Stocks offer an expected rate of return of 18%, with a standard deviation of 22%
ID: 2772475 • Letter: S
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%.
a. In light of the apparent inferiority of gold with respect to both mean return and volatility,
would anyone hold gold? If so, demonstrate graphically why one would do so.
b. Given the data above, reanswer ( a ) with the additional assumption that the correlation coef-
ficient 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?
Explanation / Answer
Answer :-
a.) 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 low, It will be held as an asset in a portfolio. Look at the graph below and see that the Line for the diversified portfolio Line 1 may be steeper than Line for the portfolio which contains stock only Line 2.
b.) If Gold had a correlation coefficient with stocks of High (+1), It would not 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. The Line for the portfolio with stock only is steeper than any other Line passing through all other possible portfolios on the combination line.
Particulars Expected Return (Ri) Standered Deviation Stock 18% 22% Gold 10% 30%