Portfolio Management and Support System Report of Multi-Disciplinary Project

Submitted to Dr. Wasim A. Khan

Group Members Abdul Arsalan Siddiqui Danish Iqbal Allahwala M. Salman Shahab Syed Mohsin Mazher Syed Umair Saleem

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PREFACE This report has been prepared for Dr. Wasim A. Khan as fulfillment of a partial requirement for our ‘MIS Project’. The objective of preparing this report is to give an insight of the different aspects of our project which we would be trying to cover and methodology we would be applying to prepare our project. For our project we would be following the ‘Portfolio Management Theory’ based on an article written by Harry Markowiz titled ‘Portfolio selection’, which describes how to combine assets into efficiently diversified portfolios. A portfolio is a collection of investments that an investor has made in different propositions. For this purpose a detail study of risk and return of a portfolio is necessary. This report has been prepared to provide a basic understanding of the process of formation of a portfolio with an overall objective of maximizing returns and minimizing risks. In this report we would be looking at the different variables involved in the preparation of a portfolio consideration of which would allow us to analyze the effects of each variable on the individual stocks in the portfolio. The concept of diversification would be applied here that is how much to invest where keeping in mind the expected return and the individual risks involved so be able to maximize the return and minimize the risk of the portfolio. As a requirement of our project we would be to take into consideration the rate of return of individual stocks and the risk associated with them, also important is the understanding and application of the variance and correlation of each stock. Making use of the information gained through these variables we would be able to optimize a portfolio which would eventually lead to an efficient portfolio. Other factors that would be having a bearing over the preparation of an optimized portfolio would be the risk taking propensity of individual investors and the individual security weight in the investment portfolio. With proper analyses and application of all these factors and variables we should be able to achieve optimized portfolio. The use and application of the variables and the methodology described in this report are not to be taken as the best option to optimize a portfolio. The theories discussed are not perfect and complete – no theory is. The content of this report only directs us towards one of the applicable options of optimizing a portfolio. Therefore we have started from a basic level so as to be able to cover as many options as possible and avoid unnecessary complications in our project. However, an elementary knowledge of how the markets works and familiarity with the terms used in the report would be helpful in understanding the project.

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ACKNOWLEDGMENTS The contribution of several individuals towards the preparation of the project and compilation of this report is highly appreciated. First of all we would like to thank Dr. Wasim A. Khan our project instructor for providing us with an opportunity to work on this project, and for his help and guidance at every stage of this report. The teachings of Mr. Ahmed Raza our course instructor for ‘Quantitative methods in Business research’ have been very helpful in understanding and stating the subject matter of this report and in the interpretation and formulation of optimization problem. We would also like to thank Mr. Syed Akbar Ali – Head Research Analyst at MCB Asset Management and Mr. Imran Khan – Head of Research at First capital Investments for their valuable time and sharing their expert opinion and the knowledge of the market with us. Their contributions are highly appreciated.

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TABLE OF CONTENT

EXECUTIVE SUMMARY ........................................................................................... 7

PROBLEM DEFINITION ............................................................................................ 8

PROPOSED SOULUTION........................................................................................... 9

2.1 MODULE I: INVESTMENT SUPPORT SYSTEM (ISS) ................................. 9

2.2 MODULE II: INVESTMENT DECISION SUPPORT SYSTEM (IDSS) ......... 9

2.3 MODULE III: - RETURN AND INVESTMENT MONITORING (RIM) ...... 10

KARACHI STOCK EXCHANGE ............................................................................. 11

3.1 INTRODUCTION OF KSE-100 INDEX ......................................................... 11

3.1.1 Calculation Methodology ........................................................................... 11

3.1.2 Calculating the KSE-100 ............................................................................ 11

3.1.3 Calculating the KSE-100 Index.................................................................. 12

3.2 INTRODUCTION OF KSE-30 INDEX ........................................................... 12

3.2.1 Free-Float Methodology ............................................................................. 13

3.2.2 Base Period ................................................................................................. 13

3.3 KSE 30 INDEX LISTED COMPANIES .......................................................... 14

PORTFOLIO DEVELOPMENT AND MANAGEMENT ......................................... 15

4.1 PORTFOLIO THEORY .................................................................................... 15

4.2 BASIC COMPUTATION REGARDING PORTFOLIO MODEL .................. 15

4.2.1 Return Calculation...................................................................................... 15

4.2.2 Covariance and Calculation of Portfolio Variance .................................... 16

4.2.3 Correlation Matrix ...................................................................................... 17

4.3 BASIS TO DEVELOP A WELL DIVERSIFIED PORTFOLIO ..................... 17

4.3.1 Correlation Coefficient ............................................................................... 17

4.3.2 Dissimilar Price Movements ...................................................................... 17

4.3.3 Diversification ............................................................................................ 17

4.3.4 Effective Diversification ............................................................................ 18

4.3.5 Efficient Frontier ........................................................................................ 18

4.3.6 Efficient Portfolio ....................................................................................... 18

4.3.7 Expected Return ......................................................................................... 18

4.3.8 Risk............................................................................................................. 19

4.3.9 Risk Tolerance............................................................................................ 19

4.3.10 Standard Deviation ................................................................................... 19

4.3.11 Variance Reduction .................................................................................. 19

4.4 OUTCOME OF A WELL DIVERSIFIED PORTFOLIO ................................ 20

4.4.1 Asset Allocation ......................................................................................... 20

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4.4.2 Investment Policy Statement ...................................................................... 20

