you are considering Investing $1000 in a compete portfolio. the compete portfoli

Question

you are considering Investing $1000 in a compete portfolio.   the compete portfolio is composed of treasury bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities x and y. the weight of x and y in p are 60% and 40% respectively. x has an expected rate of return of 14% and y 10%. to form a complete portfolio with an expected return of 8%, how much should you invest in the Tbills x and y respectively?

a. 59.46, 24.32, 16.22
b. 55.20, 27.80, 45.0
c. 24.32, 55.45, 20.23
d. none

Explanation / Answer

Let proportion invested in risky portfolio be K. Then investment in X = 0.6K and investment in Y = 0.4K

Also, investment proportion in riskless Treasury Bills = 1 - K. Return on x = 14% and Return on y = 10%

Complete Portfolio Return = 8 % and Treasury Bill Return = 5%

Therefore, 8 = 5 x (1-K) + 14 x 0.6K + 10 x 0.4K

8 = 5 - 5K + 8.4K + 4K

3= 7.4 K

K = 0.4054

Investment in T Bills = 1 - K = 0.5946 or 59.46

Investment in x = 0.6 K = 0.2432 or 24.32

Investment in y = 0.4 K = 0.1622 or 16.22

Hence correct answer is option (a).

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