A Portfolio Manager Claims That the Mean Annual Return on One

question 96

Essay

A portfolio manager claims that the mean annual return on one of the mutual funds he manages exceeds 8%. To substantiate his claim, he states that over the past 10 years, the mean annual return for the mutual fund has been 9.5% with a sample standard deviation of 1.5%. Assume annual returns are normally distributed.
A) Specify the competing hypotheses to test the portfolio manager's claim.
B) Calculate the value of the test statistic.
C) At the 5% significance level, use the p-value approach to state the decision rule.
D) Is the portfolio manager's claim substantiated by the data? Explain.

• A) Specify the competing hypotheses to test the portfolio manager's claim.
• B) Calculate the value of the test statistic.
• C) At the 5% significance level, use the p-value approach to state the decision rule.
• D) Is the portfolio manager's claim substantiated by the data? Explain.

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Definitions:

Weighted Average

A calculation that takes into account the varying degrees of importance of the numbers in a data set, giving more weight to some numbers than others.

Basic Earnings

The net income earned by a company divided by the number of outstanding shares, providing a measure of the company’s profitability on a per-share basis.

Common Stock

A type of security that represents ownership in a corporation, granting shareholders voting rights and a share in the company's profits via dividends.

Stock Options

Financial instruments allowing the possessor to buy or sell shares at an agreed upon price before a certain deadline, without being compelled to do so.