Consider the two (excess return) index-model regression results for stocks A and 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% + 0.8(rM – rf ) R-square 0.576 0.436 Residual standard deviation, σ(e) 10.3% 19.1% Standard deviation of excess returns 21.6% 24.9% Calculate the following statistics for each stock: Alpha Information ratio Sharpe ratio Treynor measure Which stock is the best choice under the following circumstances? This is the only risky asset to be held by the investor. This stock will be mixed with the rest of the investor’s portfolio, currently composed solely of holdings in the market-index fund. This is one of many stocks that the investor is analyzing to form an actively managed stock portfolio.
- Consider the two (excess return) index-model regression results for stocks A and 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% + 0.8(rM – rf ) |
|
R-square
|
0.576 |
0.436 |
|
Residual standard deviation, σ(e) |
10.3% |
19.1%
|
|
Standard deviation of excess returns |
21.6% |
24.9%
|
- Calculate the following statistics for each stock:
- Alpha
- Information ratio
- Sharpe ratio
- Treynor measure
- Which stock is the best choice under the following circumstances?
- This is the only risky asset to be held by the investor.
- This stock will be mixed with the rest of the investor’s portfolio, currently composed solely
of holdings in the market-index fund.
- This is one of many stocks that the investor is analyzing to form an actively managed stock
portfolio.
William F. Sharpe, a Nobel Laureate, devised the Sharpe ratio, which is used to help investors understand the return on an investment in relation to its risk. The ratio is defined as the return achieved above the risk-free rate per unit of volatility or overall risk. Volatility is a measure of how quickly the price of an asset or a portfolio changes. To measure risk-adjusted performance, the Treynor Index examines an investment portfolio's excess return per unit of risk. The profit earned over and above what would have been obtained in a risk-free investment is referred to as excess return in the context of the Treynor Index.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
