Question

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 13% with a standard deviation of 17.9%. The relatively less risky fund promises an expected return and standard deviation of 3.3% and 5.4%, 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.)

Probability

Riskier fund

Less risky fund

b-1. Calculate the probability of earning a return above 8.8% for each fund. (Round "z" value to 2 decimal places and final answers to 4 decimal places.)

Probability

Riskier fund

Less risky fund

Answer 1

from the given data of information

the risk return profile of two mutual funds for investment

mean=13

standard deviation= 17.9

relatively less risky fund if y is the return of that fund at particular moment

mean=3.3

standard deviation=5.4

for negative return

pr(negative return for relatively risker fund)= pr(x<0)

= pr(x<0;13%,17.9%)

z=(0-13)/17.9

= 0.72

pr(x<0)=pr(x<0;13%,17.9%)

= pr(z< -0.72)=0.2358

pr(negative return for less risker fund)=pr(x<0)

=pr(x<0;3.3%,5.4%)

z=(0-3.3)/5.4

= 0.61

pr(x<0)=pr(x<0;3.3%,5.4)

pr(z< -0.61) = 0.2709

the relatively more risker fund

here thr return morethan 8.8%

pr(return more than 8.8%for relatively risker fund)= pr(x>8.8%) =pr(x>8.8%;13%,17.9%)

z=(8.8-13)/17.9= 0.2346

pr(x>8.8)= pr(x>8.8%;13%,17.9%)

pr(z>-0.2346)=1- 0.4090= 0.591

pr(return more than 8.8for less risker fund)=pr(x>8.8)=pr(x>8.8%;3.3%,5.4%)

z=(8.8-3.3)/5.4= 1.0185

pr(x>8.8%)=p(x>8.8%;3.3%5.4%)= pr(z>1.0185)

=0.1538