You are considering the risk-return profile of two mutual funds for investment.
ID: 3173291 • Letter: Y
Question
You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 9.2% with a standard deviation of 17.6%. The relatively less risky fund promises an expected return and standard deviation of 4.3% and 5.8%, respectively. Assume that the returns are approximately normally distributed. Use Table 1.
a-1.
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.)
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 return?
b-1.
Calculate the probability of earning a return above 8.7% for each fund. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Probability
Riskier fund
Less risky fund
You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 9.2% with a standard deviation of 17.6%. The relatively less risky fund promises an expected return and standard deviation of 4.3% and 5.8%, respectively. Assume that the returns are approximately normally distributed. Use Table 1.
Explanation / Answer
(a1) Riskier fund:
= 9.2, = 17.6
z = (x - )/ = (0 - 9.2)/17.6 = -0.52
P(x < 0) = P(z < -0.52) = 0.3015
Less risky fund:
= 4.3, = 5.8
z = (x - )/ = (0 - 4.3)/5.8 = -0.74
P(x < 0) = P(z < -0.74) = 0.23
(a2) We should pick up the less risky fund
(b1) Riskier fund:
= 9.2, = 17.6
z = (x - )/ = (8.7 - 9.2)/17.6 = -0.03
P(x > 8.7) = P(z > -0.03)) = 0.5120
Less risky fund:
= 4.3, = 5.8
z = (x - )/ = (8.7 - 4.3)/5.8 = 0.76
P(x > 8.7) = P(z > 0.76) = 0.2236
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