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 5.8%. The probability distributions of the risky funds are:

Expected Return Standard Deviation

Stock fund (S) 19% 48%

Bond fund (B) 9% 42%

The correlation between the fund returns is .0762.

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

Explanation / Answer

Given E(Rs) = 19%

E(Rb) =9%

Ss = Std. dev of stock = 48%

Sb= Std. dev of bond = 42%

Rf = 5.8%

Correlation = 0.0762

Cov(B,S) = 0.0762* 48*42 = 153.6192

Wieght of Stock Ws = {[E(Rs) -Rf]*Sb^2 - [E(Rb) -Rf)*COv(B,S) }/ {[E(Rs)-Rf]*Sb^2 +[Er(b)-Rf]*Ss^2 -[E(Rs) - Rf + E(rb) - Rf]*Cov(B,)}

Ws = (19-5.8)*1764 -(9-5.8)* 153.6192/(19-5.8)*1764 + (9-5.8)* 2304 - (19-5.8+9-5.8)* 153.6192

Ws = 0.8214

Wd = 1 - Ws = 0.1786

E(Rp) return on portfolio= 0.8214 * 19 + 0.1786 * 9

E(Rp) = 17.214%

Sp = Std.dev of portfolio = sqrt( 0.8214^2*2304 + 0.1786^2*1764 + 2* 0.8214*0.1786 * 153.6192)

Sp = 40.69%

Reward to Volatility ratio of the best feasible CAL is given by:

=( E(Rp) - Rf)/Sp

= (17.214 - 5.8)/40.69

= 0.2805

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