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Exam 8: Risk and Rates of Return

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Question 1

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Mike Flannery holds the following portfolio: $\begin{array} { l r r } \underline { \text { Stock }} & \underline { \text { Investment } } & \underline { \text { Beta } } \\ \text { A } & \$ 150,000 & 1.40 \\\text { B } & 50,000 & 0.80 \\\text { C } & 100,000 & 1.00 \\\text { D } &\underline { {75,000 }} & 1.20 \\\text { Total } & \underline { \$375,000 }\end{array}$ What is the portfolio's beta?

A) 1.06
B) 1.17
C) 1.29
D) 1.42
E) 1.56

F) D) and E)
G) A) and C)

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Question 2

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When adding a randomly chosen new stock to an existing portfolio, the higher (or more positive) the degree of correlation between the new stock and stocks already in the portfolio, the less the additional stock will reduce the portfolio's risk.

A) True
B) False

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Question 3

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An individual stock's diversifiable risk, which is measured by its beta, can be lowered by adding more stocks to the portfolio in which the stock is held.

Because of differences in the expected returns on different investments, the standard deviation is not always an adequate measure of risk. However, the coefficient of variation adjusts for differences in expected returns and thus allows investors to make better comparisons of investments' stand-alone risk.

Stock A has a beta of 0.8 and Stock B has a beta of 1.2. 50% of Portfolio P is invested in Stock A and 50% is invested in Stock B. If the market risk premium (rM − rRF) were to increase but the risk-free rate (rRF) remained constant, which of the following would occur?

Stock A has a beta of 0.7, whereas Stock B has a beta of 1.3. Portfolio P has 50% invested in both A and B. Which of the following would occur if the market risk premium increased by 1% but the risk-free rate remained constant?

Someone who is risk averse has a general dislike for risk and a preference for certainty. If risk aversion exists in the market, then investors in general are willing to accept somewhat lower returns on less risky securities. Different investors have different degrees of risk aversion, and the end result is that investors with greater risk aversion tend to hold securities with lower risk (and therefore a lower expected return) than investors who have more tolerance for risk.

Diversification will normally reduce the riskiness of a portfolio of stocks.

Which is the best measure of risk for a single asset held in isolation, and which is the best measure for an asset held in a diversified portfolio?

Bill Dukes has $100,000 invested in a 2-stock portfolio. $35,000 is invested in Stock X and the remainder is invested in Stock Y. X's beta is 1.50 and Y's beta is 0.70. What is the portfolio's beta?

Kollo Enterprises has a beta of 1.10, the real risk-free rate is 2.00%, investors expect a 3.00% future inflation rate, and the market risk premium is 4.70%. What is Kollo's required rate of return?

The slope of the SML is determined by investors' aversion to risk. The greater the average investor's risk aversion, the steeper the SML.

If you plotted the returns on a given stock against those of the market, and if you found that the slope of the regression line was negative, the CAPM would indicate that the required rate of return on the stock should be greater than the risk-free rate for a well-diversified investor, assuming that the observed relationship is expected to continue into the future.

A highly risk-averse investor is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolio. The three stocks currently held all have b = 1.0, and they are perfectly positively correlated with the market. Potential new Stocks A and B both have expected returns of 15%, are in equilibrium, and are equally correlated with the market, with r = 0.75. However, Stock A's standard deviation of returns is 12% versus 8% for Stock B. Which stock should this investor add to his or her portfolio, or does the choice not matter?

Bob has a $50,000 stock portfolio with a beta of 1.2, an expected return of 10.8%, and a standard deviation of 25%. Becky also has a $50,000 portfolio, but it has a beta of 0.8, an expected return of 9.2%, and a standard deviation that is also 25%. The correlation coefficient, r, between Bob's and Becky's portfolios is zero. If Bob and Becky marry and combine their portfolios, which of the following best describes their combined $100,000 portfolio?

Nile Food's stock has a beta of 1.4, while Elba Eateries' stock has a beta of 0.7. Assume that the risk-free rate, rRF, is 5.5% and the market risk premium, (rM − rRF) , equals 4%. Which of the following statements is CORRECT?

Suppose you hold a portfolio consisting of a $10,000 investment in each of 8 different common stocks. The portfolio's beta is 1.25. Now suppose you decided to sell one of your stocks that has a beta of 1.00 and to use the proceeds to buy a replacement stock with a beta of 1.35. What would the portfolio's new beta be?

Jim Angel holds a $200,000 portfolio consisting of the following stocks: $\begin{array}{lrr}\underline{\text { Stock }} &\underline{ \text { Investment }} &\underline{ \text { Beta }}\\\mathrm{A} & \$ 50,000 & 0.95 \\\mathrm{B} & 50,000 & 0.80 \\\mathrm{C} & 50,000 & 1.00 \\\mathrm{D} & 50,000 & 1.20\\\text { Total }&\underline{ \$ 200.000}\end{array}$ What is the portfolio's beta?

Taggart Inc.'s stock has a 50% chance of producing a 25% return, a 30% chance of producing a 10% return, and a 20% chance of producing a −28% return. What is the firm's expected rate of return?

A stock's beta is more relevant as a measure of risk to an investor who holds only one stock than to an investor who holds a well-diversified portfolio.