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Exam 8: Risk and Rates of Return

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Question 21

True/False

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It is possible for a firm to have a positive beta, even if the correlation between its returns and those of another firm is negative.

A) True
B) False

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Question 22

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Which of the following statements is CORRECT?

A) If a stock has a beta of to 1.0, its required rate of return will be unaffected by changes in the market risk premium.
B) The slope of the Security Market Line is beta.
C) Any stock with a negative beta must in theory have a negative required rate of return, provided rRF is positive.
D) If a stock's beta doubles, its required rate of return must also double.
E) If a stock's returns are negatively correlated with returns on most other stocks, the stock's beta will be negative.

F) B) and C)
G) C) and D)

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Question 23

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Which of the following is NOT a potential problem when estimating and using betas, i.e., which statement is FALSE?

Assume that your uncle holds just one stock, East Coast Bank (ECB) , which he thinks has very little risk. You agree that the stock is relatively safe, but you want to demonstrate that his risk would be even lower if he were more diversified. You obtain the following returns data for West Coast Bank (WCB) . Both banks have had less variability than most other stocks over the past 5 years. Measured by the standard deviation of returns, by how much would your uncle's risk have been reduced if he had held a portfolio consisting of 60% in ECB and the remainder in WCB? (Hint: Use the sample standard deviation formula.) $\begin{array} { l c r } \text { Year } & \text { ECB } & \text { WCB } \\2009& 40.00 \% & 40.00 \% \\2010 & - 10.00 & 15.00 \% \\2011 & 35.00 \% & - 5.00 \% \\2012 & - 5.00 \% & - 10.00 \% \\2013 & 15.00 \% & 35.00 \% \\\\\text { Average return = } & 15.00 \% & 15.00 \% \\\text { Standard deviation = } & 22.64 \% & 22.64 \%\end{array}$

One key conclusion of the Capital Asset Pricing Model is that the value of an asset should be measured by considering both the risk and the expected return of the asset, assuming that the asset is held in a well-diversified portfolio. The risk of the asset held in isolation is not relevant under the CAPM.

Returns for the Dayton Company over the last 3 years are shown below. What's the standard deviation of the firm's returns? (Hint: This is a sample, not a complete population, so the sample standard deviation formula should be used.) $\begin{array} { l r } \text { Year } & \text { Return } \\2013 & 21.00 \% \\2012 & - 12.50 \% \\2011 & 25.00 \%\end{array}$

Assume that you hold a well-diversified portfolio that has an expected return of 11.0% and a beta of 1.20. You are in the process of buying 1,000 shares of Alpha Corp at $10 a share and adding it to your portfolio. Alpha has an expected return of 13.0% and a beta of 1.50. The total value of your current portfolio is $90,000. What will the expected return and beta on the portfolio be after the purchase of the Alpha stock?

Which of the following statements is CORRECT?

Jane has a portfolio of 20 average stocks, and Dick has a portfolio of 2 average stocks. Assuming the market is in equilibrium, which of the following statements is CORRECT?

If the returns of two firms are negatively correlated, then one of them must have a negative beta.

The SML relates required returns to firms' systematic (or market) risk. The slope and intercept of this line can be influenced by a manager's actions.

If investors are risk averse and hold only one stock, we can conclude that the required rate of return on a stock whose standard deviation is 0.21 will be greater than the required return on a stock whose standard deviation is 0.10. However, if stocks are held in portfolios, it is possible that the required return could be higher on the stock with the lower standard deviation.

Assume that the risk-free rate remains constant, but the market risk premium declines. Which of the following is most likely to occur?

Stock A has an expected return of 10% and a standard deviation of 20%. Stock B has an expected return of 13% and a standard deviation of 30%. The risk-free rate is 5% and the market risk premium, rM − rRF, is 6%. Assume that the market is in equilibrium. Portfolio AB has 50% invested in Stock A and 50% invested in Stock B. The returns of Stock A and Stock B are independent of one another, i.e., the correlation coefficient between them is zero. Which of the following statements is CORRECT?

Risk-averse investors require higher rates of return on investments whose returns are highly uncertain, and most investors are risk averse.

The risk-free rate is 6%; Stock A has a beta of 1.0; Stock B has a beta of 2.0; and the market risk premium, rM − rRF, is positive. Which of the following statements is CORRECT?

Assume that you manage a $10.00 million mutual fund that has a beta of 1.05 and a 9.50% required return. The risk-free rate is 4.20%. You now receive another $5.00 million, which you invest in stocks with an average beta of 0.65. What is the required rate of return on the new portfolio? (Hint: You must first find the market risk premium, then find the new portfolio beta.)

Mikkelson Corporation's stock had a required return of 11.75% last year, when the risk-free rate was 5.50% and the market risk premium was 4.75%. Then an increase in investor risk aversion caused the market risk premium to rise by 2%. The risk-free rate and the firm's beta remain unchanged. What is the company's new required rate of return? (Hint: First calculate the beta, then find the required return.)

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

In portfolio analysis, we often use ex post (historical) returns and standard deviations, despite the fact that we are really interested in ex ante (future) data.