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 14.42 percent. Morningstar.com also reported that the Fidelity Small Cap Discovery Fund has a standard deviation of returns equal to 29.36 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 .02 level of significance, and assume normality.

Calculate the critical value.

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   <=   1  
Ha:    sigma1^2 / sigma2^2   >   1  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical F, as alpha =    0.02   ,      
alpha =    0.02          
df1 = n1 - 1 =    35         
df2 = n2 - 1 =    35          

F (crit) = 2.026604676 [ANSWER, CRITICAL VALUE]
              
Getting the test statistic, as              
s1 =    29.36          
s2 =    14.42          
              
Thus, F = s1^2/s2^2 =    4.145544503 [TEST STATISTIC]

As F > 2.0266, we reject the null hypothesis.

There is significant evidence that 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 at 0.02 level. [CONCLUSION]

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