You are considering the riskreturn profile of two mutual fun

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 12.5% with a standard deviation of 19.2%. The relatively less risky fund promises an expected return and standard deviation of 4.1% and 5.9%, respectively. Assume that the returns are approximately normally distributed.

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

Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return?

Calculate the probability of earning a return above 10.5% for each fund. (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

Which mutual fund will you pick if your objective is to maximize the probability of earning a return above 10.5%?

Solution

Probability of a negative return = P (X < 0)

let r = risky fund

rf = risk free fund (or less rsiky fund)

a)

Zr =0 - 0.125 / 0.192

= -0.65

P ( Zr < 0 ) = 0.2578

= 25.78%

Zrf = 0 - 0.041 / 0.059

= - 0.69

P(Zrf < 0) = 0.2451

= 24.51%

Hence to minimize a loss or a negative return, invest in less risky fund

2)

To obtain return = 10.5%

Zr = 10.5 - 12.5 / 19.2

= -0.10

P (Zr > -0.10) = 1 - 0.4602

= 0.5398

= 53.98 %

P ( X > 10.5)

Zrf = 10.5 - 4.1 / 5.9

= 1.08

P (Z > 1.08) = 1 - P (Z < 1.08)

= 1 - 0.8599

= 0.1401

= 14.01 %

Thus, to obtain returns higher than 10.5% invest in the riskier fund