Question

You currently own shares in Buckeye Mutual Fund (BMF). Your broker calls and recommends buying shares in a small-capitalization fund managed by Wolverine Investment Group (WIG). Your broker says that this fund will provide significant diversification benefits for your existing holdings. She gives you the following statistics based on the performance of the two funds over the last year. Portfolio E(Return) Std. Dev. Buckeye Mutual Fund 20% 14% Wolverine Investment Grp. 12% 11% 23) Assume you can earn an average annual yield of 8% on a risk-free security. Which of these funds would be the optimal fund to combine with the risk-free security? A. Buckeye B. Wolverine C. Neither Buckeye nor Wolverine D. Both are equally good E. There is not enough information to answer this question

Using the fund you selected, how much portfolio weights in the fund and the risk-free security would be required to earn a target return of 22%?

A. The fund weight is 98% and the risk-free asset weight is 2%

B. The fund weight is 50% and the risk-free asset weight is 50%

C. The fund weight is 102% and the risk-free asset weight is -2%

D. The fund weight is 117% and the risk-free asset weight is -17%

Answer 1

23. To find the optimal fund to combine with risk free rate of return, we will use Coefficient of variation,

Coefficient of variation(CoV) = Standard Deviation/Expected Return

CoV of Buckeye = 14%/20% = 0.7

CoV of Wolverine = 11%/12% = 0.9167

So, higher the CoV higher the risk, we will take Buckeye to combine with Risk Free Return.

Hence, Option A

- Required target return of portfolio = 22%

Risk Free return = 8%

Buckeye Return = 20%

Let the weight of Buckeye be X ,& weight of risk free be (1-X)

Required return = (W_RF)*(R_RF) + (W_B)*(R_B)

22 = (1-X)(8) + (X)(20)

22 = 8-8X + 20X

14 = 12X

X = 1.17

SO, weight of Buckeye is 1.17 or 117%

while weight of Risk free is -0.17 (1-1.17) or -17%

Hence, ans is OPTION D

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