Question

Problem 3 (15 marks). 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%. a) In light of the apparent inferiority of gold with respect to both mean return and volatil- ity, would anyone hold gold? If so, demonstrate graphically why one would do so. [7 marks) b) Given the data above, reanswer a) with the additional assumption that the correlation coefficient between gold and stocks equals 1. Draw a graph illustrating why one would or would not hold gold in one's portfolio. Could this set of assumptions for expected returns, standard deviations, and correlation represent an equilibrium for the security market? [8 marks]

Answer 1

Answer:

From the given data,

a)

Although it appears that gold is dominated by stocks, gold can still be an attractive diversified asset. If the correlation between gold and stocks is sufficiently low, gold will be held as a component in the optimal portfolio.

b)

If gold had a perfectly positive correlation with stocks, gold would not be a part of efficient portfolios. The set of risk/return combinations of stocks and gold would plot as a straight line with a negative slope. (Refer to the above graph when correlation is 1). The graph shows that when the correlation coefficient is 1, holding gold provides no benefit of diversification. The stock-only portfolio dominates any portfolio containing gold. This cannot be equilibrium; the price of gold must fall and its expected return must rise. Even though gold seems dominated by stocks, it still might be an attractive asset to hold as a part of portfolio. If the correlation between gold and stocks is sufficiently low, it will be held as an element in a portfolio - the optimal tangency portfolio. Look at the picture below and notice that the CAL for the diversified portfolio (CAL (a)) may be steeper than CAL for the portfolio which contains stock only (CAL (b)). If gold had correlation coefficient with stocks of +1, it would be held. The set of risk/return combinations of stocks and gold would plot as a straight line with a negative slope (see the following graph). The graph shows that in this case, any portfolio that contains any gold is dominated by the stock-only portfolio. Therefore, no one will hold gold. Stated differently, the CAL for the portfolio with stock only is steeper than any other passing through all other possible portfolios on the combination line. (Of course, this situation could not persist. If no one desired gold, its price would fall and its expected rate of return would increase until it became an attractive enough asset to hold.)

Expected retuan (o/) Calcb) 25 Callal 20 Istocks 15 Gold 10 5. 10.00 H0.00 30.00 0.00 20.00 standaard deviation (%)