21 February, 07:07

# A fund of funds has investments in 36 hedge funds. At the end of the year, the mean return of the constituent hedge funds was 18%. The standard deviation of the funds' returns was 12%. The benchmark return for the fund of funds was 14%. Is the difference between the average return and the benchmark return statistically significant at the 95% confidence level?

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1. 21 February, 07:24
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the difference between the average return and the benchmark return is not statistically significant since it is in the 95% confidence interval.

Explanation:

In order to solve this problem we have to use the confidence level formula to see if the return of the funds is statistically significant compared to the benchmark. The formula is: (μ - zα/2 · (σ/√n), μ + zα/2 · (σ/√n))

At the 95% confidence level (or 1-α=0.95), the value of α/2 is 0.025. And according to the normal distribution, z α/2 = 1.96. Then, replacing in the all the data in the equation:

(0.18 ± 1.96 * (0.12/6)) = (0.1408, 0.2192) = (14.08%, 21.92%)

Then, 18% is between the confidence interval.