978-0077861704 Chapter 13 Solutions Manual Part 2

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24. We know the total portfolio value and the investment of two stocks in the portfolio, so we can find

the weight of these two stocks. The weights of Stock A and Stock B are:

Since the portfolio is as risky as the market, the  of the portfolio must be equal to one. We also know the

 of the risk-free asset is zero. We can use the equation for the  of a portfolio to find the weight of the

third stock. Doing so, we find:

Solving for the weight of Stock C, we find:

So, the dollar investment in Stock C must be:

We also know the total portfolio weight must be one, so the weight of the risk-free asset must be one

minus the asset weight we know, or:

So, the dollar investment in the risk-free asset must be:

Challenge

25. We are given the expected return of the assets in the portfolio. We also know the sum of the weights

of each asset must be equal to one. Using this relationship, we can express the expected return of the

portfolio as:

E(RP) = .1360 = wX(.1140) + wY(.0868)

And the weight of Stock Y is:

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The amount to invest in Stock Y is:

A negative portfolio weight means that you short sell the stock. If you are not familiar with short

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 CAPM to find the  of Stock I, we find:

The total risk of the asset is measured by its standard deviation, so we need to calculate the standard

deviation of Stock I. Beginning with the calculation of the stock’s variance, we find:

Using the same procedure for Stock II, we find the expected return to be:

Using the CAPM to find the  of Stock II, we find:

And the standard deviation of Stock II is:

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Although Stock II has more total risk than I, it has much less systematic risk, since its beta is much

27. Here we have the expected return and beta for two assets. We can express the returns of the two

assets using CAPM. If the CAPM is true, then the security market line holds as well, which means all

(.1079 – Rf) / 1.21 = (.0843 – Rf) / .83

Now using CAPM to find the expected return on the market with both stocks, we find:

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.

SlopeSML = Rise / Run

SlopeSML = Increase in expected return / Increase in beta

Since the market’s beta is 1 and the risk-free rate has a beta of zero, the slope of the Security

We could also solve this problem using CAPM. The equations for the expected returns of the

two stocks are:

Subtracting the CAPM equation for Stock B from the CAPM equation for Stock A yields:

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