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Aportfolio manager produced an alpha of 3% based on monthly returns over a 6 year period. Under the assumption of a normal distribution, the portfolio manager claims that the probability of observing such a large alpha by chance is only 2%. To test her claim, one would use a t-test using which level of confidence?


A) 90%.

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B) 95%.

C) 98%.

D) 99%.

答案：C

解析：Confidence level = 1 - significance level = 1-0.02 = 98% This means that we are 98% confident that superior performance was not due to chance.

During the last fifteen years, Norma, a portfolio manager, earned excess returns (over risk-free rate) of 16% with a standard deviation of 12%. During the same time period, excess returns (over risk-free rate) and standard deviation of a benchmark portfolio were 11% and 14% respectively. Norma claims to have beaten the benchmark portfolio at 95% confidence level. Based on our

estimation:

I.We reject her claim.

II.We fail to reject her claim.

Which of the above statements is (are) correct given that the t-statistic for the Sharpe ratio is 1.5?

A) II only.

B) I only.

C) Both I and II.

D) Neither I nor II.

答案：B

解析：t = 1.5 < 2 (critical t at 95%), so we fail to reject the null hypothesis: H0: difference in Sharpe ratios is zero. Thus, we can reject her claim to have beaten the benchmark portfolio at 95% confidence level.