Question

You are an investment manager considering two mutual funds. The first is an equity fund and the second is a long- term corporate bond fund. It is possible to borrow or to lend limitless sums safely at 1.25%pa. The data on the risky funds are as follows: Fund Expected return Expected standard deviation Equity Fund 8% 16% Bond Fund 3% 5% The correlation coefficient between the fund returns is 0.10 a You form a risky portfolio P that is equally weighted between the bond fund and the equity fund. Calculate the forecast expected return and the estimated risk of your portfolio. Show your working. (2 marks) b Draw the capital allocation line (CAL) of your portfolio on an expected return-standard deviation diagram. What is the slope of the CAL? Show your working. (2 marks)

Answer 1

a
Fund	Expected return	Expected standard deviation
Equity fund	8%	16%
Bond fund	3%	5%
Weight of equity fund	0.5
Weight of bond fund	0.5
Correlation coefficient of euqity and debt funds	0.1
Expected return = weight of equity * equity return +weight of bond * bond return	5.50%
Portfolio risk = Square root of [(Equity weight)^2*(Equity risk)*2+ (Debt weight)^2*(Debt risk)^2+2*(Equity weight)*(Equity risk)*(Debt weight)*(Debt risk)*(Correlation coefficient)]	8.6168%
b. Slope of CAL
Slope of CAL = (Portfolio return - risk free rate)/Portfolio excess risk	0.49
c. Portfolio return = 8%
Fund	Expected return	Expected standard deviation
Equity fund	8%	16%
Bond fund	3%	5%
Weight of equity fund	1
Weight of bond fund	0
Correlation coefficient of euqity and debt funds	0.1
Expected return = weight of equity * equity return +weight of bond * bond return	0.08x+0.03(1-x)=8%
On solving for x we get 1, i.e., weight of equity fund is 100% and nothing attributed to debt fund
Portfolio risk = Square root of [(Equity weight)^2*(Equity risk)*2+ (Debt weight)^2*(Debt risk)^2+2*(Equity weight)*(Equity risk)*(Debt weight)*(Debt risk)*(Correlation coefficient)]	16.00%