You are considering the risk-return profile of two mutual funds for investment.

Question

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 11.3% with a standard deviation of 14.6%. The relatively less risky fund promises an expected return and standard deviation of 4.4% and 6.9%, respectively. Assume that the returns are approximately normally distributed.

Calculate the probability of earning a negative return for each fund. (Round final answer to 4 decimal places.)

Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return?

Calculate the probability of earning a return above 8.7% for each fund. (Round final answer to 4 decimal places.)

Which mutual fund will you pick if your objective is to maximize the probability of earning a return above 8.7%?

Calculate the probability of earning a negative return for each fund. (Round final answer to 4 decimal places.)

Explanation / Answer

riskier fund : P(X<0)=P(Z<(0-11.3)/14.6)=P(Z<-0.774)=0.2195

less riskier fund :P(X<0)=P(Z<(0-4.4)/6.9)=P(Z<-0.6377)=0.2618

a-2) Riskier fund

2) riskier fund:P(X>8.7)=1-P(Z<(8.7-11.3)/14.6)=1-P(Z<-0.1781)=1-0.4293=0.5707

less riskier fund:P(X>8.7)=1-P(Z<(8.7-4.4)/6.9)=1-P(Z<0.6231)=1-0.7334=0.2666

hence Riskier fund

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