TOPIC 4

RISK AND RETURN

RETURN DEFINED Return represents the total gain or loss on an

investment.

Basic concept: Each investor desires a return for every single dollar of their investment.

EXAMPLE

Damia invests in 10 unit shares valued at RM1000. At the end of year, she sold all the shares @ RM1100. How much return received by Damia for her investment?

r = RM1,100 + 0 – RM1,000 RM1,000

= 10% (so holding period rate of return is 10%)

EXPECTED RETURN

Expected Return ( r )- the return that an investor expects to earn on an asset, given its price, growth potential, etc.

Required Return ( r )- the return that an investor requires on an asset given its risk and market interest rates.

Expected rate of return from investment is determined by the different possible outcomes such probabilities of the occurrence of the various states of the economy.

In the unstable situation, it is hard for the investors to be assured on the expected rate of return.

EXPECTED RATE OF RETURN

Expected rate of return - The weighted average of all possible returns where the returns are weighted by the probability that each will occur.

OR, WE CAN PUT THIS WAY r = Pb1*r1 + Pb2*r2 + ...+ Pbn*rn

where;Pb = probability of occurrence of the outcomer = return for the outcomen = number of outcomes considered

EXPECTED RATE OF RETURN

EXAMPLE

r = (0.2)(10%) + (0.3)(12%) + (0.5)(14%) = 12.6%

State of the economy

Probability Return

Recession 20% 10%

Normal 30% 12%

Boom 50% 14%

EXERCISEState of the

economyProbability (Pb) Return

Company AReturn

Company B

Recession 0.20 4% -10%

Normal 0.50 10% 14%

Boom 0.30 14% 30%

What is the expected return for each company?

RISK DEFINED Risk is potential variability in future cash flow. The possibility that an actual return will differ from our

expected return. The wider the range of possible future events that can occur,

the greater the risk. Concept: (High risk, high return)

Return

Risk

Probability- Chances that an investment will generate expected rate of return for investor.

STANDARD DEVIATIONHOW DO WE MEASURE RISK? Standard deviation (SD) is one way to measure risk. It

measures the volatility or riskiness of portfolio returns (dispersion of possible outcomes).

SD (-sigma) = square root of the weighted average squared deviation of each possible return from the expected return.

The greater the standard deviation, the greater the uncertainty, and the greater the risk.

Standard Deviation Formula:

STANDARD DEVIATION

Example

Which stock would you prefer?How would you decide?

STANDARD DEVIATION

CompanySummary A B

Expected Return 10% 14%Standard Deviation 3.46% 13.86%

We can conclude that, company A has lower risk compared to investment B BUT Company B has higher return.

Final choice is determined by our attitude toward risk and there is NO single right answer

COEFFICIENT OF VARIATION It is NOT TRUE to conclude that asset with high standard

deviation has a high risk where comparison of risk was made between assets with a different expected rate of return.

The coefficient of variation, CV, is a measure of relative dispersion that is useful in comparing risks of assets with differing expected returns.

Formula: CV = σr r

The higher the CV, the higher the risk.

COEFFICIENT OF VARIATION

Example Asset A Asset B

r 10% 14%σr 3.46% 13.86%

a. Which assets do you prefer? b. Is it true that Asset B is more risky compared to Asset

A?

CVA = 0.346 while CVB = 0.99 A unit of risk in return for asset B is higher than asset

A. As a conclusion, asset A is less risky than asset B. In comparing risk, it is more effective if we are using

CV because it’s consider the relative size or the rate of return of that asset.

EXERCISE2 Assets- Asset C and T are currently being considered by Green Corp. The distributions are shown in the following table.

a. Calculate the expected rate of return, r, for each of the assets.b. Calculate the standard deviation, for each of the assets.c. Calculate the coefficient of variation, CV, for each of the assets.

Asset C Asset T

Pb r Pb r

Boom 0.30 15% 0.30 25%

Normal 0.50 10% 0.50 20%

Recession ??? 2% ??? 1%

PORTFOLIO AND RISK DIVERSIFICATION A portfolio = any collection or combination of several

financial assets (investments) at the same time or period. Combining several securities in a portfolio can actually

reduce overall risk. If an investor holds a single asset, he or she will fully suffer the

consequences of poor performance. This is not the case for an investor who owns a diversified

portfolio of assets.

PORTFOLIO WEIGHTED (PW)

You have RM15,000 to invest in a selected of stocks in Bursa Malaysia as follows:

What is the weighted of portfolio for each security? DCLK =RM2000 DCLKw = 2000/15000 KO =RM3000 Kow = 0.2 INTC = RM4000 INTCw = 0.267 KEI = RM6000 KEIw = ??

PORTFOLIO EXPECTED RETURN

Is the weighted average of expected return for each security of a portfolio.

FORMULA

m

jjjP REwRE

1

)()(

EXAMPLE

Weighted

DCLK 0.133 KO 0.2 INTC 0.267 KEI 0.4

Expected Return

19.69% 5.25% 16.65% 18.24%

E(RP) = .133(19.69) + .2(5.25) + .167(16.65) + .4(18.24) = 13.75%

DIVERSIFICATION

Diversification-spreading out of investments to reduce risks.

Market rewards diversification. The main motive for holding multiple assets or creating a

portfolio of stocks (called diversification) is to reduce the overall risk exposure.

The degree of reduction depends on the correlation among the assets.

Correlation-a statistical measurement of the relationship between two variables.

