Question

Assume that you would like to invest in a portfolio of both Australian ten-year government debt and BHP stocks. The 10-year government debt has an expected return of 6%. You expect the BHP stocks to generate an average return of 17% with a variance of 9%.

(a) Comparing with a portfolio that fully invested in BHP, Would you expect to have a higher proportion of BHP stocks or government debt in your portfolio that has an expected standard deviation of 10%? Please briefly explain.

(b) Suppose you want to construct a portfolio, that has an expected standard deviation of 10%, comprising Australian ten-year government debt and BHP stocks. Calculate the portfolio weights. Explain your assumptions and workings.

Answer 1

a). Government debt is risk-free so standard deviation will be zero. A portfolio combining government debt and BHP stock will have a standard deviation equal to weight of BHP stock*standard deviation of BHP stock.

Variance of BHP stock = 9% so standard deviation = 9%^0.5 = 30%

If standard deviation of the portfolio has to be 10% then proportion of BHP stock has to be lower than that of government debt. This will bring down the overall standard deviation of the portfolio from BHP's standard deviation of 30%.

b). Standard deviation of portfolio = weight of BHP stock*standard deviation of BHP stock

weight of BHP stock = 10%/30% = 33.33%

weight of government debt = 100%-33.33% = 66.67%