indifference curves on the

graph with the feasible or attainable set of portfolios will indicate the investorÊs optimal portfolio·the one at which an indifference curve meets the efficient frontier. This represents the highest level of satisfaction for that investor.

3. The two kinds of risk associated with a portfolio are diversifiable (or

unsystematic) risk and nondiversifiable (or systematic) risk. Diversifiable (unsystematic) risk is the risk unique to each investment vehicle that can be eliminated through diversification, by selecting stocks possessing different risk-return characteristics. Nondiversifiable risk is possessed by every investment vehicle. It is the risk that general market movements will alter a securityÊs return. The total risk of a portfolio is the sum of its nondiversifiable and diversifiable risk. A fully diversified portfolio will possess only nondiversifiable risk.

4. Relevant risk is this type of risk that represents the contribution of an asset

to the risk of the portfolio. It is also known as Nondiversifiable risk possessed by every investment vehicle. One cannot eliminate nondiversifiable risk through diversification. Beta measures only the nondiversifiable, or relevant, risk of a security or portfolio.

5. Beta is an index that measures the expected change in a securityÊs or

portfolioÊs return relative to a change in the market return. For example, if a security has a beta of 2.0 and the market return moves up by 10 percent, the

ANSWERS

206

security return increases by 2.0 times that amount·that is, 20 percent. Typical beta values fall between 0.5 and 1.75. The portfolio beta is the weighted average of the betas of the individual assets in the portfolio.

6. The feasible or attainable set of all possible portfolios refers to the risk-

return combinations achievable with all possible portfolios. It is derived by first calculating the return and risk of all possible portfolios and plotting them on a set of risk-return axes as shown in the diagram below.

7. Modern portfolio theory (MPT) is based on the use of statistical measures

including mathematical concepts such as correlation (of rates of return) and beta. Combining securities with negative or low positive correlation reduces risk through statistical diversification. By analysing securities using correlation and beta (which is a statistical measure of the relative volatility of a security or portfolio return as compared to a broadly derived measure of stock market return), the investor attempts to create a portfolio with minimum diversifiable risk that provides the highest return for a given level of acceptable diversifiable risk.

8. Modern portfolio theory requires diversification in order to ensure

satisfactory performance. Hence, from the perspective of individual investor, he or she should

(a) Determine how much risk he or she is willing to bear.

(b) Seek diversification among different types of securities and across industry lines, paying attention to the correlation of returns between securities.

ANSWERS 207

(c) Using beta, assemble a diversified portfolio consistent with an acceptable level of risk.

(d) Evaluate alternative portfolios in order to make sure that the chosen portfolio provides the highest return for the given level of acceptable risk.

TOPIC 5: CAPITAL ASSET PRICING MODEL

Self-Test 1

1. Beta is a measure of systematic or non-diversifiable risk. It is found by relating the historical returns on a security with the historical returns for the market. In general, the higher the beta, the riskier the security. The relevant risk measured by beta is the non-diversifiable risk of an investment. It is relevant since any intelligent investor can eliminate unsystematic risk by holding a diversified portfolio of securities.

2. The market return is typically measured by the average return of all stocks

or large sample of stocks. In our example, KLCI as a broad index is used to measure market return. The beta for the overall market is the benchmark beta i.e. 1.0.

3. The beta and other betas are viewed in relation to this benchmark. The

positive or negative sign on a beta indicates whether the stockÊs return changes in the same direction as the general market (positive beta) or in the opposite direction (negative beta). In terms of the size of beta, the higher the stockÊs beta, the riskier the security.

Stocks with betas greater than 1.0 are more responsive to changes in market returns, and stocks with betas less than 1.0 less responsive than the market.

4. Betas are typically positive and range in value between 0.5 and 1.75. Most

securities have positive betas. This means that the returns on most stocks move in a direction (though not in magnitude) similar to the market as a whole. This is quite intuitive to understand as macro economic factors affect most securities in a similar manner. Hence the betas tend to be positive.

ANSWERS

208

5. The capital asset pricing model (CAPM) links together risk and return to help investors make investment decisions. It describes the relationship between required return and systematic risk, as measured by beta. The equation for the CAPM is:

[ ( )]i F m Fr R b r R

As beta increases, so does the required return for a given investment. The risk premium, [b (rm RF)], is the amount by which return increases above the risk-free rate to compensate for the investmentÊs nondiversifiable risk, as measured by beta.

6. The security market line (SML) is a graphic representation of the CAPM

and shows the required return for each level of beta.

