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CHAPTER 13
RISK, RETURN, AND THE SECURITY
MARKET LINE
Answers to Concepts Review and Critical Thinking Questions
1. Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of
Doesn’t the answer to (e) assume that the market was certain the legislation would actually pass? Even if
CHAPTER 13 - 2
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this solutions
manual, rounding may appear to have occurred. However, the final answer for each problem is found
without rounding during any step in the problem.
Basic
2. The expected return of a portfolio is the sum of the weight of each asset times the expected return of
each asset. The total value of the portfolio is:
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4. Here we are given the expected return of the portfolio and the expected return of each asset in the
5. The expected return of an asset is the sum of each return times the probability of that return occurring.
So, the expected return of the asset is:
6. The expected return of an asset is the sum of each return times the probability of that return occurring.
So, the expected return of the asset is:
7. The expected return of an asset is the sum of each return times the probability of that return occurring.
So, the expected return of each stock asset is:
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8. The expected return of a portfolio is the sum of the weight of each asset times the expected return of
each asset. So, the expected return of the portfolio is:
9. a. To find the expected return of the portfolio, we need to find the return of the portfolio in each
b. This portfolio does not have an equal weight in each asset. We still need to find the return of the
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10. a. This portfolio does not have an equal weight in each asset. We first need to find the return of the
b. To calculate the standard deviation, we first need to calculate the variance. To find the variance,
11. The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta
of the portfolio is:
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13. CAPM states the relationship between the risk of an asset and its expected return. CAPM is:
16. Here we need to find the risk-free rate using the CAPM. Substituting the values given, and solving for
the risk-free rate, we find:
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b. We need to find the portfolio weights that result in a portfolio with a of 0.93. We know the
c. We need to find the portfolio weights that result in a portfolio with an expected return of 9
d. Solving for the of the portfolio as we did in part a, we find:
18. First, we need to find the of the portfolio. The of the risk-free asset is zero, and the weight of the
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The slope of the SML is equal to the market risk premium, which is 0.0696. Using these equations to fill in
the table, we get the following results:
19. There are two ways to correctly answer this question. We will work through both. First, we can use
the CAPM. Substituting in the value we are given for each stock, we find:
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We can also answer this question using the reward-to-risk ratio. All assets must have the same reward-
20. We need to set the reward-to-risk ratios of the two assets equal to each other, which is:
Intermediate
21. For a portfolio that is equally invested in large-company stocks and long-term bonds:
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22. We know that the reward-to-risk ratios for all assets must be equal. This can be expressed as:
23. a. We need to find the return of the portfolio in each state of the economy. To do this, we will
b. The risk premium is the return of a risky asset minus the risk-free rate. T-bills are often used as
the risk-free rate, so:
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c. The approximate expected real return is the expected nominal return minus the inflation rate, so:
The approximate real risk premium is the approximate expected real return minus the risk-free
rate, so:
24. We know the total portfolio value and the investment of two stocks in the portfolio, so we can find the
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Challenge
25. We are given the expected return of the assets in the portfolio. We also know the sum of the weights
.
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26. The amount of systematic risk is measured by the of an asset. Since we know the market risk
premium and the risk-free rate, if we know the expected return of the asset we can use the CAPM to
solve for the of the asset. The expected return of Stock I is:
Using the same procedure for Stock II, we find the expected return to be:
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27. Here we have the expected return and beta for two assets. We can express the returns of the two assets
RM = .1159, or 11.59% RM = .1159, or 11.59%
28. a. The expected return of an asset is the sum of the probability of each return occurring times the
probability of that return occurring. So, the expected return of each stock is:
b. We can use the expected returns we calculated to find the slope of the Security Market Line. We
