(See attached file for full problem descriptions)
Use the following expectations on Stocks X and Y to answer questions 9 through 11 (round to the nearest percent).
Bear Market Normal Market Bull Market
Probability 0.2 0.5 0.3
Stock X -20% 18% 50%
Stock Y -15% 20% 10%
9. What are the expected returns for Stocks X and Y?
10. What are the standard deviations of returns on Stocks X and Y?
11. Assume that of your $10,000 portfolio, you invest $9,000 in Stock X and $1,000 in Stock Y. What is the expected return on your portfolio?
5. Abigail Grace has a $900,000 fully diversified portfolio. She subsequently inherits ABC Company common stock worth $100,000. Her financial advisor provided her with the following forecasted information:
Risk and Return Characteristics
Expected Standard Deviation
Monthly Returns of Monthly Returns
Original Portfolio 0.67% 2.37%
ABC Company 1.25 2.95
The correlation coefficient of ABC stock returns with the original portfolio returns is 0.40
a. The inheritance changes Grace's overall portfolio and she is deciding whether to buy the ABC stock. Assuming Grace keeps the ABC stock, calculate the:
i. Expected return of her new portfolio which includes the ABC stock.
ii. Covariance of ABC stock returns with the original portfolio returns.
iii. Standard deviation of her new portfolio which includes the ABC stock.
6. Consider the following information regarding the performance of a money manager in a recent month. The table presents the actual return of each sector of the manager's portfolio in column (1), the fraction of the portfolio allocated to each sector in column (2), the benchmark or neutral sector allocations in column (3), and the returns of sector indexes in column (4).
(1) (2) (3) (4)
Actual Actual Benchmark Index
Return Weight Weight Return
Equity 2.0% 0.70 0.60 2.5% (S&P 500)
Bonds 1.0 0.20 0.30 1.2 (Aggregate Bond index)
Cash 0.5 0.10 0.10 0.5
a. What was the manager's return in the month? What was her over- or underperformance?
b. What was the contribution of security selection to relative performance?
c. What was the contribution of asset allocation to relative performance? Confirm that the sum of selection and allocation contribution equals her total "excess" return relative to the bogey.
15. A portfolio manager summarizes the input from the macro and micro forecasts in the following table:
Asset Expected Return (%) Beta Residual Standard
Stock A 20 1.3 58
Stock B 18 1.8 71
Stock C 17 0.7 60
Stock D 12 1.0 55
Asset Expected Return (%) Standard Deviation (%)
T-bills 8 0
Passive equity portfolio 16 23
a. Calculate expected excess returns, alpha values, and residual variances for these stocks.
b. Construct the optimal risky portfolio.
c. What is Sharpe's measure for the optimal portfolio and how much of it is contributed by the active portfolio? What is the M2?
This solution is comprised of a detailed explanation to answer what are the expected returns for Stocks X and Y, what are the standard deviations of returns on Stocks X and Y, what is the expected return on your portfolio, calculate the expected return of her new portfolio which includes the ABC stock, covariance of ABC stock returns with the original portfolio returns.
and standard deviation of her new portfolio which includes the ABC stock.