The SML clearly shows that as the beta (i.e. the systematic risk) increases, so does the required rate of return. Any point along the SML is considered as the equilibrium rate of return.

The security market line (SML)

7. CAPM provides only a rough forecast of future returns, because it is based

on historical data. Investors using CAPM typically adjust return forecasts for their expectations of future returns.

8. The coefficient of determination (R2) is used to statistically identify the

relevance of a beta coefficient. It indicates the percentage of an individual securityÊs return that can be explained by its relationship with the market return. Securities that are highly correlated with the market will have betas with high R2 values.

ANSWERS 209

Self-Test 2

1. Required rate of return for ABC stock E(Ri) = Rf + (RM- Rf) = 0.10 + 0.85 (0.14-0.10) = 0.134

Required rate of return for XYZ stock E(Ri) = Rf + (RM- Rf) = 0.10 + 1.25(0.14-0.10) = 0.150

Required rate of return for PQR stock E(Ri) = Rf + (RM- Rf) = 0.10 +(-0.20) (0.14-0.10) = 0.092 2. Use of beta: Change in security return = Beta change in market return

(a) Security A return 1.4 13.2% 18.48% Security B return 0.8 13.2% 10.56% Security C return 0.9 13.2% –11.88%

(b) Security A return 1.4 –10.8% –15.12% Security B return 0.8 –10.8% –8.64% Security C return 0.9 –10.8% 9.72% (c) Security A is the most risky. It has the highest relevant risk, as

determined by the beta values and the greater changes in security AÊs return for a given change in the market return. Security C could be called defensive since it moves in the opposite direction from the market (its return increased when the market return fell and vice versa). Security B is the least risky since its return is least responsive (regardless of direction) to changes in the market return.

3. Capital Asset Pricing Model: ri = RF [bi (rm – RF)]

Investment ri RF � [bi �(rm �RF)]

A 8.9% �= 5% [1.30 � (8% 5%)]

B 12.5% �= 8% [0.90 � (13% 8%)]

C 8.4% �= 9% [ 0.20 � (12%

9%)]

D 15.0% �= 10% [1.00 � (15% 10%)]

E 8.4% �= 6% [0.60 � (10% 6%)]

ANSWERS

210

4. Given that the risk-free rate is 7% and the market return is 12%, Asset class

E is the most risky because it has the highest beta, 2.00. Asset class D, with a beta of 0, is the least risky.

5. Capital Asset Pricing Model: ri = RF [bi (rm – RF)]

Investment r RF [bi (rm – RF)]

A 14.5% = 7% [1.50 (12% – 7%)]

B 12% = 7% [1.00 (12% 7%)]

C 10.75% = 7% [0.75 (12% – 7%)]

D 7% = 7% [0.0 (12% - 7%)

E 17% = 7% [2.00 (12% – 7%)] 6. The figure below shows the security market line (SML).

ANSWERS 211

7. (a) and (b)

8. (a) Portfolios B, J, F, C and H lie on the efficient frontier. These portfolios

are the efficient portfolios, those that provide the best tradeoff between risk and return (the highest return for a particular risk level or the lowest risk for the specified level of return). These portfolios dominate because all those to the left of the frontier are unattainable and all those to the right of the frontier are not desirable because they are not efficient.

(b) By plotting an investorÊs utility function or risk-indifference curves,

which show those risk-return combinations for which an investor would be indifferent, on the efficient frontier graph, the investor can determine the optimal portfolio. This portfolio would be the one that occurs where an indifference curve meets the efficient frontier and represents the highest level of satisfaction for that investor for this set of portfolios.

ANSWERS

212

TOPIC 6: THE ARBITRAGE PRICING MODEL APT

Self-Test 1

1. Arbitrage Pricing Theory is a new approach to explain the pricing of financial assets. It is based on the law of one price i.e. two items that are similar must be sold at the same price.

2. (a) The existence of homogeneous expectation among investors; and

(b) The existence of the process generating security returns. 3. The steepness of the slope reflects the sensitivity of stock to the changes in

the factor. 4. The general form is

ijijiiii eIbIbIbaR ...2211

Where

ia = the expected level of return for stock i if all indices have a value of zero

jI = the value of the jth index that impacts the return on stock i

ijb = the sensitivity of stock iÊs return to the jth index

ie = a random error term with mean equal to zero and variance equal to 2ei

All indices are assumed to be uncorrelated with each other. 5. The empirical issues of APT Model are the testability of APT and

determination of number of APT factors. 6. APT is used in passive management, active management and portfolio

evaluation. 7. Generally, APT differs from CAPM in a few aspects:

(a) APT recognises that there are other factors than market index that can have effect on securities returns.

