Question

Stocks offer an expected rate of return of 10% with a standard deviation of 20%, and gold offers an expected return of 5% with a standard deviation of 25%.

a. In light of the apparent inferiority of gold to stocks with respect to both mean return and volatility, would anyone hold gold? If so, demonstrate graphically why one would do so.

b. How would you answer (a) if the correlation coefficient between gold and stocks were 1? Draw a graph illustrating why one would or would not hold gold. Could these expected returns, standard deviations, and correlation represent an equilibrium for the security market?

Short answer

a. Yes. Gold can still be an attractive diversification asset.

b. No. The price of gold must fall and its expected return must rise.

Step-by-step solution

Explanation on holding gold in comparison to stocks (a)

Yes! Gold can be an attractive component in the portfolio if the correlation between gold and stocks is low.

Calculation of correlation coefficient between gold and stocks (b)

(a) In that case, gold would not be a part of the efficient portfolios.

The graph shows that in the event where the correlation coefficient is 1, the gold holding doesn’t provide any benefit of diversification.

Moreover, here the stock-only portfolio dominates, which cannot be equilibrium. Therefore the price of gold must fall, and its expected return must rise.