2349 Words10 Pages

Problem Set
1. 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. Explain.
Answer:
Even though it seems that gold is dominated by stocks, gold might still be an attractive asset to hold as a part of a portfolio. If the correlation between gold and stocks is sufficiently low, gold will be held as a component in a portfolio, specifically, the optimal tangency portfolio.
Efficient frontier
Efficient frontier
b. Given the data above, re-answer part (a) with the additional assumption that the correlation coefficient between gold and stocks equals 1.0. 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 coefficients represent an equilibrium for the financial markets? Explain.
Answer:
If the correlation between gold and stocks equals +1, then no one would hold gold. The optimal portfolio would be comprised of bills and stocks only. Since the set of risk/return combinations of stocks and gold would plot as a straight line with a negative slope (see the following graph), these combinations would be dominated by the stock portfolio. 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 sufficiently attractive to include in a portfolio.
2.
Assume that the following two investment classes are available in the market:
Asset | E(ri) | σi | Debt | 0.18 | 0.20 | Equity | 0.24 | 0.35 |
Determine the portfolio standard deviation and expected return if you

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