(b) APT is a more general model as it has many factors as compared to CAPM with only one factor.

(c) APT has fewer assumptions than CAPM.

ANSWERS 213

(d) The focus of APT is not on market portfolio, but rather portfolio which is sensitive to other macroeconomic factors such as inflation or industrial production.

Self-Test 2

1. Inflation, Industrial production, bond risk premium and Interest rates.

2. Inflation reduces the nominal gain realised from investment.

3. Indexing.

4. Index funds.

5. Examples like firm size or book-to-market ratios.

6. An empirical version of the APT where the investor chooses the exact number of the common risk factors used to describe an assetÊs risk-return relationship.

7. APT model does not require to have:

Investors have quadratic utility functions.

Security returns are normally distributed.

The market portfolio contains all securities and is mean variance efficient.

8. ER = fR + 11F + 22 F = 0.06 + (0.5)(0.02) + 2 (0.01) = 0.09 or 9%.

TOPIC 7: EFFICIENT MARKETS HYPOTHESIS

Self-Test 1

1. Information flow in these advanced markets is faster. In addition, the trading system is also more efficient with the use of modern telecommunication technology.

2. EMH is based on expected return theory. It can be denoted by jttitjtitj pREpE )]|(1[)|( ,, (7.1)

ANSWERS

214

Where : E is the expected value operator; jtp is the price of security j at time t; ,j t ip is random variable at time t; ,j t iR is the one-period percentage return; t is a general symbol for information set. 3. The third type is strong efficiency. This is the strongest form which states

that all information in a market, whether they are private or public information, will be reflected in the stock price. No one can have excess returns in these markets, even insider information cannot give investors any advantage.

4. Fair value is the amount at which an asset could be exchanged or a liability

settled, between knowledgeable, willing parties in armÊs length transaction. 5. Investors must begin to think the market is inefficient and possible to beat.

Investment strategies intended to take advantage of inefficiencies are actually the fuel that keeps the market efficient.

6. Weak form efficiency states the stock prices only reflect its own historical

prices. Semi-strong form states that stock prices reflect its own historical prices and also public information.

7. Sufficient conditions for capital market efficiency are:

(i) There are no transaction costs in trading securities;

(ii) All available information is costless to all market participants; and

(iii) All participants agree on the implications of current information for the stock price.

8. In real practice to have costless information available to all participants is

not what something we can observe. In addition, the not all participants may agree on the implications of current information for the stock price.

Self-Test 2

1. Runs test, Von NeumannÂs ratio test and Ljung-Box Q Test. 2. Event studies, determination of event date and calculation of abnormal

returns (AR) and cumulative abnormal returns (CAR). 3. H0: The stock returns are independent.

ANSWERS 215

H1: The stock returns are not independent. 4.. This field argues that people are not nearly as rational as stated by

traditional finance theory. 5. (a) There are no transaction costs in trading securities;

(b) All available information is costless to all market participants; and

(c) All participants agree on the implications of current information for the stock price.

6. In real practice to have costless information available to all participants is

not what something we can observe. In addition, the not all participants may agree on the implications of current information for the stock price.

7. This is because when strong form hypothesis is valid with regards to

private information, private information is quickly reflected into the stock price. Hence, investment analysts are not able to have superior returns based on their private information.

8. Market anomalies are January effect, turn of the month effect, Monday

effect, etc. January effect states that stocks in general have high historically generated

abnormally high returns during the month of January. Turn of the month effect states that stocks consistently show higher returns

on the last day and first four days of the months. Monday effect shows that Monday tends to be the worst day to invest in

the stock market. Both of these phenomenon pose a challenge to EMH.

TOPIC 8: FUNDAMENTAL ANALYSIS AND SECURITY SELECTION

Self-Test 1

1. From the context of portfolio investment management, fundamental analysis will enable the fund manager to have a sense of direction of the economy. Using the top-down approach, fund manager will be able to select stock or company that perform well in the given industries and

ANSWERS

216

macroeconomic environment. Within these context, forces of supply and demand, business cycle and characteristics of specific industries are examined to select the would-be successful company.

