Question

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 11.7% with a standard deviation of 20.1%. The relatively less risky fund promises an expected return and standard deviation of 4.2% and 6.2%, respectively. Assume that the returns are approximately normally distributed. [You may find it useful to reference the z table.]


a-1. Calculate the probability of earning a negative return for each fund. (Round "z" value to 2 decimal places and final answers to 4 decimal places.)

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 9.5% for each fund. (Round "z" value to 2 decimal places and final answers to 4 decimal places.)

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 9.5%?

• Less risky fund

• Riskier fund

Answer 1

Let ,

X→denote riskier fund

Y→denote less riskier fund

X~N(11.7,20.1²)

Mean (mu1)= 11.7

Standard deviation (s1)=20.1

Y~N(4.2,6.2)

Mean(mu2)=4.2

Standard deviation (s2)=6.2

Now,

1)

For riskier fund:

the probability of earning a negative return for each fund.

= Prob(X<0)

Prob(z<(0-mu1/s1))

=Prob(z<-11.7/20.1)

=Prob(z<-0.5821)

= Prob(z<-0.58)=0.2810

For less riskier fund:

Prob(y<0)

= Prob(z<-4.2/6.2)

=Prob(z<-0.6774)

=Prob(z<-0.68)

=0.2482

Que

a-2. Which mutual fund will you pick if your objective is to minimize the probability of earning a negative returns.

Ans: less risky fund.

Que b1)

b-1. Calculate the probability of earning a return above 9.5% for each fund.

#For riskier fund:

Prob(x>9.5)

=Prob(z>(9.5-mu1)/s1)=prob(z>-0.11)=1-ptob(z<-0.11)=1-0.4562=0.5438

For less riskier fund:

Prob(y>9.5)

= Prob(z>0.85)=0.1977

Que '. Which mutual fund will you pick if your objective is to maximize the probability of earning a return above 9.5%

Ans:riskier fund.

Thanks!