Chapter 8 Risk & Rates of Return

The average stock has a Beta of:

1

The standard deviation of the returns of Stock Y is 47.5%, and the expected return from the stock is 16%. Calculate the coefficient of variation of the stock. (Round to two decimal places.)

2.97

The risk-free rate is 2.80%, and the expected market return is 4.00%. If the expected return on Security X is 7.50%, what is the beta of the security? (Round final answer to two decimal places.)

3.92

The risk of which of the following portfolios is equal to the market risk?

A portfolio with a beta of 1.0

Key Risk and Return Concepts

A stock is deemed to be in equilibrium when its expected return, , equals the return investors require (demand), r; that is, . When , the stock's market price, , will be less than its intrinsic value, , as determined by using models similar to those described in Chapter 7. When , the stock is considered undervalued and investors will purchase the stock until and . page 16 of notes

Key Risk and Return Concepts

According to the capital asset pricing model (CAPM), an investment's required rate of return can be computed as ..... page 15 top of notes

Which of the following is included in diversifiable risk?

Default risk

Key Risk and Return Concepts

In finance, we define risk as the chance you will not receive the return you expect, regardless of whether the actual outcome is better than expected or worse than expected.

Assume that you invest 40% of your wealth in stock A and 60% of your wealth in the S&P 500. The variance of your portfolio's return will be: 66.67%2 50.92%2 48.36%2 21.15%2 Probability of "state" Stock A S&P 500 Portfolio Return (.4*A + .6*S&P) 1/3 19% 5% 10% 1/3 3% 10% 7.2% 1/3 23% 15% 18.2% Now treat the portfolio as an individual security and calculate its variance.

RISK AND RETURN BLACKBOARD QUESTIONS

Assume that the risk free rate of interest is 3%, the market risk premium is 5%, and that the Betas for Dell and General Mills are 1.2 and 0.8 respectively. According to the CAPM, what should be the required rate of return for these two stocks?

RISK AND RETURN BLACKBOARD QUESTIONS 9.0%, 7.0%

A limitation of the Capital Asset Pricing Model is that it does not account for inflation, i.e. the CAPM is likely to underestimate the nominal rate of return required by investors in high inflation periods and overestimate the nominal rate of return required by investors in low inflation periods.

RISK AND RETURN BLACKBOARD QUESTIONS FALSE Again, here is the CAPM equation. Remember from your lecture on interest rates that rrf goes up and down with inflation - when inflation is high, interest rates are high too because investors at least want to retain the same purchasing power that they would have had if they had used their investment for immediate consumption. Thus, the CAPM does implicitly adjust for inflation.

Assume that you invest 40% of your wealth in stock A and 60% of your wealth in the S&P 500. The expected return of your portfolio will be:

RISK AND RETURN BLACKBOARD QUESTIONS Portfolio Expected Return =(.4 * 15%) + (.6 * 10%) = 12%

Diversification effectively eliminates an investor's exposure to non-systematic risk but not systematic risk. Thus, stocks with high exposure to systematic risk factors must offer investors high rates of return in equilibrium. In contrast, investors should not expect higher rates of return when investing in stocks with high exposure to non-systematic risk factors.

RISK AND RETURN BLACKBOARD QUESTIONS TRUE

A stock that is priced such that investors' expected rate of return from investing in the stock is greater than the required rate of return as given by the CAPM is likely to go up in price.

RISK AND RETURN BLACKBOARD QUESTIONS TRUE Let's offer a brief example: Assume that stock XYZ is expected to pay a $1 dividend next year (D1), that investors believe the dividend will grow at 10%. And that the price per share is currently $20. This implies that investors should expect a rate of return of 15% from XYZ. Now let's assume that CAPM says the required rate of return for a stock like XYZ (given its exposure to systematic risk factors) should be 13%. What happens - investors start buying XYZ because its expected rate of return is greater than the necessary required rate of return. Because of all of the buying pressure, price goes up. We reach equilibrium when the expected rate of return equals the required rate of return, i.e. 15%. At this point, the price will be:

Assume that you can invest in any of the following three securities today. You will hold them for a year, however, there is uncertainty about how well your investments will do over the ensuing year. This uncertainty is represented by the three "states of nature" that can potentially occur with probabilities of 1/3, 1/3, 1/3. The returns for each security in the three states of nature are given in the table below. Probability of "state" Stock A Stock B S&P 500 1/3 19% 0% 5% 1/3 3% 12% 10% 1/3 23% 20%

