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 4.0%. The probability distributions of the risky funds are:

What is the reward-to-volatility ratio of the best feasible CAL? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

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 4.0%. The probability distributions of the risky funds are:

Explanation / Answer

Given parameters of the opportunity set :

E(rS) = 10%, E(rB) = 7%, ?S= 32%, ?B= 24%, ?= 0.1250, rf= 4%

covariance matrix therefore Cov(rS, rB) = ??S?B]:

minimum-variance portfolio proportions :wmin(S) =?B2– Cov(rS, rB) /  ?S2+ ?B2– 2Cov(rS, rB)

576 – 96 /1,024 + 576 – (2 ×96)

= 480/1408

= .3409

wmin(B) = 1 – .3409 = .6590

The mean of the minimum variance portfolio:

E(rmin) = (.3409 ×10%) + (.6590 ×7%) = 8.0226%

standard deviation of the minimum variance portfolio

?min= [wS2?S2+ wB2?B2+ 2wSwBCov(rS, rB)]1/2

= [(.11621×1,024) + (.43428×576) + (2 ×.3409 ×.6590 ×96)]1/2= 20.30%

Reward-to-volatility ratio = E(Rp) - Rf ) / ?P =  0.212053837

This is the tangency portfolio from minimun variance portfolio.

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