Ch 08 - CHAPTER 8: OPTIMAL RISKY PORTFOLIOS 2. Proportion...

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CHAPTER 8: OPTIMAL RISKY PORTFOLIOS 2. Proportion in stock fund Proportion in bond fund Expected return Standard Deviation 0.00% 100.00% 12.00% 15.00% 17.39% 82.61% 13.39% 13.92% minimum variance 20.00% 80.00% 13.60% 13.94% 40.00% 60.00% 15.20% 15.70% 45.16% 54.84% 15.61% 16.54% tangency portfolio 60.00% 40.00% 16.80% 19.53% 80.00% 20.00% 18.40% 24.48% 100.00% 0.00% 20.00% 30.00% Graph shown on next page. 3. 0.00 5.00 10.00 15.00 20.00 25.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 Tangency Portfolio Minimum Variance Portfolio Efficient frontier of risky assets CML INVESTMENT OPPORTUNITY SET The graph indicates that the optimal portfolio is the tangency portfolio with expected return approximately 15.6% and standard deviation approximately 16.5%. 7. Using only the stock and bond funds to achieve a portfolio expected return of 14%, we must find the appropriate proportion in the stock fund (w S ) and the appropriate proportion in the bond fund (w B = 1 - w S ) as follows: 8-1
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14 = 20w S + 12(1 - w S ) = 12 + 8w S w S = 0.25 So the proportions are 25% invested in the stock fund and 75% in the bond fund. The standard deviation of this portfolio will be: σ P = [(0.25 2 × 900) + (0.75 2 × 225) + (2 × 0.25 × 0.75 × 45)] 1/2 = 14.13% This is considerably greater than the standard deviation of 13.04% achieved using T-bills and the optimal portfolio. 9. a. Standard Deviation(%) 0.00 5.00 10.00 15.00 20.00 25.00 0 10 20 30 40 Gold Stocks Optimal CAL P 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. b. If the correlation between gold and stocks equals +1, then no one would hold gold. The optimal CAL 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 8-2
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portfolio. Standard Deviation(%)
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Ch 08 - CHAPTER 8: OPTIMAL RISKY PORTFOLIOS 2. Proportion...

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