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 5.2%. 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	%

Answer 1

R_S = Expected return of the stock fund = 13%

R_B = Expected return of the bond fund = 6%

_S = Standard deviation of the return on stock fund = 42%

_B = Standard deviation of the return on bond fund = 36%

R_f = T-bill money market fund yield = 5.2%.

= 0.0222

As a first step we will calculate the weights of the stock fund and bond fund in the optimal risky portfolio. For that purpose we will have to calculate the co-variance first.

Cov(R_S, R_B) = x _S x _B = 0.0222 x 42% x 36% = 0.00335664

Proportion of stock fund in the optimal risky portfolio

= 89.77%

Hence, w_B = 1 - w_S = 1 - 89.77% = 10.23%

R_P = Expected return of the optimal risky portfolio = w_S x R_S + w_B x R_B = 89.77% x 13% + 10.23% x 6% = 12.28%

= Standard deviation of the optimal risky portfolio

= 0.37962728 = 37.96%

Part (a)

The expected return on the portfolio is 12%.

The equation for the CAL is

R_C = R_f + [(R_P - R_f) / _P ] x _C ==

Hence, 12% = 5.2% + [(12.28% – 5.2%)/37.96%] x

Or, 12% - 5.2% = 6.8% =0.186594599 x _C

Hence, _C = 36.44%

Please enter 36.44 in the answer box

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Part (b) - 1

Lets say w is the proportion invested in T bill fund.

R_C = 12% = w x R_f + (1 - w) x R_P = w x 5.2% + (1 - w) x 12.28% = 12.28% - 7.08% x w

Hence, w = (12.28% - 12%) / 7.08% = 4.00%

Hence, the proportion invested in T bill fund = 4.00%

Please answer 4.00 in the answer box.

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Part (b) - 2:

Proportion invested in optimal risky portfolio = 1 - w = 1 - 4% = 96%

Proportion invested in stock fund = (1 - w) x w_S = 96% x 89.77% = 86.17%

Proportion invested in bond fund = (1 - w) x w_B = 96% x 10.23% = 9.82%

Please enter your answer as:

	Proportion Invested
Stocks	86.17%
Bonds	9.82%