1. What is a common weakness of Jensen’s alpha and the Treynor ratio? 2. What is

Question

1. What is a common weakness of Jensen’s alpha and the Treynor ratio?

2. What is one advantage and one disadvantage of the Sharpe ratio?

3. Most sources report alphas and other metrics relative to a standard benchmark, such as the S&P 500. When might this method be an inappropriate comparison?

4. What is the Sharpe ratio, Treynor ratio, and Jensen’s alpha for each portfolio?

A stock has an annual return of 12 percent and a standard deviation of 56 percent. Assuming returns are normally distributed, what is the smallest expected loss over the next year with a probability of 1 percent? Does this number make sense? Why or why not?

Explanation / Answer

1. A common weakness of both the Jensen alpha and the Treynor ratio is that both require an estimate of beta, which can differ a lot depending on the source, which in turn can lead to a mismeasurement of risk adjusted return.

2.An advantage of the Sharpe ratio is that a beta estimate is not required; however, the Sharpe ratio is not appropriate when evaluating individual stocks because it uses total risk rather than systematic

3. Some portfolios and mutual funds include asset classes with characteristics that do not accurately compare against the S&P 500, such as bond funds, sector funds, real estate, etc. Therefore, the S&P 500 may not be the appropriate benchmark to use in that case.

4. The Sharpe ratio is calculated as a portfolio’s risk premium divided by the standard deviation of the portfolio’s return. The Treynor ratio is the portfolio risk premium divided by the portfolio’s beta coefficient. Jensen’s alpha is the difference between a stock’s or a portfolio’s actual return and that which is predicted by the CAPM. A positive alpha implies returns above the CML line (as drawn using the CAPM).

5. Prob(R 0.12 + 2.326(0.56)) = 1%
Prob(R 1.42) = 1% = 142.25%
While this is a large return, it is plausible, and even possible. Since it is not possible for a stock to lose more than 100% but it is possible for a stock to gain more than 100%, stock returns are not truly normal.

a. 142.25%

b. Yes

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