Homework 2.
1. Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 6%, and the market’s average return
was 14%. Performance is measured using an index model regression on excess return.
Stock A Stock B
Index model regression estimates 1% + 1.2 (RM – rF) 2% + 0.8 (RM – rF)
R-Square 0.576 0.436
Residual standard deviation, s(e) 10.3% 19.1%
Standard deviation of excess return 21.6% 24.9a%
a. Calculate the following statistics for each stock
I. Alpha
II. Sharpe ratio
III. Treynor ratio
b. Which stock is the best choice under each of the following circumstances? And Why?
I. This is the only risky asset to be held by the investor.
II. This stock will be mixed with the rest of the investor’s portfolio, currently composed solely of holdings in the market index fund.
III. This is one of many stocks that the investor is analyzing to form an actively managed stock portfolio.
2. An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The
following table provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the S&P 500), and the U.S. Treasury bills during the
past eight years:
Average annual rate of return Standard deviation of return Beta
Portfolio X 10% 18% 0.60
S&P 500 12 13 1.00
T-Bills 6 N/A N/A
a. Calculate the Treynor and Sharpe measures for both Portfolio X and the S&P 500. Briefly explain whether Portfolio X underperformed, equaled, or outperformed
the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure.
b. Based on the performance of Portfolio X relative to the S&P 500 calculated in part (a, briefly explain the reason for the conflicting results when using the
Treynor measure versus the Sharpe measure.
3. An index model regression applied to past monthly returns in General Motors’ stock price produces the following estimates, which are believed to be stable over
time:
rGM = 0.10% + 1.1rM
If the market index subsequently rises by 8% and General Motors’ stock price rises by 7%, what is the abnormal return in General Motors’ stock?
4. Currently, the term structure is as follows: One-year bonds yield 7%, two-year bonds yield 8%, three-year bonds and greater maturity bonds yield 9%. An
investor is choosing between one-, two-, and three-year maturity bonds all paying annual coupons of 8%, once a year. Which bond should the investor buy if she
strongly believes that at year-end the yield curve will be flat at 9%?
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