Q 1. A manager buys three shares of stock today, and then sells one of those shares each year for: next 3 years. His actions and the price history of the stock are summarized below. The stockpra no dividends.
Time
|
Price |
Action |
| 0 |
$90
|
Buy 3 shares
|
1
|
100
|
Sell 1 share
|
| 2 |
100
|
Sell 1 share
|
| 3 |
100
|
Sell 1 share
|
a. Calculate the time-weighted geometric average return on this "portfolio."
b. Calculate the time-weighted arithmetic average return on this portfolio.
c. Calculate the dollar-weighted average return on this portfolio.
Q 2. 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 returns.
Stock A Stock B
Index model regression estimates 1% + 1.2(rm- rf) 2% + .8(rm - rf)
R-square .576 .436
Residual standard deviation, 0(e) 10.3% 19.1%
Standard deviation of excess returns 21.6% 24 9%
a. Calculate the following statistics for each stock:
i. Alpha
ii. Information ratio
iii. Sharpe ratio
iv. Treynor measure
b. Which stock is the best choice under the following circumstances?
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.