2. Top-down approach would enable the investment managers to cast a wider

view as compared to bottom-up approach. Take for an example, during the price hike of crude oil from June to October 2008 to as high as USD147 per barrel, there are many potential companies in the oil and gas sector in Malaysia. A top-down approach would enable the investment managers to view every potential stock in oil and gas sector rather than concentrating on just one or two companies in the sector.

3. Economic indicator such as CPI is a very useful tool in portfolio investment

analysis. CPI will indicate whether inflation rate is increasing or decreasing in a given period. High inflation rate would trigger further increase of interest rate by Central Bank. Higher interest rate will cause the value of bond in the portfolio to fall. In anticipating of this, investment managers can have lesser weight of bonds in their asset allocation.

4. Economic analysis enables demand forecasting of certain product to be

conducted. For example, during the period between 1993 to 1996, fundamental analysis will enable us to forecast the economic boom, there are more construction projects and hence there are more demand for building materials. Therefore, investing in stocks of building materials companies is a right decision during this period.

5. Stage 1: The initial stage of the industry. Investors are not familiar with the

new industry. The industry is new and untried so the risk in investing in this new industry is very high, especially the financial leverage risk.

Stage 2: The rapid expansion of the industry. During this stage, product acceptance is spreading and investors can foresee the industryÊs future more clearly. Economic variables have little to do with the industryÊs overall performance during this stage. As a result, investors will be interested in investing almost regardless of the economic condition.

Stage 3: The mature stage. During this stage, most industries do not experience rapid growth for a long period. Most eventually slip into the category of mature growth. However, during this stage, investors must take into account the economic situation.

Stage 4: This is the last stage of the industry; the industry is either stable or in decline. During this stage, the demand for the industryÊs products is diminishing, and firms are leaving the industry since profits are shrinking in the decline phase. Furthermore, the investment opportunities are almost nonexistent, so investors seek only dividend income. In reality, few

ANSWERS 217

companies reach this stage because they try to introduce product changes and to develop other product lines that will help to continue mature growth. Avoiding this stage is obviously a concern for most investors.

6. Share price is determined or valued based on the present value of its future

dividends. Hence, a stock that can provide streams of future cash inflow from future profitable projects will have higher price than other stock assuming similar market capitalization and risk. From the projected dividends, we can value the stock using different models such as the dividend discount model (DDM), the Gordon growth model or multi-stage dividend discount model.

7. Dividend Discount Model (DDM) is a general model. It calculates the value

of a share of stock as the present value of future dividends. The equation is:

Value per share =

1 )1(tt

t

r

DPS

Since a share of stock has no finite end, the dividends go forever. Hence the weakness of this general model is that the dividends have to be estimated

over an infinite number of periods. The idea from DDM form as the basis of more relevant models in the future.

8. Dividend Discount Model (DDM) serves as the basis where Gordon

Growth Model is discussed. In DDM, we need to estimate dividends over an infinite number of periods. In contrast, Gordon growth model assumes that dividends grow at a constant rate forever. The equation is:

Value per share = gr

DPS

1

DPS1 is the expected dividend per share in one year, r is the shareholdersÊ required rate of return, and g is the constant growth rate in dividends.

Hence, Gordon growth model is also referred as constant dividend

discount model.

Self-Test 2

1. Kps = Dps / Pps, where Dps = the expected dividend per share in one year Dps = $100 x 8%= $8. Hence, Kps = 8 / 85 = 9.4%.

2. Value per share = gr

DPS

06.016.0

00.1 RM10

ANSWERS

218

3. Value per share = gr

gDPS t

)1(0 =

06.016.0

)06.1(00.1 1

RM10.60

4. One of the weaknesses of the Gordon growth model is that it assumes a

single constant growth rate in dividends. In order to overcome this not realistic assumption, we can use a multi-stage dividend discount model which can accomodate firms with different growth characteristics.

5. Using constant divident discount model

gPD

k0

1*

k = (3 /30) + 0.11 = 0.21 The market discount rate is 21 percent. 6. When the original stock is priced at RM70 with EPS of RM7, the stock was

trading at 10 times P/E. When the stock price was at RM60 and EPS was at RM5, ABCÊs P/E was increased to 12 times. We can conclude that ABCÊs stock experienced P/E expansion.

