An investor is trying to decide between 2 mutual funds. Mutual fund #1 offers a
ID: 3440285 • Letter: A
Question
An investor is trying to decide between 2 mutual funds. Mutual fund #1 offers a
slightly higher return than mutual fund #2 so the investor decides that he will invest
in mutual fund #1 unless the risk of mutual fund #1 is significantly higher than the
risk of mutual fund #2. Using the standard deviation of 101 daily returns as a measure
of risk of the two mutual funds, the investor finds that the standard deviation of
mutual fund #1’s daily returns is .95 and the standard deviation of mutual fund #2’s
daily returns is .81. At the 10% level of significance, should the investor invest in
mutual fund #1 or #2?
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 = 0.1 ,
alpha = 0.1
df1 = n1 - 1 = 100
df2 = n2 - 1 = 100
F (crit) = 1.293439013
Getting the test statistic, as
s1 = 0.95
s2 = 0.81
Thus, F = s1^2/s2^2 = 1.375552507
As F > F(crit), we REJECT THE NULL HYPOTHESIS.
There is significant evidence that the risk at fund #1 is greater than that of fund 2. [CONCLUSION]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.