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 rate of 5.5%. The probability distribution of the risky funds is as follows:

The correlation between the fund returns is 0.15.

Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places.)

Explanation / Answer

Weight of the optimal risky portfolio is given by:

Ws= weight of the stock funds in the portfolio = [E(rs)-rf](sd-b)^2-[E(rb)-rf]Cov(rs,rb)/{[E(rs)-rf](sd-b)^2+[E(rb)-rf](sd-s)^2-[E(rs)-rf+E(rb)-rf]Cov(rs,rb)

Here, E(rs) = expected return of the stock fund

E(rb) = expected return of the bond fund

rf = risk free rate or return on the treasury bill

sd-s = standard deviation of the stock fund

sd-b = standard deviation of the bond fund

Cov(rs,rb) = covariance between the stock and bond fund = (sd-s)*(sd-b)*correlation between them

So, putting these values in we get :

Ws= 0.6466

Hence Wb = weight of the bond fund in the portfolio = 1-Ws = 0.3534

So, E(Rp) = expected return on the portfolio = 0.6466 * 15 + 0.3534* 9 = 12.88%

sd-p = standard deviation of the portfolio = ((0.6466*32)^2+(0.3534*23)^2+(0.6466*0.3534*2*0.15*32*23))^1/2

= (544.65)^1/2 = 23.34%

Hence,

Portfolio invested in stocks = 64.66%

Portfolio invested in bonds = 35.34%

Expected return on the optimally risky portfolio = 12.88%

Standard deviation on the portfolio = 23.34%

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