A pension fund manager is considering three mutual...

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 5.2%. The probability distributions of the risky funds are:

	Expected Return		Standard Deviation
Stock fund (S)	13	%	42	%
Bond fund (B)	6	%	36	%

The correlation between the fund returns is .0222.

Suppose now that your portfolio must yield an expected return of 12% 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.)

Standard deviation

%

b-1.	What is the proportion invested in the T-bill fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Proportion invested in the T-bill fund

%

b-2.	What is the proportion invested in each of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Proportion Invested
Stocks	%
Bonds	%

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Solution:

Cov (rs, rB) = r*s*B = 0.0222*42*36 = 33.5664

The proportion of the optimal risky portfolio invested in the stock fund is given by:

Ws = [E (Rs) rf]B^2 [E(RB) rf](Cov (rs, rB)/[ [E(rs )- rf ]B^2+ [E(rB )- rf]S^2 - [E(rS ) rf + E(rB) - rf ]Cov(rs ,rB )

Ws = [(13 5.2)](42)^2 [(6 5.2)](33.5664)/[(13 5.2)(42)^2 + (6 5.2)(36)^2 [13 -5.2+6 -5.2](33.5664)

Ws = 0.9466

WB = 1 0.9466 = 0.0534

The mean and standard deviation of the optimal risky portfolio are:

E (Rp) = 0.9466*13 + 0.0534*6 = 12.63%

p = (0.9466)^2(42)^2 + (0.0534)^2(36)^2+2*0.9466*0.0534*33.5664)= 39.85%

a. The expected return on the portfolio is 12%. The equation for the CAL is

E (rc) = rf + [(E (Rp) rf)/p]c

12 = 5.2 + [(12.63 5.2)/39.85]c

6.8 = 0.18644c

c = 36.47%

Hence, the standard deviation of the portfolio is 36.47%

b-1. To find the proportion invested in the T-bill fund, remember that the mean of the complete portfolio (i.e., 14%) is an average of the T-bill rate and the optimal combination of stocks and bonds (P). Let y be the proportion invested in the portfolio P. The mean of any portfolio along the optimal CAL is:

E(rC) = (l y)rf + yE(rP) = rf + y[E(rP) rf] = 5.2 + y(12.63 5.2)

Setting E(rC) = 12% we find: y = 0.9152 and (1 y) = 0.0848 (the proportion invested in the T-bill fund).

b-2: Proportion of stocks in complete portfolio = 0.9152 0.9466 = 0.8663 or 86.63%

Proportion of bonds in complete portfolio = 0.9152 0.0534 = 0.0489 or 4.89%

THE PORTION INVESED IN T-BILL FUND IS WRONG!!!!

I NEED TO FIND THE PORTION INVESTED IN T-BILL FUND