TOPIC 4 Risk and Returns

The Objective of this chapter is to help us to understand the principle:

Axiom 1: The Risk-Return Tradeoff - Axiom 1: The Risk-Return Tradeoff - Investor Won’t Take on Additional Risk Investor Won’t Take on Additional Risk Unless They Expect to be Unless They Expect to be Compensated with Additional return.Compensated with Additional return.

Important Guidelines:

1. The expected benefits or returns that an investment generates is measured in the form of cash flows and not accounting profits. Axiom 3: Cash - Not Profit - Is King. Thus, the riskiness of the investment is measured in term of the riskiness of its cash flows.

Consider the 2 possible investments:

1. Consider investing in a risk-free government security with an annual return of 6% matures in 90 days, against

2. Investing in a company which has the following estimate annual returns:

Expected Return

kˆ = P1k1 + P2k2………Pnkn

= .10(0%)+.20(5%)+.40(15%)+.20(25%)

+.10(30%) = 15%

Determine kˆ

What is Risk?

“Risk is the potential variability in future cash flows - the wider the range of possible events that can occur, the greater the risk.”

What is Risk?

“Risk is the potential variability in future cash flows - the wider the range of possible events that can occur, the greater the risk.”

“The tighter, or more peaked, the probability distribution, the more likely it is that the actual outcome will be closed to the expected outcome, and, consequently, the less likely is that the actual return will end up far below the expected return, Thus, the tighter the probability distribution, the lower the risk assigned to a stock”. Pg.. 149

2.Riskiness of an assets can be measured in either as (a) STAND-ALONE BASIS, or (2) in a PORTFOLIO CONTEXT.

An asset which has a great deal of risk if held by itself,may be much less risky if it is held as part of a larger portfolio.

Measuring Stand-Alone Risk“The tighter the probability distribution of

expected future returns, the smaller the risk of a given investment:

sigma σ = the definite value to measure the tightness of the probability distribution. THE SMALLER THE “σ” THE TIGHTER THE PROBABILITY DISTRIBUTION AND THUS THE LOWER THE RISK.

Steps in Measuring Stand-Alone RiskSteps in Measuring Stand-Alone Risk1. Calculate The Expected Return

2. Calculate the Deviation

3. Square the Deviation and x by the

Probability to get the Variance

4. Square the Variance

(refer to page 175)

The Coefficient of Variation (CV)Given same return, investor would choose

lower risk

Given same risk, investors would choose higher return

Given different return and different risk, we will calculate the risk per return

CV = σ/kˆ

σ kˆ CV = σ/kˆ

Martin 65.84 15% 4.39:1%

US Water 3.87 15% 0.26:1%

“If you choose the less risky investment, you are risk averse. Most investors are indeed risk averse, and certainly the average investors is risk averse with regards to his/her “serious money”. Because this is a well documented fact, we shall assume risk aversion throughout the remainder of the book.”

Risk in Portfolio Context

“ A security held as part of a portfolio is usually less risky then the same security held in isolation.

The fact that a particular stock goes up or down is not important; what is important is the return on his/her portfolio’s risk.”

Portfolio ReturnsPortfolio Returns

The Expected Return on a Portfolio :

kˆp = w1kˆ1+ w2kˆ2+……….+ w nkˆ n

kp = 0.25(14%)+0.25(13%)+0.25(20%)

0.25(18%) = 16.25% (pg.182 )

Investment of RM100000; RM25000 in each stock

Portfolio RiskPortfolio Risk The riskiness of a portfolio, σp, is NOT the

weighted average risk of the standard deviation of individual stocks in the portfolio; the portfolio risk will be SMALLER than the weighted average risk of the individual assets. Theoretically the portfolio might have a risk of ZERO; σp=0 (riskless)

The risk of the portfolio is measured by using the correlation or correlation coefficient, r,: it measures the tendency of two or more variables (stocks) to move together in a portfolio.

The two extreme correlation is the -1.0 negative correlation and the +1.0 correlation

Scan page 159

Scan page 160

Scan pg 161

r = -1.0 perfectly negative correlated will result in a riskless portfolio

r = +1.0 perfectly positive correlated means diversification will do nothing to reduce the risk

a positive correlation of more than zero but less than 1.0 means combining stocks into portfolios will reduce risk but does not eliminate risk completely.

As a rule the riskiness of a portfolio will decline as the number of stocks in the portfolio increases

the smaller the correlation, r, the lower the risk in a large portfolio.

In the real world it is impossible to form a completely riskless stock portfolios.

Diversifying Away RiskDiversifying Away Risk

1. Investment across different securities

2. Securities do not move together

3. The unique return variability (risks) of one stock tends to be countered by the unique variability of another security.

4. We should expect that we cannot eliminate all risk from the portfolio becos stocks prices have some tendency to move together.

Type of Risk:Type of Risk:

1. Diversifiable Risks - company-unique risk- unsystematic risk.

E.g. strikes, lawsuit, successful/ unsuccessful marketing program, winning a major contract etc.

2. Non-Diversifiable Risk- market-related risks-systematic risk.

E.g. inflation, recession, war, fluctuation in interest rates etc.

BETA,BETA,, Concept, Concept is used to measure the tendency of a stock to

move, up or down, with the market (market risk).

An average-risk stock is defined as a stock that move in step with the general market.

By definition these stocks has a = 1.0

Page 220

Page 221

Remember thatRemember that The slope of the characteristics line is called

beta,, and it is a measure of a stock’s systematic risk. The slope indicates the average response of the stock’s return to the change in the market as a whole.

Axiom 9: All Risk Is Not Equal - Some Risk Can Be Diversified Away, Some Cannot. Through diversification we can remove the company-related unsystematic risk. Market-systematic risk cannot be eliminated.

Portfolio Beta, p, Coefficient

The beta of a portfolio is a weighted average of the individual securities betas.

p = w1b1+w2b2 …….+wnbn

Portfolio Beta,Portfolio Beta,ppSecurity Investment Beta

A RM25000 0.7

B RM25000 0.5

C RM50000 0.4

p = 25%(0.7)+25%(0.5)+50%(0.4)

= 0.50

The Relationship Between Risk And the Rate of Return (Required Rate)

The investor required rate of return is the minimum rate of return to attract the investor to purchase the stock.

The investment will be made only if the price is low enough relative to expected future cash flow to provide a rate of return greater than or equal to our required rate of return.

In general, the required rate of return for any investment can be expressed as

Required Return = Risk-free Return + Premium Risk

k = krf + krp

The tough task is how to estimate the risk premium.

The CAPM Approach

k = krf + krp, thus

krp = k - krf , or

Security market Line = SML

= krp = (km-krf)

CAPM

using SML = k = krf + (km-krf)

Page 172

The Impact of Inflation

krf = k* + IP IP krf k (required return)

Changes in a Stock’s Beta

k = krf + (km-krf)

Premium Risk k

“Beta is deadBeta is dead” - Fama and French

Stock returns is influenced by

- The size of firm -the total market value of the firm equity, and

- The Market/Book ratio - ratio of the firm equity book value to its equity market value

End of Chapter