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 5.5%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 15 % 32 % Bond fund (B) 9 23 The correlation between the two sets of fund returns is 0.15. If you were to use only the two risky funds and still require an expected return of 12%. Required: (a) What would be the investment proportions of your portfolio? (Answer is in % form (XX%), not decimal form (0.XX) Round your answers to nearest whole percent number. Omit the "%" sign in your response.) Stocks % Bonds % (b) Calculate the standard deviation of the portfolio which yields an expected return of 12%.(Answer is in % form (XX.XX%), not decimal form (0.XXXX) Round your answers to 2 decimal places. Omit the "%" sign in your response.) Standard deviation %

Answer 1

Mutual Fund	Expected Return (%)	Standard Deviation(%)
A - Stock Fund	15	32
B - long-term government and corporate bond fund	9	23

The correlation between the two sets of fund returns is 0.15

We need to use only these 2 funds and still require an expected return of 12%

a. Hence we need to calculate the optimum proportion of fund allocation.

Let’s assume, wa is the proportion of stock fund and wb is the proportion of bond fund

wa + wb = 1 i.e. wb = 1 - wa

Ep = Expected portfolio return = 12%

Ea = Expeted stock fund return = 15%

Eb = Expected bond fund return = 9%

Ep = (wa * Ea) + (wb * Eb)

12 = 15wa + 9 (1 – wa) = 6wa + 9

On solving this equation, wa is calculated as 0.5 or 50%. Wb can be calculated as 1 – 0.5 = 0.5 or 50%

So the proportion of stock fund and bond fund for an expected portfolio return shall be 50% each.

b. The standard deviation of this portfolio shall be calculated as per below

SDp = [(wa * SDa)^2 + (wb * SDb)^2 + 2*wa*wb* COV(A, B)]^0.5

Where,

SDp = Standard Deviation of Portfolio

SDa = Standard Deviation of Stock Fund = 0.32

SDb = Standard Deviation of Bond Fund = 0.23

COV (A, B) = Correlation between Stock and Bond Fund = 0.15

SDp = [(0.5*0.32)^2 + (0.5*0.23)^2 + 2*0.5*0.5*0.15]^0.5 = 0.34