Question

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 7.2% with a standard deviation of 15.7%. The relatively less risky fund promises an expected return and standard deviation of 3.9% 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 and Less risky fund

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

Less risky or fund Riskier fund

b-1. Calculate the probability of earning a return above 8.3% for each fund. (Round final answer to 4 decimal places.) Probability Riskier fund and Less risky fund

b-2. Which mutual fund will you pick if your objective is to maximize the probability of earning a return above 8.3%?

Riskier fund or Less risky fund

Answer 1

Answer :

(a-1). For riskier is fund:

We first get the z score for the critical value

As z = (x - u) / s,

critical value = x = 0
mean =u =7.2

standard deviation = s = 15.7

Thus,

z = (x - u) / s

=((0-7.2)/15.7)

= -0.458598

Thus, using a table/technology, the left tailed area of this is

P(z < -0.458598 ) = 0.21805555 [ANSWER]

** For less risky fund: We first get the z score for the critical value.

As z = (x - u) / s, then as

critical value =x = 0
mean =u = 3.9
standard deviation = s = 6

Thus,
z = (x - u) / s

= ((0-3.9)/6)

= -0.65.

Thus, using a table/technology, the left tailed area of this is

P(z < -0.65. ) =-0.153846153[ANSWER].

( a-2). From part A, I will choose LESS RISKY FUND.

(b-1). For riskier fund:

We first get the z score for the critical value. As z = (x - u) / s,

were as

critical value =x = 7.2
mean = u = 7.2

standard deviation = s =15.7

Thus,
z = (x - u) / s = 0

by using a table/technology, the right tailed area of this is

P(z > 0 ) = 0.5 [ANSWER]

For less risky fund: We first get the z score for the critical value.

As z = (x - u) / s,

were as

critical value = x = 7.2

mean = u =3.9

standard deviation = s = 6
Thus,
z = (x - u) / s

=((7.2-3.9)/6)

= 6.55

by using a table/technology, the right tailed area of this is

P(z > 6.55 ) = -0.3076923076 [ANSWER] .

(b-2). From b-1, we choose RISKIER FUND. [ANSWER].