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You are considering the risk-return profile of two mutual funds for invastment. The relatively risky fund...

Question

You are considering the risk-return profile of two mutual funds for invastment. The relatively risky fund...

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
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

Answers

Given:

Riskier fund:

Mean, μ 11.1%

Standard Deviation, σ-14.7%

Less Risky Fund:

Mean, μ =4%

Standard Deviation. σ-6%

a-1: Probability of earning a negative fund:

Riskier fund:

μ 11.1, σ= 14.7

11.1 一 14.7 14.7

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:

mu=4,;sigma=6

X-μ 0-4-4 一0.6667

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:

μ 11.1, σ= 14.7

X _ μ . 9.1-11-=-=-0.1361 3 2 14.70.1361

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:

mu=4,;sigma=6

X-μ 9.1-4 5.1 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


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