4.4.3 Optimal Portfolio........................................................................................ 20

4.4.4 Passive Management .................................................................................. 20

2.4.5 Re-Optimization ......................................................................................... 21

SYSTEM DESIGN ..................................................................................................... 22

5.1 USE CASE DIAGRAM .................................................................................... 22

5.2 DATA FLOW DIAGRAM ............................................................................... 23

5.2.2 Level 0 DFD ............................................................................................... 23

5.2.3 Detailed DFD ............................................................................................. 24

5.2.3.1 Detailed DFD of ISS ........................................................................... 24

5.2.3.2 Detailed DFD of Portfolio Calculation ............................................... 25

5.2.3.3 Detailed DFD of Buy/Sell Call Generation......................................... 25

5.3 UML ACTIVITY DIAGRAM .......................................................................... 26

5.3.1 Activity Diagram ISS ................................................................................. 26

5.3.2 Activity Diagram IDSS .............................................................................. 27

5.4 ENTITY RELATIONSHIP DIAGRAM ........................................................... 28

5.4.1 ERD Description ........................................................................................ 28

5.4.1.1 Stock .................................................................................................... 28

5.4.1.2 Sector ................................................................................................... 29

5.4.1.3 Price ..................................................................................................... 30

5.4.1.4 Beta_n_Return ..................................................................................... 30

5.4.1.5 Portfolio ............................................................................................... 31

5.4.1.6 PLP ...................................................................................................... 31

5.4.1.7 Bought_ Stocks ................................................................................... 32

5.4.1.8 Sell_Call .............................................................................................. 32

5.4.1.9 Buy_Call.............................................................................................. 33

5.5 LAYOUT OF FRONTEND .............................................................................. 34

THE PORTFOLIO SELECTION PROBLEM ........................................................... 35

6.1 PROBLEM FORMULATIONS ........................................................................ 35

6.1.1 Minimize Variance Subject To Given Return ............................................ 35

6.1.2 Maximize Return Subject To Given Variance ........................................... 35

6.2 COMBINING THE MODELS.......................................................................... 35

6.2.1 Balancing Risk and Return ......................................................................... 35

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TABLE OF FIGURES

Figure 5.1: Use Case Diagram of the System ............................................................. 22 Figure 5.2: Context Level DFD of the System............................................................ 23 Figure 5.3: Level 0 DFD of the System ...................................................................... 24 Figure 5.4: Detailed DFD of ISS ................................................................................. 24 Figure 5.5: Detailed DFD of Portfolio Calculation ..................................................... 25 Figure 5.6: Detailed DFD of Buy/Sell Call Generation .............................................. 25 Figure 5.7: Activity Diagram ISS ............................................................................... 26 Figure 5.8: Activity Diagram IDSS............................................................................. 27 Figure 5.9: Entity Relationship Diagram .................................................................... 28 Figure 5.10: Layout of Frontend ................................................................................. 34

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EXECUTIVE SUMMARY The objective of this project is to develop an application software, that uses the historic price data of 30 companies listed on KSE, in order to develop an Optimal Portfolio of stocks based Mean Variance Optimization Model that maximizes the return to an investor while satisfying his/her risk taking propensity. The project is concerned about developing an application that facilitates the investor in the selection of optimal combination of assets on their investment portfolio so that they can maximize return on their investments with a given level of risk assumed. The basis of the software is the Mean Variance Optimization Method. The project is executed in two phases; first phase includes the complete understanding of the problem and proposing different solutions. Then different solutions are analyzed in order to get the best possible solution. Once a solution is selected a complete system design is developed including the hardware and software design. First phase of the project includes:

• Understanding portfolio management and development technique • KSE indices basic understanding and calculation methodology • Understanding the optimization model • Modules and their description of proposed system (PMSS) • Collection of price data of 30 stocks for last five years • Preparation of database design • Data entry in the designed database (backend on Microsoft Access)

Second phase of the project is the implementation of the designed database, development of a frontend application, connecting the frontend to the database and the coding of the model. Testing of the entire system will commence on the completion of the implementation process. Second phase of the project will include:

• Calculation of basic inputs to the portfolio calculation model i.e. β, and covariance

• Designing of frontend • Coding of optimization model • Interface development for integration of backend and frontend • Testing

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PROBLEM DEFINITION

“To develop an application software, that uses the historic price data of 30 companies listed on KSE, in order to develop an Optimal Portfolio of stocks based Mean Variance Optimization Model that maximizes the return to an investor while satisfying his/her risk taking propensity” The project is concerned about developing an application that facilitates the investor in the selection of optimal combination of assets on their investment portfolio so that they can maximize return on their investments with a given level of risk assumed. The basis of the software is the Mean variance optimization method. Portfolio theory assumes that for a given level of risk, investors prefer higher returns to lower returns. Similarly, for a given level of expected return, investors prefer less risk to more risk. It is standard to measure risk in terms of the variance, or standard deviation, of return. We measure return as the average annual rate. Therefore, we want to develop an efficient portfolio, that is, one in which there is no other portfolio that offers a greater return with the same or less risk, or less risk with the same or greater expected return. As many of us can imagine, all of the stocks traded in the stock market do not move together. In general the market has been moving up, but at the same time there are stocks that are losing value. There are some stocks that tend to move together, some that move in opposite directions, and others that seem to have no relation to one another. This tendency to move together or opposite can be measured by covariance (or if scaled, correlation). By using the covariance, we can measure the variability or risk in our portfolio. To reduce the volatility of the entire portfolio, it makes sense to include some stocks that move in opposite directions1.

1 http://www-new.mcs.anl.gov/otc/Guide/CaseStudies/port/introduction.html

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PROPOSED SOULUTION The software we are going to develop under this project will be comprise of three modules and will work as described below. 2.1 MODULE I: INVESTMENT SUPPORT SYSTEM (ISS) The module start working with the calculation of beta of individual stock, then it takes input from the user regarding sectors of interest in which he intends to invest. After getting the input from the user, system will automatically retrieve data like target price, beta, current market price and data regarding return potential. Then the system will match return potential with the return cushion (As per business rule) to identify the sectors which has require return potential. After selecting companies with the required return potential the system will calculate the beta of portfolio (proposed) with different combination of stock and calculate the return of those portfolios with beta close to 1. For the no. of proposed portfolio the system will also perform some additional calculations to select the best portfolio for investment. These checks include:

• Market capitalization • Free float of individual stock in the portfolio • Value traded • Impact cost

Exceptions and Options

• User can also rate the companies in sector according to preference • User can also restrict system to not include certain companies in the analysis. • Re-optimization

2.2 MODULE II: INVESTMENT DECISION SUPPORT SYSTEM (IDSS)

• The system will help the investor/manager to monitor the stock prices in order to make decision regarding selling and buying of the stock. The system will generate a sell call/ buy call after analyzing certain sets of a data daily with a frequency of 3 to 5 runs per business day.

