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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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