Solutions-Chapter10

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Chapter 10
Capital Markets and the Pricing of Risk
10-1. The figure below shows the one-year return distribution for RCS stock. Calculate
a. b.
The expected return.
The standard deviation of the return.
a. b.
E R  0.25 (0.1)  0.1(0.2)  0(0.15)  0.1(0.25)  0.25 (0.3)  5.5% VarianceR0.250.0552 0.10.10.0552 0.2(00.055)2 0.15
0.10.0552 0.250.250.0552 0.3  0.026
Standard Deviation  0.026  16.13%
10-2. The following table shows the one-year return distribution of Startup, Inc. Calculate
a. The expected return.
b. The standard deviation of the return.
a. ER10.40.750.20.50.20.250.1100.132.5%
b. VarianceR10.3252 0.40.750.3252 0.20.50.3252 0.2
0.250.3252 0.1100.3252 0.1  10.46
StandardDeviation 10.463.235323.5%

10-7. The last four years of returns for a stock are as follows:
a. What is the average annual return?
b. What is the variance of the stock’s returns?
c. What is the standard deviation of the stock’s returns?
Given the data presented, make the calculations requested in the question.
4%28%12%4%
a. Average annual return  4 10%
b. Variance of returns 
 0.01867
(.04.10)2 (.28.10)2 (.12.10)2 (.04.10)2 3
c. Standard deviation of returns  variance  0.01867  0.1366  13.66%
The average annual return is 10%. The variance of return is 0.01867. The standard deviation of returns
is 13.66%.
10-16. How does the relationship between the average return and the historical volatility of individual stocks differ from the relationship between the average return and the historical volatility of large, well-diversified portfolios?
For large portfolios there is a relationship between returns and volatility—portfolios with higher returns have higher volatilities. For stocks, no clear relation exists.
10-22. Consider the following two, completely separate, economies. The expected return and volatility of all stocks in both economies is the same. In the first economy, all stocks move together—in good times all prices rise together and in bad times they all fall together. In the second economy, stock returns are independent—one stock increasing in price has no effect on the prices of other stocks. Assuming you are risk-averse and you could choose one of the two economies in which to invest, which one would you choose? Explain.
A risk-averse investor would choose the economy in which stock returns are independent because this risk can be diversified away in a large portfolio.
10-25. Explain why the risk premium of a stock does not depend on its diversifiable risk.
Investors can costlessly remove diversifiable risk from their portfolio by diversifying. They, therefore, do not demand a risk premium for it.
10-26. Identify each of the following risks as most likely to be systematic risk or diversifiable risk:
a. The risk that your main production plant is shut down due to a tornado.
b. The risk that the economy slows, decreasing demand for your firm’s products.
c. The risk that your best employees will be hired away.
d. The risk that the new product you expect your R&D division to produce will not materialize.
a. diversifiable risk
b. systematic risk
c. diversifiable risk
d. diversifiable risk