• System calculates the difference between the weight of the bought stocks and weight of the stock in the optimal portfolio and with the weightage of the stock defined by the user to generate a sell call.

• If the difference between the target price and the current market price of the stock is reduced to a certain level given by user system will generate a sell call to offload the investment.

• System will also generate a buy call if the user includes a certain stocks in prospective list of purchasing (PLP). The buy call only triggers when the return potential is greater than or equal to return cushion and the stock name is entirely in the PLP.

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• System will also generate sell call for the whole portfolio with preference given to those stocks which close to their target price if the index hits below a certain level to minimize losses.

2.3 MODULE III: - RETURN AND INVESTMENT MONITORING (RIM) This module of the software will build record of the stocks that have been purchased by the investor and also calculate the return of individual stock and portfolio on every sale proceeds. This system will also calculate the return generated from the Fixed Income Investment (Idle Cash). Prospective List of Purchasing This list includes the name of the stocks recommended by Module I to be invested in and also the priority rating .It also provides details about the investment that one can make in particular stocks. Stock on Portfolio: (SoP) The system will have an updated list of SoP when the purchase is made or any sale of stocks is done. This list will provide the investor a quick report of the investment and the weights of investment in the individual sector. Sell Call and Buy Call Sell call and buy call generated by the system is update to the list called TBS i.e. to be sol if the sell call is generated and to the list called TBP i.e. to be purchased if the buy call is generated. These lists will provide quick information to the user (investor/broker) in order to select the stocks for buying and selling.

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KARACHI STOCK EXCHANGE This is the market place where financial investment (normally of long term nature) can be acquired or disposed off. The stock exchange (also referred to as stock market) is where shares and bonds issued by business entities (companies) are traded. There is sub category called the money market which is normally the market for acquiring and disposing of financial investments. Financial investments are normally represented by certificates generally referred to as security. 3.1 INTRODUCTION OF KSE-100 INDEX The KSE-100 index comprises of 100 companies selected on the basis of sector representation and the highest market capitalization. The KSE-100 index was introduced in November 1999 with the base value of 1000 points. These 100 listed companies capture around 80% of the total market share. One company from each sector is selected on the basis of largest market capitalization and the remaining 66 companies are selected on the basis of largest market capitalization in descending order. The primary objective of the KSE100 index is to have a benchmark by which the stock price performance can be compared to over a period of time. In particular, the KSE 100 is designed to provide investors with a sense of how the Pakistan equity market is performing 3.1.1 Calculation Methodology In a very layman term, the KSE-100 index is a basket of price and the number of shares outstanding. Thus, the value of basket is regularly compared to a starting point or a base period. To make the computation simple, the total market value of base period has been adjusted to 1000 points. For making other to understand this computation we take an example. Taking stock A’s share price of Rs. 20 and multiplying it by its total common shares outstanding of 50 million in the base period provides a market value of one billion Rupees. This calculation is repeated for stocks B and C with the resulting market values of three and six billion Rupees, Respectively. The three market values are added up, or aggregated, and set equal to 1000 to form the base period value. All future market values will be compared to base period market value in indexed form. 3.1.2 Calculating the KSE-100 Step 1

Table 1.1: The Base Period Day 1

Stock Share Price (in Pak Rs.) Number of Shares Market Value

(in Rs.) A. 20.00 50,000,000 1,000,000,000.00 B. 30.00 100,000,000 3,000,000,000.00 C. 40.00 150,000,000 6,000,000,000.00

Total Market Capitalization = 10,000,000,000.00 Note: Base Period Value/Base Divisor = Rs. 10,000,000,000.00 = 1000.00

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3.1.3 Calculating the KSE-100 Index Step 2

Table 1.2: Index Value as on Day 2

Stock Share Price (in Rs.) Number of Shares Market Value

(in Rs.) A. 22.00 50,000,000 1,100,000,000.00 B. 33.00 100,000,000 3,300,000,000.00 C. 44.00 150,000,000 6,600,000,000.00

Total Market Capitalization 11,000,000,000.00

11,000,000,000.00 Index = ————————————— = 1.10 * 1000 = 1100

10,000,000,000.00 Thus, the formula for calculating the KSE-100 Index is: Sum of Shares Outstanding x Current Price ——————————————————— x 1000 Base Period Value Or Market Capitalization ————————————— x 1000 Base Divisor The KSE100 Index calculation at any time involves the same multiplication of share price and shares outstanding for each of the KSE100 Index component stocks. The aggregate market value is divided by the base value and multiplied by 1000 to arrive at the current index number. 3.2 INTRODUCTION OF KSE-30 INDEX The primary objective of the KSE-30 Index is to have a benchmark by which the stock price performance can be compared to over a period of time. In particular, the KSE-30 Index is designed to provide investors with a sense of how large company’s scrips of the Pakistan’s equity market are performing. Globally, the Free-float Methodology of index construction is considered to be an industry best practice and all major index providers like MSCI, FTSE, S&P, STOXX and SENSEX have adopted the same. KSE-30 Index is calculated using the “Free-Float Market Capitalization” methodology. In accordance with methodology, the level of index at any point of time reflects the free-float market value of 30 companies in relation to the base period. The free-float methodology refers to an index construction methodology that takes into

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account only the market capitalization of free-float shares of a company for the purpose of index calculation. 3.2.1 Free-Float Methodology Free-Float means proportion of total shares issued by a company that are readily available for trading at the Stock Exchange. It generally excludes the shares held by controlling directors/sponsors/promoters, government and other locked-in shares not available for trading in the normal course. Free-Float calculation can be used to construct stock indices for better market representation than those constructed on the basis of total market capitalization of companies. It gives weight for constituent companies as per their actual liquidity in the market and is not unduly influenced by tightly held large-cap companies. Free-Float can be used by the Exchange for regulatory purposes such as risk management and market surveillance. Free-Float Calculation Methodology: Total Outstanding Shares XXX Less: Shares held by Directors/sponsors XXX Government Holdings as promoter/acquirer/controller XXX Shares held by Associated Companies (Cross holdings) XXX Shares held with general public in Physical Form XXX Free-float XXX 3.2.2 Base Period The base period of KSE-30 Index is June 2005 and the base value is 10,000 index points. This is indicated by the notation 2005 = 10,000. The calculation of KSE-30 Index involves dividing the free-float market capitalization of 30 companies in the Index by a number called the Index Divisor. The Divisor is the only link to the original base period value of the KSE-30 Index. It will keep the Index comparable over a period of time and will also be the adjustment point for all future corporate actions, replacement of scrips etc.