7. Required rate of return K = Rf + (Rm-Rf) = 0.06 + 0.9 (0.11-0.06) = 0.105 Dividend Discount Model

Po = )(

)1(0

gk

gD

= 1.40 / (0.105 0.08) = RM56

8. Sustainable Growth Rate , g = ROE * ( 1 dividend payout ratio) g = 75,000 / 450,000 * (1- 35,000 /75,000) = 0.089 or 8.9%

ANSWERS 219

TOPIC 9: MANAGING PORTFOLIOS - ACTIVE AND PASSIVE STRATEGIES

Self-Test 1

1. Limited capital and insufficient information. 2. With the advent of the Internet, individual investors are better informed;

however, they are still less informed than institutional investors 3. Herd behaviour refers to the irrational behaviour of group of investors

whom act in the same direction. For example, these investors keep buying a particular stock although the stock price has exceeded many times of its fair value.

4. Herd behaviour will eventually lead to stock market bubble. One such

example was IT bubbles or dot-com bubbles in 2000-2001. 5. Institutional investors include pension funds, mutual funds, insurance

funds and banks. They have more capital and sufficient information relative to investors. In contrast, they are limited by laws, regulations, rules and constraints, objectives and investment policies of their funds.

6. Two major types are defined benefit and defined contribution. Defined

benefit pension plans promise to pay retirees a specific income stream after retirement. The company contributes a certain amount to the fund each year and the company also takes up the risk of paying the future pension to the retirees. Any shortfall (due to poor performance of the fund) should be compensated for in the future. On the other hand, defined contribution pension plans make no promise on return. The benefits depend on the employeeÊs contribution and the return on investment. The contribution plans are tax-exempted.

7. Active management investment style attempts to add value to the portfolio

by two strategies i.e. selectivity and timing. Selectivity refers to identifying securities or portfolios that are winners (and losers). Timing refers identifying when weights in asset classes should be changed in line with changes in macroeconomic environment.

8. Passive management style is different from other investmnet style

management. It involves buying and holding a well diversified portfolio, typically with the objective of tracking a particular index fund.

ANSWERS

220

Self-Test 2

1. The approaches for individual investors are

(i) Security selection;

(ii) Security selection coupled with asset allocation;

(iii) Security selection coupled with sector selection and asset allocation;

(iv) Market timing; and

(v) Portfolio revision 2. There are three stages for institutional investors when they implement

active portfolio investment strategies. These are planning, implementation and monitoring stages.

3. They are Strategic asset allocation (SAA) and Tactical asset allocation

(TAA). SAA refers to what the investor wants the weights to look like, on average, over the long term. TAA refers to what the investor wants the weights to look like now, given the current conditions in the financial markets.

4. The initial planning stage is of utmost importance to an institutional

investor. There are five steps involved in this stage.

Investor conditions · From the perspective of institutional investors, their clients are small investors. In this case, they need to know the financial situation of their clients. Whether their clients need to invest in marketable or non-marketable assets depends upon the expected liquidation date. The institutional investor needs to know the financial distress of the clients as well as their tolerance for volatility risk.

Market conditions · The institutional investor needs to know the market conditions both in the long term and the short term, for instance how the macroeconomic variables might change in the short term versus the long term. In addition, the movements of interest rates particularly in the short run are the most important market information for their clients.

Investment/speculative policies · This process involves strategic asset allocation as well as speculation strategy such as tactical asset allocation and security selection. I will discuss the framework of strategic asset allocation in greater detail in the next section.

Statement of investment policy · The statement of investment policy includes the objective of the investment, the strategy or investment policies and the constraints of the investment.

ANSWERS 221

Strategic asset allocation · Based on the investment objective, how could the institutional investor allocate assets for investment more strategically? The strategic asset allocation should match exactly with the investment objective set in advance.

5. Full replication as a variation of the buy and hold strategy, all securities in

an index are purchased in proportion to their weights in that index. For example, in a Bursa Malaysia Composite Index portfolio, you would have to buy the 100 constituent stocks according to their market value. What are the disadvantages of this strategy? High transaction costs and the reinvestment risk of dividends cannot be ignored! A good example is the Tracker Fund which tries to track the performance of the Bursa Malaysia Composite Index.

6. The strategy of sampling entails buying only a representative sample of

stocks that comprise the benchmark of an index. That is, the difference between sampling and full replication is that sampling considers a sample of stocks that can represent the movement of the index instead of holding all the constituent stocks. Sampling saves on transaction costs, but it may not closely track the index.

7. As part of active management of bond portfolio management, the portfolio

manager believes he can predict whether or not the future interest rate level will change the portfolioÊs sensitivity to interest rate changes.

If the interest rate is expected to increase, he will reduce the duration, and vice versa. How should the duration be adjusted? Think about this; you should be able to come up with the answer.

