Standard deviation of returns is often used as a measure of a mutual fund’s vola

Question

Standard deviation of returns is often used as a measure of a mutual fund’s volatility (risk). A larger standard deviation of returns is an indication of higher risk. According to Morningstar.com (June 17, 2010), the American Century Equity Income Institutional Fund, a large cap fund, has a standard deviation of returns equal to 13.68 percent. Morningstar.com also reported that the Fidelity Small Cap Discovery Fund has a standard deviation of returns equal to 27.79 percent. Each standard deviation was computed using a sample of size 36. Perform a hypothesis test to determine if the variance of returns for the Fidelity Small Cap Discovery Fund is larger than the variance of returns for the American Century Equity Income Institutional Fund. Perform the test at the .01 level of significance, and assume normality. (a) Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Test statistic (b) Calculate the critical value. (Round your answer to 2 decimal places.) Critical value (c) At the .01 significance level, what it the conclusion? Reject Fail to reject

Explanation / Answer

a.
Null, Small Cap Discovery Fund is larger variance than Equity Income Institutional Fund Ho: ^2 > ^2
Alternate, Small Cap Discovery Fund is smaller variance than Equity Income Institutional Fund H1: ^2 < ^2
Test Statistic
Sample 1
s1^2=778.41, n1 =36
Sample 2
s2^2 =187.1424, n2 =36
Fo =778.41/187.1424 = 4.16
| Fo | =4.16
b.
Critical Value
The Value of |F | at LOS 0.01 with d.f F(n1-1,n2-1)=F(35,35) is 2.231
We got |Fo| =4.159 & | F | =2.231
c.
Make Decision
Hence Value of | Fo | > | F | and Here we Reject Ho

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