Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky funds are as follows:

	Expected Return			Standard Deviation
Stock fund (S)		20	%		30	%
Bond fund (B)		12			15

The correlation between the fund returns is 0.10.

You require that your portfolio yield an expected return of 14%, and that it be efficient, that is, on the steepest feasible CAL.

a. What is the standard deviation of your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

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

	Proportion Invested Money market fund % Stocks % Bonds %

Answer 1

Ans a)

Expected Return of Stock Fund E(S) = 20% =0.20

Expected Return of Stock Fund E(B) = 12% = 0.12

Risk Free Return R(f) = 8% = 0.08

Standard Deviation of Stock Fund SD(S) = 30% = 0.30

Standard Deviation of Bond Fund SD(B) = 15% = 0.15

Covariance Betweeen Stock and Bond Cov(S,B)

Cov(S,B) = Corelatioon * SD(S) * SD(B) = 0.10 * 0.30 * 0.15 = 0.0045

Weightage of Stock Fund W(S)

Weightage of Bond Fund W(B)

W(B) = 1 - W(S)

Now

W(S) = 0.4516

W(B) = 0.5488

Expected Return of the Portfolio ER(P) = W(S)*E(S) + W(B) * E(B) = 0.4516 * 20% + 0.5488* 12% = 15.61%

Portfolio Variance V

V = 0.014717

SD(P) = 12.13%

Ans a : standard deviation of your portfolio = 12.13%

Expected Return of Portfolio = W(S) * E(S) + W(B) * E(B) = 0.4516 * 0.20 + 0.5483 * 0.12 = 15.61%

Assume y is weightage of Two asset Portfolio

Required Return in CAL E = 14%

E = R(f) + y* [ E(P) - R(F)]

14% = 8% + y* [ 15.61% - 8%]

y = 78.81%

So

Weightage in Money Market Fund = 1 - y = 1 - 78.81% = 21.18%

Stocks = y * W(S) = 78.81% * 0.4516 = 35.59%

Bonds Weight = y * W(B) = 78.81% * 0.5483 = 43.22%