Question

Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold

offers an expected return of 10% with a standard deviation of 30%.

1. In light of the apparent inferiority of gold with respect to average return and volatility, would anyone hold gold in his portfolio?
2. Assume that the correlation between Stocks and Gold is -0.5. Find the weights wS and wG of the efficient risky portfolio which is invested in Stocks and Gold and which has an expected return of 15%.

Answer 1

a) Gold offers less returns with more volatility as compared to stocks. So, as a standalone investment, it is not attractive. However, Gold may be attractive to be included in a well diversified portfolio because of the following reasons

1. It may be less positively or negatively correlated with the stocks. So, it may prove to be useful for portfolio diversification.

2. It may have less systematic risk and more of unsystematic risk, which can be removed by diversification and hence for well diversified investors, gold may be attractive for less systematic risk or less beta.

For the above reasons, investors may hold gold in the portfolio

b) For a portfolio composed of stocks and gold to have an expected return of 15%

Weighted average return of the portfolio = 15%

=> wS*18% + wG*10% = 15%

As wG= 1-wS

=> wS*18% + (1-wS)*10% = 15%

=>wS*8% = 5%

=> wS= 0.625 and

wG= 1-wS= 0.375   

So, the portfolio weights are

wS=0.625 or 62.50% and

wG =0.375 or 37.5%