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:

Box and Whisker Plot

A graphical method to depict groups of numerical data through their quartiles, highlighting the median and variability of the data set.

Percentiles

Measures that divide a dataset into 100 equal parts, each portion representing 1% of the dataset, to indicate distribution.

Standard Deviation

A framework for quantifying how much a collection of data points varies or spreads.

Relative Standing

An indication of the position of a value within a dataset, often represented through percentiles, z-scores, or standard scores.