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3.3 KSE 30 INDEX LISTED COMPANIES

Table 1.3: KSE 30 Index Listed Companies

S. No. Symbol Index Weights (%)

Outstanding Shares (million)

Market Capt.

(million)

1 Pak PetroleumXB 12.85 189.03 36605.11

2 Oil and Gas Dev.XD 12.29 370.83 35017.85

3 Fauji Fertiliz 10.52 299.63 29962.66

4 Pak Oilfields 8.41 98.45 23972.54

5 P.S.O. SPOT 7.76 78.99 22115.88

6 Engro Chemical 7.44 117.47 21196.32

7 P.T.C.L.A 7.07 639.06 20130.3

8 Hub PowerXD 6.25 830.34 17819.17

9 Fauji Fert Bin Qasim 2.89 360.93 8221.92

10 UniLever XD 2.86 3.49 8157.67

11 D.G.K.Cement 2.32 167.94 6596.66

12 National Refin.SPOT 1.87 27.11 5314.04

13 Sui South Gas 1.77 222.28 5045.87

14 Shell Pakistan 1.54 14.18 4399.85

15 ICI PakistanXD 1.49 33.47 4250.12

16 Nishat Mills 1.45 88.2 4119.75

17 Attock Refinery 1.36 27.46 3869.59

18 Sui North Gas 1.34 121.24 3808.09

19 Indus MotorXD 1.31 26 3726.28

20 Pioneer Cement 1.08 121.15 3077.25

21 Fauji Cement 1.05 432.95 2987.35

22 Attock Petroleum 1 10.6 2840.16

23 Pak Suzuki 0.7 23.73 1988.4

24 Abbott (Lab) 0.62 15.96 1755.89

25 Bosicor Pakistan 0.59 194.79 1694.68

26 BOC (Pak) 0.57 9.22 1631.89

27 Maple Leaf Cem. 0.54 205.48 1528.79

28 Thal Limited 0.45 10.08 1279.73

29 Pak RefineryXD 0.39 10.74 1112.14

30 Kohat Cement 0.24 32.31 687.45

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PORTFOLIO DEVELOPMENT AND MANAGEMENT 4.1 PORTFOLIO THEORY “If two portfolios have the same expected return, the one with the lower volatility will have the greater compound rate of return.” Both risk is reduced and compound rates of return are enhanced simultaneously2. Modern portfolio theory enables an investor to classify, estimate, and control both the kind and amount of expected risk and return as measured statistically. It is also called “Modern Portfolio Theory” or “Portfolio Management Theory”. Holding securities that tend to move in concert with each other does not lower one’s risk. In other words, the average risk of a portfolio is not the average of the individual component investments of the portfolio if all of their prices move in tandem or in concert with each other. Therefore, what may be perceived to be a low risk portfolio could actually be a high-risk portfolio and vice versa. Diversification reduces risk only when assets are combined whose prices move inversely or at different times in relation to each other.3 4.2 BASIC COMPUTATION REGARDING PORTFOLIO MODEL 4.2.1 Return Calculation In our application various return are to be calculated that will serve as the input to the application in order to calculate the return on the portfolio.

1. Total Return (annual rate of return of individual stock) Total Return represents one of the easiest estimations, which also includes dividends as part of our considerations. The formula for calculating total return is: Total Return = [(End-of-the-Year Investment Value - Beginning-of-the-Year Investment Value) + Dividends] / Beginning-of-the-Year Investment Value Example: An investor purchased a stock for Rs. 6000. At the end of the year the stock is worth Rs. 7500. Therefore, he has an unrealized gain of Rs. 1,500. He was paid dividends of Rs. 260. So, total return is calculated as follows: Total Return = [(7,500 - 6,000) +260] / 6,000 = 0.293 Therefore, the stock of John has a total return of 29.30%.

2. Simple Return Simple return calculations are executed after you have sold the investment. The formula you use to calculate it is: Simple Return = (Net Proceeds + Dividends) / Cost Basis – 1

2 “Portfolio Selection,” H. Markowitz, Journal of Finance, March, 1952, pp. 77-91 3 Asset Allocation for Institutional Portfolios, Mark P. Kritzman, CFA, Business One Irwin, 1990

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The Total Return of individual stocks will help in calculating the return of optimal portfolio and also in the selection of the optimal portfolio as it serve as an input to the portfolio optimizer model. Simple return is used in the calculation of return on the individual stocks held for specific period in the firm’s investment portfolio.

3. Expected Return of portfolio Portfolio return is just the weighted average of the returns of the individual securities in the portfolio. Rp= WA * rA+ WB * rB

In our application weight of individual securities are decided by the portfolio optimizer which in turn returns the overall portfolio return based on the above calculation.

