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1 A portfolio is created by investing 1750 in Stock A and 2750 in Stock B. Stock A has an
expected return of 14% and a volatility of 25%. Stock B has an expected return of 6% and a
volatility of 40%. The correlation of the returns of the two stocks is 0.2. The risk free rate is
3.1%.
Suppose that an additional investment of 1000 is made into Stock A. Calculate the increase
in Stock A’s required return resulting from this additional investment.
2 A portfolio consists of three stocks: Stock A, Stock B, and Stock C. The table below
provides the covariances between the returns of each pair of stocks, the expected return
for each stock, and the proportion of the portfolio’s value that is represented by each stock.
The risk free rate is 2.5%. Calculate Stock A’s required return.
Stock A
Stock A 0.090
Stock B 0.036
Stock C 0.045
Stock B
Stock C
0.036
0.360
–0.060
0.045
–0.060
0.250
0.07936
0.0612
0.196
Expected
Return
13%
30%
21%
Weight
40%
20%
40%
3 A portfolio of several stocks has a Sharpe ratio of 1.3 and a risk premium of 12%. Stock XYX
has a Sharpe ratio of 0.6 and a risk premium of 25%. The expected return of Stock XYZ is 29.5%
and the correlation between Stock XYZ and the portfolio is 0.5. Find the required return for
Stock XYZ with respect to the portfolio.
4 A portfolio consists of two stocks, Stock A and Stock B. The volatility of Stock A is 0.5
and the volatility of Stock B is 0.25. The proportion of the portfolio’s value that is
represented by shares of Stock A is 0.3. The correlation of the returns of the two stocks is
0.6. Calculate the beta of Stock A with the portfolio.
1.5066
5 A portfolio consists of three stocks: Stock A, Stock B, and Stock C. The table below
provides the covariances between the returns of each pair of stocks, the expected return
for each stock, and the proportion of the portfolio’s value that is represented by each stock.
Calculate the beta of Stock A with the portfolio.
Stock A
Stock A 0.360
Stock B 0.018
Stock C –0.090
1.4887
Stock B
Stock C
0.018
0.040
0.024
–0.090
0.024
0.090
Expected
Return
0.27
0.18
0.11
Weight
0.25
0.25
0.5

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