A pension fund manager is considering three mutual funds. The first is a stock f

Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.6%. The probability distributions of the risky funds are: The correlation between the fund returns is.0600. Suppose now that your portfolio must yield an expected return of 15% and be efficient, that is, on the best feasible CAL. a. What is the standard deviation of your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.) What is the proportion invested in the T-bill fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) What is the proportion invested in each of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Explanation / Answer

The proportion of stocks in the optimal risky portfolio is given by:

Ws = {[E(Rs) – (Rf)] 2B – [E(RB) – (Rf)] Cov(B,S)} / {[E(Rs) – (Rf)] 2B + [E(RB) – (Rf)] 2S - {[E(Rs) – (Rf) + E(RB) – (Rf)] Cov(B,S)

Cov(B,S) = 0.06 x 0.46 x 0.40 = 0.011040 or 110.40
2B= 40 x 40 = 1600
2S= 46 x 46 = 2116

{[(17 – 5.6) x 1600] – [(8 – 5.6) x 110.40]} / {[(17 – 5.6) x 1600] + [(8 – 5.6) x 2116] – [((17 – 5.6) + (8 – 5.6)) x 110.40]}

= 0.82473682

So, the proportion of stock will be 82.47%

The proportion of bond will be => 1 – 82.47% = 0.1753 or 17.53%

The standard deviation of the optimal risky portfolio will be:
= [0.82472(2116) + 0.17532(1600) + 2(0.8247)(0.1753)(110.40)]1/2 = 38.99%

E(RP) = (0.8247 x 17) + (0.1753 x 8) = 15.42%

So, weight of t-bill in the portfolio for the expected return of 15%:

15% = 5.6%*w + 15.42%*(1-w)
15% = 5.6%w + 15.42% - 15.42w
W = 0.42%/9.82% = 4.28%

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