4.2.2 Covariance and Calculation of Portfolio Variance The calculation of the portfolio expected return is a fairly straightforward. But the calculation of the standard deviation and variance of the portfolio is more complicated, because portfolio variability (standard deviation) is not the weighted-average of the variability of the individual assets. Diversification reduces the variability of the portfolio, because the prices of different assets vary differently. The decrease in price of one asset is compensated by the price growth for another. For calculation of the variance σ² and the standard deviation σ of the portfolio return, we first calculate the covariance between assets A and B. Covariance is the measure of how much returns of two assets vary together. This is distinct from variance, which measures how much a single asset varies. The formula for the covariance is4: σ AB = E(RA - rA)(RB - rB) It follows from the formula above, that the covariance of an asset with itself σ11 is its variance σ1². The coefficient of correlation is a dimensionless measure and can be expressed as the standardized covariance. The correlation coefficient varies between -1 and +1. The correlation coefficient formula is5: ρAB = σ AB /σAσB The correlation coefficient ρ12 and the covariance σ12 are positive, if the returns of assets move in the same direction (in most cases). Correlation and covariance are

4 http://learning.mazoo.net/archives/001380.html 5 http://learning.mazoo.net/archives/001380.html

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negative, when returns move in the opposite directions. If the returns are independent then the correlation coefficient is 0. General case of N assets6:

4.2.3 Correlation Matrix A Correlation matrix describes correlation among M variables. It is a square symmetrical MxM matrix with the (ij)th element equal to the correlation coefficient r_ij between the (i)th and the (j)th variable. The diagonal elements (correlations of variables with themselves) are always equal to 1.00. Correlation (often measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables. 4.3 BASIS TO DEVELOP A WELL DIVERSIFIED PORTFOLIO 4.3.1 Correlation Coefficient Correlation coefficients quantify the probability of two or more investments moving in the same direction at the same time. Values range from +1 to -1. A correlation coefficient of +1 implies that the returns of the assets will move in lockstep with each other, although not necessarily by equal increments (i.e., they can start at different levels). A measure of -1 means they move in opposite directions to each other. By combining asset classes having low correlation, volatility can be lowered for portfolios while enhancing risk-adjusted rates of return.7 The use of low and/or negative correlation provides a powerful tool in providing “effective diversification”. 4.3.2 Dissimilar Price Movements Some investments have historically shown a pattern of moving dissimilarly, either in time, in degree, or in direction. When such investments are combined into asset classes they become a proven tool to effectively diversify away many risks, reduce volatility, and simultaneously increase expected compounded rates of return. 4.3.3 Diversification Diversification is a prudent method to manage investment risk. However, not all diversification is effective. If all investments were to decrease in value at the same time, that type of diversification would be ineffective.

6 http://learning.mazoo.net/archives/001380.htm 7 Asset Allocation for Institutional Portfolios, Mark P. Kritzman, CFA, Business One Irwin, 1990, pp.

11-18.

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4.3.4 Effective Diversification While all diversification is good, certain types of diversification are better. This was the premise of Harry Markowitz’s Nobel Prize winning theory. He showed that to the extent that securities in a portfolio do not move in concert with each other, their individual risks can be effectively diversified away. Diversification among securities that move together is ineffective diversification. Effective diversification reduces portfolio price fluctuations and smoothes out returns. Generally, anything that reduces price fluctuations increases compound returns.8 Effective diversification requires that chosen and combined assets that are measured statistically to have dissimilar price movements. 4.3.5 Efficient Frontier Once expected returns, standard deviation and correlation coefficients (dissimilar price movements) have been determined, “optimal” portfolios can be created. These portfolios lie on a graph line called the “efficient frontier,” which represents the asset mix with the highest expected returns for each given level of risk. By plotting every portfolio representing a given level of risk and expected return, we are able to trace a line connecting all the efficient portfolios. This line forms the efficient frontier. In dimensions of expected return and standard deviation, the efficient frontier is a continuum of efficient portfolios.9 Rational and prudent investors restrict their choice of a portfolio to those which appear on the efficient frontier and to the specific portfolio that represents their own risk tolerance level. 4.3.6 Efficient Portfolio A portfolio that offers the maximum level of expected return for any level of risk or alternatively a portfolio that has the minimum level of risk for any level of expected return.10 The combination is arrived at mathematically, taking into account the expected rate of return and standard deviation of returns for each security as well as the similarity or dissimilarity of price movements (and their magnitude) between securities in the portfolio.11 Only by selecting investments that have dissimilar price movements one can diversify away risk, reduce volatility, and increase compounded rates of return at the same time. Harry Markowitz, called portfolios that have dissimilar price movement diversification “efficient portfolios.” This strategy is based on the “Modern Portfolio Theory” concept. 4.3.7 Expected Return This is a term of specialized use. It is generally understood to mean the statistically achievable return (based on historical data and future probability assumptions) over a sufficiently long time horizon. Expected returns are theoretical returns; they are not

8 “Building an Investment Plan” Dimensional Fund Advisors, Inc., August, 1991, p. 6. 9 Asset Allocation for Institutional Portfolios, Mark P. Kritzman, CFA, Business One Irwin, 1990, pp. 19-20. 10 Asset Allocation for Institutional Portfolios, Mark P. Kritzman, CFA, Business One Irwin, 1990, p.19. 11 Dictionary of Finance and Investment Terms, Third Edition, Barron’s Educational Series, 1991.

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estimated returns and are in no way returns for the investments that comprise the portfolio.12 The success of the strategy is highly dependent upon the assumptions made to calculate the expected return. The expected rate of return is what the prudent investor attempts to maximize at his selected level of risk. 4.3.8 Risk Risk is the possibility of financial loss and/or uncertainty of future rates of return. Its derivation comes from the fact that the future cannot be accurately forecasted. The less certain we are that an asset’s actual return will be close to its expected return, the more risk that asset carries. Historical variance or volatility (risk) of an investment can be statistically measured using standard deviations. The return of an investment is set according to its perceived risk lower the risk the lower the return. Harry Markowitz showed that to the extent a diversified portfolio has assets that do not move in concert with each other, risk can be diversified away while maintaining and actually increasing return.13 4.3.9 Risk Tolerance Each investor has his own risk tolerance. It is the trade-off between risk the investor is willing to take to receive a specified expected rate of return in light of his financial condition, objectives and needs. Investor risk levels range from defensive to aggressive. Investors will tolerate slightly higher risks for higher expected rates of return along a utility curve. 4.3.10 Standard Deviation A key component of any investment plan is to understanding and measuring risk. Investment risk can be measured using standard deviations to signify the volatility in terms of past performance. Standard deviations describe how far from the mean the performance has been, either higher or lower. The higher the standard deviation of return, the higher the risk involved with the investment. To compute the standard deviation for a combination of assets, we must also account for the interaction of price movements between each asset. 4.3.11 Variance Reduction Markowitz showed that for a given expected return, reducing a portfolio’s variance increases the compound rate of return. For example, a $100 portfolio that is up 20% in one period and unchanged in a second period has $120 after the two periods. If we reduce the portfolio’s variance to zero (up 10% the first period and up 10% the second period) we maintain our average rate of return (of 10%) but end up with $121 after the two periods, increasing our compounded rate of return. “Modern Portfolio Theory” is based on the following concept: “If two portfolios have the same expected return, the one with the lower volatility will

