Question

You are considering the risk-return profile of two mutual funds for invastment. The relatively risky fund promises an expected return of 11 1% with a standard deviation of 14.7%. The relatively less risky fund promises an tandard deviation of 4% and 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 retum? Riskier fund O Less risky fund b.1 Calculate the probability of earning a return above 91% for each fund. places.) Round final answer to 4 decimal Probability Riskier fund Less risky fund b Whichmtual tund will ou bectves to maxinize the probabilily f aning a retun above 91%? Riskier fund O Less risky fund O Type here to search

Answer 1

Given:

Riskier fund:

$\dpi{100} Mean,\;\mu=11.1\%$

$\dpi{100} Standard\;Deviation,\;\sigma=14.7\%$

Less Risky Fund:

$\dpi{100} Mean,\;\mu=4\%$

$\dpi{100} Standard\;Deviation,\;\sigma=6\%$

a-1: Probability of earning a negative fund:

Riskier fund:

$\dpi{100} \mu=11.1,\;\sigma=14.7$

$\dpi{100} Z=\frac{X-\mu}{\sigma}=\frac{0-11.1}{14.7} = \frac{-11.1}{14.7}=-0.7551$

P(X < 0) = P(Z < - 0.7551) = 0.2251 (From standard normal table or using function NORMSDIST in Excel. Input in excel is =NORMSDIST(-0.7551))

Less Risk fund:

$\dpi{100} \mu=4,\;\sigma=6$

$\dpi{100} Z=\frac{X-\mu}{\sigma}=\frac{0-4}{6} = \frac{-4}{6}=-0.6667$

P(X < 0) = P(Z < - 0.6667) = 0.2525 (From standard normal table or using function NORMSDIST in Excel. Input in excel is =NORMSDIST(-0.6667))

a-2 To minimize the probability of earning negative return

Riskier fund has less probability (0.2251) compared to less risk fund (0.2525) for earning negative return. Therefore, choose Riskier fund.

b-1 Probability of earning a return above 9.1%

Riskier fund:

$\dpi{100} \mu=11.1,\;\sigma=14.7$

$\dpi{100} Z=\frac{X-\mu}{\sigma}=\frac{9.1-11.1}{14.7} = \frac{-2}{14.7}=-0.1361$

P(X > 9.1) = P(Z > - 0.1361) = 1 - P(Z < -0.1361) = 1 - 0.4459 = 0.5541 (From standard normal table or using function NORMSDIST in Excel. Input in excel is =NORMSDIST(-0.1361))

Less Risk fund:

$\dpi{100} \mu=4,\;\sigma=6$

$\dpi{100} Z=\frac{X-\mu}{\sigma}=\frac{9.1-4}{6} = \frac{5.1}{6}=0.85$

P(X > 9.1) = P(Z > 0.85) = 1 - P(Z < 0.85) = 1 - 0.8023 = 0.1977 (From standard normal table or using function NORMSDIST in Excel. Input in excel is =NORMSDIST(0.85))

b-2 To maximize the probability of earning a return above 9.1%

Riskier fund has more probability (0.5541) compared to less risk fund (0.1977) for earning return above 9.1%. Therefore, choose Riskier fund.

Final Answers:

a-1)

Riskier fund: 0.2251

Less Risk fund: 0.2525

a-2)

Riskier fund

b-1)

Riskier fund: 0.5541

Less Risk fund: 0.1977

b-2)

Riskier fund