Question

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 13.7% with a standard deviation of 19.3%. The relatively less risky fund promises an expected return and standard deviation of 3.3% and 6.6%, respectively. Assume that the returns are approximately normally distributed. a-1. Calculate the probability of earning a negative return for each fund. (Round final answer to 4 decimal places.) Probability Riskier fund Less risky fund a-2. Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return? Riskier fund Less risky fund b-1. Calculate the probability of earning a return above 10.2% for each fund. (Round final answer to 4 decimal places.) Probability Riskier fund Less risky fund b-2. Which mutual fund will you pick if your objective is to maximize the probability of earning a return above 10.2%? Riskier fund Less risky fund

Answer 1

Here for relatively riskier fund if x is the return of that fund at particular moment.

Mean = 13.7%

standard deviation = 19.3 %

Here for relatively less risky fund if y is the returen of that fund at particular moment.

Mean = 3.3 %

standard deviation = 6.6%

Here for negative return.

Pr(Negative Return for relatively riskier fund) = Pr(x < 0) = Pr(x < 0 ; 13.7%, 19.3%)

Z = (0 - 13.7)/19.3 = -0.71

Pr(x < 0) = Pr(x < 0 ; 13.7%, 19.3%) = Pr(Z < -0.71) = 0.2389

Pr(Negative Return for less riskier fund) = Pr(x < 0) = Pr(x < 0 ; 3.3%, 6.6%)

Z = (0 - 3.3)/6.6 = -0.5

Pr(x < 0) = Pr(x < 0 ; 3.3%, 6.6%) = Pr(Z < -0.5) = 0.3085

Here we would chose the relatively more riskier fund.

Here for return more than above 10.2%

Pr( Return more than 10.2% for relatively riskier fund) = Pr(x > 10.2%) = Pr(x > 10.2%; 13.7%, 19.3%)

Z = (10.2 - 13.7)/19.3 = -0.1813

Pr(x > 10.2) = Pr(x > 10.2% ; 13.7%, 19.3%) = Pr(Z > -0.1813) = 1 - 0.4281 = 0.5719

Pr( Return more than 10.2% for less riskier fund) = Pr(x > 10.2%) = Pr(x > 10.2% ; 3.3%, 6.6%)

Z = (10.2 - 3.3)/6.6 = 1.0455

Pr(x > 10.2%) = Pr(x > 10.2% ; 3.3%, 6.6%) = Pr(Z > 1.0455) = 0.1479

Here we would chose the relatively more riskier fund.