have the greater compound rate of return.”14 12 Dictionary of Finance and Investment Terms, Third Edition, Barron’s Educational Series, 1991. 13 Asset Allocation for Institutional Portfolios, Mark P. Kritzman, CFA, Business One Irwin, 1990 14”Portfolio Results Enhanced--Using Markowitz increases returns without added risk,” Joseph N. Papp, Pension & Investments, February 18, 1991.

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4.4 OUTCOME OF A WELL DIVERSIFIED PORTFOLIO 4.4.1 Asset Allocation Well diversified portfolio will return the weights of the individual securities that have to be included in to the investment portfolio in order to minimize risk and maximize the return on investment. Allocation of investment funds among categories of assets, such as cash equivalents, stocks and fixed-income investments is also the subject of asset allocation that is considered by the prudent investor. Asset allocation affects both risk and returns and is a central concept in personal financial planning and investment management. The extent to which investments chosen for allocation move dissimilarly, it will determine whether the allocation of assets provides effective diversification or not. 4.4.2 Investment Policy Statement The process that defines in statement form, the investor’s financial objectives, the amount of funds available for investment, the investment methodology and the strategy that will be used to reach those objectives. The strategy is customized and matched to investors’ individual needs, objectives and chosen risk tolerance levels. 4.4.3 Optimal Portfolio After all efficient portfolios have been identified; the particular portfolio that is most suitable to the investor is the optimal portfolio. “Most suitable” refers to the portfolio that best represents the balance between investor’s stated risk tolerance and the related expected return. Normally investors will accept moderately higher levels of risk for higher expected rates of return. Those portfolios that fit within the range of their risk and reward criterion can be placed on a curve, called the utility curve or indifference curve (and sometimes the risk tolerance curve). In practice, however, expected utility curves can be somewhat indeterminate because seldom can most investors quantify their acceptable levels of risk as it relates to expected return. The optimal asset mix is defined as that point along the efficient frontier that is tangent to one’s desired utility curve, or risk tolerance curve. “The optimal portfolio is that portfolio that has the highest expected return that matches up with the risk and related return of the utility curve for a specific investor” 15 4.4.4 Passive Management The process of buying and holding a well-diversified portfolio is called passive management16 because there is not a continual process of securities selection and/or timing schemes that create constant trading activity (which drives up costs and often reduced returns), there is considerable work involved if dissimilar price movement diversification is used. Thousands of investments must be evaluated through computer analysis of historical data to select those securities that will provide the most effective diversification and highest yield for a given level of risk. Portfolios generated must also be re-balanced periodically to bring them back in line with the efficient frontier. 15 Asset Allocation for Institutional Portfolios, Mark P. Kritzman, CFA, Business One Irwin, 1990 16 Fundamentals of Investments, Second Ed., Gordon Alexander, William Sharpe, Jeff Bailey, Prentice

Hall, 1993

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The concept of passive management provide the basis to develop a software program to automate the process of developing the optimal portfolio that can be easily fine tuned with the help of the software like PMSS. 2.4.5 Re-Optimization This is an analysis and adjustment performed at regular intervals to return the investment portfolio to its most efficient frontier. The prices of some assets or asset classes will fluctuate more than others. Periodically asset classes should be brought back to the most desirable and efficient proportions (weights given to individual securities) to maintain the highest return at the investor’s chosen risk level.

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SYSTEM DESIGN The steps followed to design the PMSS (Portfolio Management and Support System) are as follows:

• Development of Use Case Diagram in which we identified the major modules or processes and the users or actors that will be interacting with those processes

• Creating a Data Flow Diagram to understand the flow of data through the system

• Creating UML Activity Diagrams of individual Processes to understand the hierarchy and flow of system

• Developing an Entity Relationship Diagram from which the database of the system is created

• Designing frontend of the system 5.1 USE CASE DIAGRAM A use case diagram is a type of behavioral diagram and its purpose is to present a graphical overview of the functionality provided by a system in terms of actors (i.e. users), their goals, and any dependencies between them. The main purpose of a use case diagram is to show what system functions are performed for which actors. In PMSS there are three actors that interact with the system; investor who is the actual user of the system, KSE (Karachi Stock Exchange) that provides all the primary data and broker who performs the physical buying and selling of shares when the system tells him to do so. Use case diagram of PMSS is given below.

Figure 5.1: Use Case Diagram of the System

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5.2 DATA FLOW DIAGRAM A data flow diagram (DFD) is a graphical representation of the "flow" of data through an information system. There are three levels of DFD’s:

• Context Level DFD • Level 0 DFD • Detailed DFD

5.2.1 Context Level DFD This level shows the overall context of the system and its operating environment and shows the whole system as just one process. The entities here are the real world organizations, people or systems that interact with the system in any way. A Context Level DFD of PMSS is given below:

Figure 5.2: Context Level DFD of the System

5.2.2 Level 0 DFD This level shows all major processes, data stores, external entities and the data flows between them. The purpose of this level is to show the major high level processes of the system and their interrelation. A level 0 diagram must be balanced with its parent context level diagram, i.e. there must be the same external entities and the same data flows, these can be broken down to more detail in the level 0. A Context Level DFD of PMSS is shown in figure 5.3:

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Figure 5.3: Level 0 DFD of the System

5.2.3 Detailed DFD This level is a decomposition of all the processes shown in level 0 diagram as such there should be a level 1 diagram for each and every process shown in a level 0 diagram. Since our system has three major processes as shown in Level 0 DFD, each of those processes will be shown in a separate detailed DFD. 5.2.3.1 Detailed DFD of ISS