8. The duration of a portfolio can be changed by swapping bonds in the portfolio for new bonds. Please refer to the reading for details. The key to this strategy is whether you have the ability to forecast the direction of the interest rate. The reading also discusses what will happen if the interest rate moves in the opposition direction.

The pros of this strategy are that we can use Excel to compute the correlation coefficient of two assets within a given period, and we only add stocks with negative correlation to the portfolio. The cons of this strategy are that it depends on historical prices, and during economic shocks such as Asia financial crisis and Subprime crisis, it is noticed the correlation structure of assets do not hold. Hence, it is important for portfolio managers to run stress test on their portfolios on different economic scenarios before making the final decision on adding the stock to their portfolios.

ANSWERS

222

TOPIC 10: EVALUATION OF PORTFOLIO PERFORMANCE

Self-Test 1

1. Compare fund with the same investment objectives and fund policies. 2. Foreign currency risk. 3. New Indices are important so as to provide more benchmarks for fund

managers. This will promote more investment products by creating funds for different type of investors with different risk profiles and investment objectives.

4. Bursa Malaysia Composite Index (formerly known as KLCI)

FTSE Bursa Malaysia EMAS Index

FTSE Bursa Malaysia Small Cap Index

FTSE Bursa Malaysia Fledgling Index

FTSE Bursa Malaysia EMAS Shariah Index

FTSE Bursa Malaysia Second Board Index

FTSE Bursa Malaysia MESDAQ Index

5. As we have studied earlier in Topic 2 and 3, optimal portfolios can only be

made if the stocks in the portfolio have negative correlation. In similar line of argument, correlation of benchmark will provide guidance on whether there is co-movement of indices or otherwise.

6.

Firstly, the calculation depends on the validity of CAPM;

Secondly, an inappropriate risk-free rate used may result in different measurement;

and Thirdly, the result is unable to differentiate luck from skill statistically.

7. A good market timer structures a portfolio to have a relatively high beta

when the market is expected to rise and low beta when the market is expected to drop.

ANSWERS 223

8. The figure below indicates that the relationship between the portfolioÊs excess returns and the marketÊs excess return was linear. In this case, it appears that the investment manager successfully identified and invested in some underpriced securities (alpha is positive).

Self-Test 2

1. ABC = 12- 7 / 18 = 0.277 XYZ = 19 -7 / 25 = 0.48 KLCI = 15-7 / 20 = 0.40

2. Fund XYZ has performed better than the benchmark market index. Fund

ABC has performed worse than the market index. 3. Using Treynor ratios,

ABC = 12-7 / 0.7 = 7.14 XYZ = 19 -7/ 1.3 = 9.23 KLCI = 15 7 / 1.0 = 8.0

4. Fund XYZ has performed better than the benchmark. Fund ABC has

performed worse than the market index. 5. Sharpe ratio is the reward to variability. TreynorÊs measure is reward to

volatility. 6. Expected Return for ABC = 7 + 0.7(15-7) = 12.6 Expected Return for XYZ = 7 + 1.3 (15-7) = 17.4 7. Differential return or alpha value

For ABC = 12-12.6 = -0.6 For XYZ = 19 17.4 = 1.6

ANSWERS

224

8. The negative alpha value for fund ABC indicates inferior performance relative to the market index.

The positive alpha value for fund XYZ indicates superior performance relative to the market index.

Bodie, Z., Kane, A., & Marcus, A. J. (2005). Investments. (6th ed.). USA: Irwin

McGraw-Hill. Elton, E. J., & Gruber M. J. (1995). Modern portfolio theory and investment

analysis (5th ed.) USA: John Wiley & Sons, Inc. Fabozzi, F. J. (2003). Bond markets, analysis and strategies (5th ed.). Upper

Saddle River, NJ: Prentice Hall Press. Fabozzi, F. J. (2003). Bond markets, analysis and strategies (5th ed.). Prentice

Hall Press. Radcliffe, R. C. (1989). Investment: (concepts, analysis, strategy (3rd ed.). Harper

Collins Publishers. Reilly, F. K., & Brown, K. C. (2006). Investment analysis and portfolio

management (8th ed.). Thomson South-Western. Rubinstein, M. (2002). MarkowitzÊs portfolio selection: A fifty-year

retrospective. (Journal of Finance). 57, 1041-1045. Sharpe, W. F., Alexander, G. J., & Bailey J. V. (1999). Investments 6th ed. NJ:

Prentice Hall.

References

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