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Exam 8: Risk and Rates of Return

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Question 1

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Which of the following statements is CORRECT?

A) An investor can eliminate virtually all market risk if he or she holds a very large and well diversified portfolio of stocks.
B) The higher the correlation between the stocks in a portfolio,the lower the risk inherent in the portfolio.
C) It is impossible to have a situation where the market risk of a single stock is less than that of a portfolio that includes the stock.
D) Once a portfolio has about 40 stocks,adding additional stocks will not reduce its risk by even a small amount.
E) An investor can eliminate virtually all diversifiable risk if he or she holds a very large,well-diversified portfolio of stocks.

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

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Question 2

Multiple Choice

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Which of the following statements is CORRECT?

A) A large portfolio of randomly selected stocks will always have a standard deviation of returns that is less than the standard deviation of a portfolio with fewer stocks,regardless of how the stocks in the smaller portfolio are selected.
B) Diversifiable risk can be reduced by forming a large portfolio,but normally even highly-diversified portfolios are subject to market (or systematic) risk.
C) A large portfolio of randomly selected stocks will have a standard deviation of returns that is greater than the standard deviation of a 1-stock portfolio if that one stock has a beta less than 1.0.
D) A large portfolio of stocks whose betas are greater than 1.0 will have less market risk than a single stock with a beta = 0.8.
E) If you add enough randomly selected stocks to a portfolio,you can completely eliminate all of the market risk from the portfolio.

F) D) and E)
G) A) and B)

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B

Question 3

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Jim Angel holds a $200,000 portfolio consisting of the following stocks: $\begin{array}{lll}\text { Stock }&\text { Investment }&\text { Beta }\\A & \$ 50,000 & 1.20 \\B & \$ 50,000 & 0.80 \\C & \$ 50,000 & 1.00 \\D & \$ 50,000 & 1.20\\\text { Total }&\$200,000\end{array}$ What is the portfolio's beta? Do not round your intermediate calculations.

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.

The Y-axis intercept of the SML represents the required return of a portfolio with a beta of zero,which is the risk-free rate.

Carson Inc.'s manager believes that economic conditions during the next year will be strong,normal,or weak,and she thinks that the firm's returns will have the probability distribution shown below.What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population,not a sample. ) Do not round your intermediate calculations. $\begin{array}{lrr}\text { Economic }\\\text { Conditions } & \text { Prob. } & \text { Return }\\\text { Strong } & 30 \% & 40.0 \% \\\text { Normal } & 40 \% & 10.0 \% \\\text { Weak } & 30 \% & -16.0 \%\end{array}$ ?

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

Your portfolio consists of $50,000 invested in Stock X and $50,000 invested in Stock Y.Both stocks have an expected return of 15%,betas of 1.6,and standard deviations of 30%.The returns of the two stocks are independent,so the correlation coefficient between them,rXY,is zero.Which of the following statements best describes the characteristics of your 2-stock portfolio?

Company A has a beta of 0.70,while Company B's beta is 1.45.The required return on the stock market is 9.00%,and the risk-free rate is 2.25%.What is the difference between A's and B's required rates of return? (Hint: First find the market risk premium,then find the required returns on the stocks. ) Do not round your intermediate calculations.

Stock A has a beta = 0.8,while Stock B has a beta = 1.6.Which of the following statements is CORRECT?

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.

Jill Angel holds a $200,000 portfolio consisting of the following stocks.The portfolio's beta is 0.88. $\begin{array}{lll}\text { Stock }&\text { Investment }&\text { Beta }\\\text { A } & \$ 50,000 & 0.50 \\\mathrm{~B} & \$ 50,000 & 0.80 \\\mathrm{C} & \$ 50,000 & 1.00 \\\mathrm{D} & \$ 50,000 & 1.20\\\text { Total }&\$200,000\end{array}$ If Jill replaces Stock A with another stock,E,which has a beta of 1.45,what will the portfolio's new beta be? Do not round your intermediate calculations.

Stock A has an expected return of 12%,a beta of 1.2,and a standard deviation of 20%.Stock B also has a beta of 1.2,but its expected return is 10% and its standard deviation is 15%.Portfolio AB has $900,000 invested in Stock A and $300,000 invested in Stock B.The correlation between the two stocks' returns is zero (that is,rA,B = 0) .Which of the following statements is CORRECT?

Nagel Equipment has a beta of 0.88 and an expected dividend growth rate of 4.00% per year.The T-bill rate is 4.00%,and the T-bond rate is 5.25%.The annual return on the stock market during the past 4 years was 10.25%.Investors expect the average annual future return on the market to be 14.75%.Using the SML,what is the firm's required rate of return? Do not round your intermediate calculations.

Which of the following statements best describes what you should expect if you randomly select stocks and add them to your portfolio?

Managers should under no conditions take actions that increase their firm's risk relative to the market,regardless of how much those actions would increase the firm's expected rate of return.

Since the market return represents the expected return on an average stock,the market return reflects a certain amount of risk.As a result,there exists a market risk premium,which is the amount over and above the risk-free rate,that is required to compensate stock investors for assuming an average amount of risk.

According to the Capital Asset Pricing Model,investors are primarily concerned with portfolio risk,not the risks of individual stocks held in isolation.Thus,the relevant risk of a stock is the stock's contribution to the riskiness of a well-diversified portfolio.

Stock A's stock has a beta of 1.30,and its required return is 13.75%.Stock B's beta is 0.80.If the risk-free rate is 2.75%,what is the required rate of return on B's stock? (Hint: First find the market risk premium. ) Do not round your intermediate calculations.

Which of the following statements is CORRECT?