Figure 5.4: Detailed DFD of ISS

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5.2.3.2 Detailed DFD of Portfolio Calculation

Figure 5.5: Detailed DFD of Portfolio Calculation

5.2.3.3 Detailed DFD of Buy/Sell Call Generation

Figure 5.6: Detailed DFD of Buy/Sell Call Generation

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5.3 UML ACTIVITY DIAGRAM Activity diagram tells us the working of modules in the system. There are only two activity diagrams of the system because the third module is just for monitoring and it does not perform any calculation and is running on the backend of the system. 5.3.1 Activity Diagram ISS

Figure 5.7: Activity Diagram ISS

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5.3.2 Activity Diagram IDSS

Figure 5.8: Activity Diagram IDSS

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5.4 ENTITY RELATIONSHIP DIAGRAM

Figure 5.9: Entity Relationship Diagram

5.4.1 ERD Description The entities in the above mentioned ER diagram are described below: 5.4.1.1 Stock This entity depicts the real world object of ‘Organization’. In this table all the information pertaining to a company whose shares is traded in the market are stored. It stores the basic data of individual companies. The attributes of Stock are:

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Stock_ID This is the primary key or the unique identifier of the table. ‘Stock_ID’ is just a number allocated to each company for the purpose of uniquely identifying them. Stock_Name This attribute stores the name of the company. Shares_Outstanding Every company in the stock market issues shares which are commonly known as outstanding shares. The total number of shares that a company issues in the open market for trading purpose is stored in this attribute. Market_Cap Market capitalization is the total number of outstanding shares multiplied by the current market price of the share. It is the actual value of the company in terms of its shares. ‘Market_Cap’ stores an organization’s market capitalization. Traget_Price This is the fair value or actual value of the company’s share in the market. This is calculated on the basis of current and future earnings of the company. It is the actual value a company’s share should have if the market was fully efficient (i.e. any information about the company is incorporated in its share’s price as soon as the information comes). Sector_ID This is a foreign key in the ‘Stock’ table. ‘Sector_ID’ comes from the table ‘Sector’ which stores the names and ID’s of the sectors to which companies trading in the stock market belong to. Stock_Weight This is the total amount that can be invested in a particular company’s stock. It is stored as a percentage. 5.4.1.2 Sector Sector_ID This is the primary key or the unique identifier of the table ‘Sector’. ‘Sector _ID’ is just a number allocated to each sector for the purpose of uniquely identifying them. Sector_Name This attribute stores the name of the sector.

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5.4.1.3 Price Stock_ID ‘Stock_ID’ is not just a foreign key that comes from the table ‘Stock’ but it is also a part of the primary key that uniquely identifies each and every record in the table. ‘Stock_ID’ along with ‘Price_Date’ composes the composite primary key of the table. Price_Date As mentioned above it is a part of primary key of the table and it stores the date on which the price of the stock was taken. Price This is the most important attribute of the database which stores the historical per share price of a company’s stock from January 1, 2004. All the calculation of beta and return potential are based upon this attribute. Turnover This attribute stores the daily quantity of shares being traded in the market of individual companies since January 1, 2004. 5.4.1.4 Beta_n_Return Stock_ID ‘Stock_ID’ is not just a foreign key that comes from the table ‘Stock’ but it is also a part of the primary key that uniquely identifies each and every record in the table. ‘Stock_ID’ along with ‘BnR_Date’ composes the composite primary key of the table. BnR_Date As mentioned above it is a part of primary key of the table and it stores the date on which the beta of the stock was calculated. It is important to store the date to keep track of the change in beta of the stock because beta is the measure of risk of individual stock compared to the market and it can change with the changing prices of the stock and the market index due to high volatility of the market. BnR_Beta It stores the beta of individual stock which is the relationship of stock with the market. It tells us about the movement of stock in comparison to the market. BnR_ReturnPotential This attribute stores the return a stock can give us if we buy it on the particular date. It is shown as a percentage and calculated as the percentage change between the market price on that date and the target price of the company’s stock.

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BnR_Variance Variance of the stock is the measure of its variability from the mean or par value. This value is stored in ‘BnR_Variance’ and it helps us measure the highs and lows of a stock. BnR_CoVariance Covariance is the measure of relationship between a stock and market and this helps us in calculation of beta and standard deviation of the portfolio we intend to propose. The value of covariance is stored in ‘BnR_CoVariance’. 5.4.1.5 Portfolio Portfolio_ID This is just a number used to uniquely identify the records in the table. Portfolio_Number This is like a serial number the system will give to each portfolio that it will generate. This is important to keep track of all the portfolios the investor (i.e. user of the system) has. Portfolio_Date This attribute holds the date on which the portfolio is generated. Portfolio_StockID This is the same number that we gave to each of our stocks in the stock table. The reason that this ‘Portfolio_StockID’ is stored in the table is to tell us the stocks that the system included in the proposed portfolio. Portfolio_StockWeight This attribute stores the weight (in percentage) that each stock in the portfolio has. 5.4.1.6 PLP PLP_ID This is the primary key or the unique identifier of the table. ‘PLP_ID’ is just a number allocated to each company for the purpose of uniquely identifying them. PLP_PortfolioNum This is the primary key that comes from the table ‘Portfolio’. This attribute holds the ID’s of bought portfolios so that they can be sold in future.

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PLP_StockID ‘PLP_StockID’ is a foreign key stored in this table that comes from the table ‘Stock’. ‘PLP_StockID’ is stored to give the system some flexibility and it gives the investor to add his favorite stocks in the PLP so that they can be monitored individually and as soon as they show some potential of future profits they can be bought. 5.4.1.7 Bought_ Stocks Stock_ID This is the primary key or the unique identifier of the table. ‘Stock_ID’ is just a number allocated to each company for the purpose of uniquely identifying them. In ‘Bought_Stocks’ the stocks that are bought by the investor are kept. Bought_Price ‘Bought_Price’ stores the prices on which each of the stocks was bought. Bought_Quantity This attribute tells us the quantity or number of shares of the particular stocks that were bought by the investor. 5.4.1.8 Sell_Call SellCall_ID This is just a number used to uniquely identify the records in the table. SellCall_Date ‘SellCall_Date’ is the date on which the sell call was generated. ‘Sell_Call’ as the name suggests generates an order to sell shares to the broker automatically. SellCall_PortfolioNum This attribute stores the number of portfolio of which the stock was a part. It is a foreign key that comes from the table portfolio. SellCall_StockID This attribute stores the ID of the stock to be sold. SellCall_Price As the name suggests ‘SellCall_Price’ stores the price at which the stocks are being sold.

