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.

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.

Answer 1

Qa) Expected return = weight of equity × return of equity + weight of bond × return of bond

= 0.5 × 8% + 0.5 × 3%

= 4% +1.5%

= 5.5%

standard deviation = √ (weight of equity)^2 (std deviation of equity)^2 + (weight of bond)^2 (std deviation of bond)^2 + 2 × weight of equity × weight of bond × std deviation of equity × std deviation of bond × correlation

= √ (0.5)^2 (0.16)^2 + (0.5)^2 (0.05)^2 + 2 × 0.5 × 0.5 × 0.16 × 0.05 × 0.10

= √ (0.25) (0.0256) + (0.25) (0.0025) + 0.0004

= √ 0.0064 + 0.000625 + 0.0004

= √ 0.007425

= 8.62%

B) Capital allocation line

Slope of CAL = Sharpe ratio = Expected return - Risk free rate / standard deviation

= 5.5% - 1.25%/ 8.62%

= 4.25%/ 8.62%

= 0.493