Positive CorrelationNegative Correlation

Possible correlations range from +1 to –1

PORTFOLIO If two stocks are perfectly positively correlated,

diversification has NO effect on risk. i.e If correlation (c) = +1, we cannot abolish all the risk meaning that both stocks move in the same direction together.

If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified. i.e If correlation (c) = -1, we can abolish the risk meaning that as one stock goes up, the other goes down.

TYPES OF INVESTMENT RISKS

Investors should NOT expect to eliminate all risk from their portfolio. Some risk can be diversified away and some cannot.

2 TYPES OF RISKSi. Market risk

(systematic risk) is non diversifiable. This type of risk cannot be diversified away.ii. Company-unique risk

(unsystematic risk) is diversifiable. This type of risk can be reduced through diversification

TYPES OF INVESTMENT RISKSCompany-Unique Risk (Unsystematic) Risk affects only a specific firm.This risk can be reduced simply by investment diversification. Example of the events: a company’s labor force goes on strike, the outcome of unfavorable litigation & CEO changes.

TYPES OF INVESTMENT RISKS

Market Risk (Systematic) Risk affects all firms because it is beyond the control of the investor and the firm. Systematic risk reflects mainly macroeconomic shocks that affect aggregate behavior of the economy. measured by beta Example unexpected changes in interest rates, tax rate changes, war, turbulent political events & foreign competition.

SYSTEMATIC RISK AND UNSYSTEMATIC RISK

MEASURING MARKET RISK Once the individual asset return and market return obtained,

a graph is prepare to see the relationship between that asset return and market return.

Asset return is plot on Y-axis and market return on X-axis. When all the returns are plotted, draw a line of best-fit for all

the stock returns relative to market returns which we call Characteristic line.

The slope of the characteristic line is called BETA. It measures of the firm’s market risk.

Example 6- XYZ returns are 1.2 times as volatile on average as those of the overall market.β = 1.2 means any increase/decrease by 1% in market return will cause an increase or decrease by 1.2% in asset return

MARKET PORTFOLIO RETURNSCHARACTERISTIC LINE

-5 -15 5 10 15

-15

-10

-10

-5

5

10

15

XYZ Co. returns

S&P 500 returns

. . . .

. . . . . . . . . . . .

. . . .

. . . .

. . . . . . . .

. . .

. . . . . . . .

Beta = slope = 1.20

MEASURING MARKET RISK - BETA

Interpreting beta (β) Specifically, beta is a measure of how an individual stock’s

returns response (sensitivity) to a change is market returns.

The market’s beta is 1• A firm that has a beta = 1 has average market risk. The

stock is no more or less volatile than the market.• A firm with a beta >1 is more volatile than the market. • A firm with a beta < 1 is less volatile than the market.• A firm with a beta=0 has no systematic risk.

Most stocks have betas between 0.60 and 1.60

MEASURING MARKET RISK - BETA The portfolio beta indicates the percentage change on average of

the portfolio for every 1 percent change in the general market It is a weighted average of the individual assets’ beta and asset has

its own beta.

βportfolio= ∑ wj βj

Exercise: What is the Beta of the portfolio?Asset Beta Proportions1 1.35 .102 1.12 .203 1.67 .304 1.04 .205 1.55 .20

β of stock j

j% invested in portfolio

REQUIRED RATE OF RETURN - CAPM Investor’s required rate of returns is the minimum rate of

return necessary to attract an investor to purchase or hold a security.

The required return for all assets is composed of two parts: the risk-free rate and a risk premium.

The risk-free rate (Rf) is usually estimated from the

return on treasury bills

The risk premium is a function of both market conditions and the asset

itself.

REQUIRED RATE OF RETURN - CAPM

Risk-free rate is the rate of return or discount rate for risk-less investments that is typically measured by Treasury bill rate.

The risk premium for a stock is composed of 2 parts: a. The Market Risk Premium which is the return required for investing in any risky asset rather than the risk-free rate.b. Beta, a risk coefficient which measures the sensitivity of the particular stock’s return to changes in market conditions.

REQUIRED RATE OF RETURN - CAPM

Example HD Corporation, a growing computer software developer,

wishes to determine the required return on asset Z, which has a beta of 1.5. The risk-free rate of return is 7%; the return on the market portfolio of assets is 11%. Substituting βZ = 1.5, rf = 7%, and rp = 11% into the CAPM yields a return of:

rZ = 7% + 1.5 [11% - 7%] = 13%

So, if the expected rate of return is a) 15% and b) 10%, is the stock underpriced or overpriced?

REQUIRED RATE OF RETURN - CAPM

CAPM (Capital Asset Pricing Model) is a model to measure the investor’s required rate of return (provides a risk-return trade off in which risk is measured in terms of beta).

CAPM provides for an intuitive approach for thinking about the return that an investor should require on an investment, given the asset’s systematic or market risk.

CAPM equation equates the expected rate of return on a stock to the risk-free rate plus a risk premium for the systematic risk.

SML is a graphic representation of the CAPM, where the line shows the appropriate required rate of return for a given stock’s systematic risk.

Required

rate of return

33

.

Risk-freerate ofreturn(7%)

Beta

13%

1.5

(SML)

This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM).

SML – The line that reflect the attitude of investors regarding the minimal acceptable return for a given level

of systematic risk.

11%

1.0

Risk Premium

Market Risk Premium

Risk Free Rate