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SellCall_Quantity It stores the number of shares that are sold by the broker due to the generation of sell call. 5.4.1.9 Buy_Call BuyCall_ID This is the primary key or the unique identifier of the table. ‘BuyCall_ID’ is just a number allocated to each company for the purpose of uniquely identifying them. BuyCall_Date ‘BuyCall _Date’ is the date on which the buy call is generated. ‘Buy_Call’ as the name suggests generates an order to buy shares to the broker automatically. BuyCall_StockID This attribute stores the ID of the stock to be bought. BuyCall_Price It stores the price at which the stocks are being bought. BuyCall_Quantity It stores the number of shares that are bought by the broker due to the generation of buy call.

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5.5 LAYOUT OF FRONTEND

Figure 5.10: Layout of Frontend

THE PORTFOLIO SELECTION PROBLEM 6.1 PROBLEM FORMULATIONS If you understand the concept of efficient portfolios, we are now ready to talk about problem formulations. We will first talk about two commonly used formulations that may not produce efficient portfolios. The first is to minimize variance subject to achieving a specified level of return and the other is to maximize return subject to achieving a specified level of variance. Let the portfolio have an expected return of

z = rTw and variance of In model 1, r* is the minimal acceptable return.

In model 2, is the maximal acceptable variance. 6.1.1 Minimize Variance Subject To Given Return The model of the first can be given as follows:

6.1.2 Maximize Return Subject To Given Variance The model of the second can be given as follows:

These models will not necessarily give efficient portfolios. The first model will provide a portfolio having the smallest standard deviation for a specified minimum level of return. However, there may exist a portfolio having a greater return and an equivalent standard deviation. In such a case, the portfolio returned by the model would not be efficient. These can happen only if the matrix definite. 6.2 COMBINING THE MODELS 6.2.1 Balancing Risk and Return Each investor is willing to take a certain amount of risk to earn another dollar in returns. As the total return goes up, the investor is less and less willing to risk more to earn just one more dollar. Each investor has a certain determines exactly how much risk he is willing to take in order to obtain an expected amount of money. We assume that this utility can be measured by a utility function, u(x). One commonly used utility function is:

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HE PORTFOLIO SELECTION PROBLEM

6.1 PROBLEM FORMULATIONS

If you understand the concept of efficient portfolios, we are now ready to talk about problem formulations. We will first talk about two commonly used formulations that may not produce efficient portfolios. The first is to minimize variance subject to

ieving a specified level of return and the other is to maximize return subject to achieving a specified level of variance. Let the portfolio have an expected return of

of .

is the minimal acceptable return.

he maximal acceptable variance.

6.1.1 Minimize Variance Subject To Given Return

The model of the first can be given as follows:

Maximize Return Subject To Given Variance

The model of the second can be given as follows:

These models will not necessarily give efficient portfolios. The first model will provide a portfolio having the smallest standard deviation for a specified minimum level of return. However, there may exist a portfolio having a greater return and an

lent standard deviation. In such a case, the portfolio returned by the model would not be efficient. These can happen only if the matrix Q is not strictly positive

6.2 COMBINING THE MODELS

Balancing Risk and Return

Each investor is willing to take a certain amount of risk to earn another dollar in returns. As the total return goes up, the investor is less and less willing to risk more to earn just one more dollar. Each investor has a certain utility determines exactly how much risk he is willing to take in order to obtain an expected amount of money. We assume that this utility can be measured by a utility function,

monly used utility function is:

HE PORTFOLIO SELECTION PROBLEM

If you understand the concept of efficient portfolios, we are now ready to talk about problem formulations. We will first talk about two commonly used formulations that may not produce efficient portfolios. The first is to minimize variance subject to

ieving a specified level of return and the other is to maximize return subject to achieving a specified level of variance. Let the portfolio have an expected return of

These models will not necessarily give efficient portfolios. The first model will provide a portfolio having the smallest standard deviation for a specified minimum level of return. However, there may exist a portfolio having a greater return and an

lent standard deviation. In such a case, the portfolio returned by the model not strictly positive

Each investor is willing to take a certain amount of risk to earn another dollar in returns. As the total return goes up, the investor is less and less willing to risk more to

for money, which determines exactly how much risk he is willing to take in order to obtain an expected amount of money. We assume that this utility can be measured by a utility function,

u(x) = 1 - exp(-kx), where the relationship between r We assume that the return vector is normally distributed with mean matrix Q. Therefore, z

. The expected value of utility can then be computed as

Since f(x)=1-exp(-x) equivalent to maximizing

Now, given a covariance matrix, aversion parameter, k, we can select a portfolio that maximizes expected utility by solving the following optimization problem:

The optimal portfolio is determined by solving for the weighting parameter,

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where k > 0 is a risk aversion constant. This function describes the relationship between risk and return for an investor.

We assume that the return vector is normally distributed with mean z is also normally distributed with mean z = r

. The expected value of utility can then be computed as

is a strictly increasing function in x, maximizing utility is equivalent to maximizing

Now, given a covariance matrix, Q, a vector of expected returns,

, we can select a portfolio that maximizes expected utility by solving the following optimization problem:

The optimal portfolio is determined by solving for the weighting parameter,

k aversion constant. This function describes

We assume that the return vector is normally distributed with mean r and covariance z = rTw and variance

. The expected value of utility can then be computed as

, maximizing utility is

, a vector of expected returns, r, and a risk-, we can select a portfolio that maximizes expected utility by

The optimal portfolio is determined by solving for the weighting parameter, w.