RISK AND RETURN BLACKBOARD QUESTIONS The expected returns for stock A and stock B are: 15%, 10.67% 45%, 32% 13.2%, 9.7% 19%, 12% Stock A: (1/3 * 19%) + (1/3 * 3%) + (1/3 * 23%) = 15% Stock B: (1/3 * 0%) + (1/3 * 12%) + (1/3 * 20%) = 10.67% The variances of stock A and stock B's returns are: 112%2, 101.33%2 8.64%, 8.22% 74.67%2 , 67.56%2 899%2, 544%2 Stock A: (1/3 * (19%-15%)2) + (1/3 * (3%-15%)2) + (1/3 * (23%-15%)2) = 74.67%2 Stock B: (1/3 * (0%-10.67%)2) + (1/3 * (12%-10.67%)2) + (1/3 * (20%-10.67%)2) = 67.56%2 The standard deviation of stock A and stock B's returns are: 8.64%, 8.22% 74.67%2 , 67.56%2 899%2, 544%2 15%, 10.67% Stock A: (74.67%2)1/2 = 8.64% Stock B: (67.56%2)1/2 = 8.22%

Key Risk and Return Concepts

Riskier investments must have higher expected returns than less risky investments; otherwise, people will not purchase investments with higher risks.

Key Risk and Return Concepts

The effects of nondiversifiable risk, which is also labeled systematic risk or market risk, can be determined by computing the beta coefficient (b) of an investment. The beta coefficient measures the volatility of an investment relative to the volatility of the market, which, in theory, is perfectly diversified and thus is affected only by systematic risk.

Key Risk and Return Concepts

The total risk of any investment can be divided into two components: diversifiable risk and nondiversifiable risk. Diversifiable risk is not important to informed investors, because they will eliminate (at least reduce) its effects through diversification. Thus, the relevant risk is the nondiversifiable risk, because it cannot be eliminated, even in a perfectly diversified portfolio.

When you calculate the variance of your portfolio, you should find that it is less than the simple weighted average of the variances of the securities in the portfolio, i.e. it should be less than (.40 * a2 + .60 * S&P2). Can you explain in words why you get this result?

This is the concept of diversification in action. When you hold multiple securities together in a portfolio, the variance of the portfolio will be less than the straight weighted average of the variances for the securities, as long as the securities are not perfectly positively correlated. By holding a portfolio of multiple securities, extremely good (or bad) returns for one security will often be balanced out by extremely bad (or good) returns from some other security. This happens in the first and second states of nature. A does pretty well in the first state and offsets the bad return of B. Conversely, B does pretty well in the second state and offsets the bad return of A. This is the way that we eliminate our exposure to non-systematic risk.

According to the CAPM, investors should

a. expect to be rewarded for only the systematic risk associated with an individual investment, the systematic risk being measured by the beta coefficient.

In a given average beta portfolio, replacing an existing investment with a higher beta investment will lead to

an increase in the required rate of return of the portfolio.

A probability distribution

lists all possible outcomes.

Standard deviation of the returns on a stock is a

measure of the tightness, or variability, of a set of returns.

Calculate the (a) expected return, (b) standard deviation, and (c) coefficient of variation for an investment with the following probability distribution: (LO 8-2) Probability Payoff 0.45 32.0% 0.35 −4.0 0.20 −15.0

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Currently, the risk-free return is 3 percent, and the expected market rate of return is 9 percent. What is the expected return of the following three-stock portfolio? (LO 8-2 & LO 8-3) Probability Payoff $350,000 1.0 250,000 0.2 400,000 2.5

page 14 of notes

Willis currently has $120,000 invested in a four-stock portfolio with a beta coefficient equal to 0.8. Willis plans to sell one of the stocks in his portfolio for $48,000, which will increase the portfolio's beta to 1.0. What is the beta coefficient of the stock Willis plans to sell? (LO 8-3)

page 14 of notes

Suppose the risk-free rate of return is 3.5 percent and the market risk premium is 7 percent. Stock U, which has a beta coefficient equal to 0.9, is currently selling for $28 per share. The company is expected to grow at a 4 percent rate forever, and the most recent dividend paid to stockholders was $1.75 per share. Is Stock U correctly priced? Explain

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The current risk-free rate of return, , is 3 percent and the market risk premium, , is 6 percent. If the beta coefficient associated with a firm's stock is 1.5, what should be the stock's required rate of return? (LO 8-4)

page 15 of notes

Other things held constant, if the expected inflation rate increases, the new security market line (SML) would

shift up.

The risk-free return is 5%, the market risk premium is 6%, and Stock A has a beta of 1.5. Based on this information, the average investor will require a return on Stock A of 14%. If the expected rate of return on Stock A is less than 14%, the average investor will

want to sell Stock A