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# chap006 - Chapter 06 - Efficient Diversification Chapter 6...

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Chapter 06 - Efficient Diversification Chapter 6 Efficient Diversification 1. E(r P ) = (0.5 x 15) + (0.4 x 10) + (0.10 x 6) = 12.1% 2. Fund D represents the single best addition to complement Stephenson's current portfolio, given his selection criteria. First, Fund D’s expected return (14.0 percent) has the potential to increase the portfolio’s return somewhat. Second, Fund D’s relatively low correlation with his current portfolio (+0.65) indicates that Fund D will provide greater diversification benefits than any of the other alternatives except Fund B. The result of adding Fund D should be a portfolio with approximately the same expected return and somewhat lower volatility compared to the original portfolio. The other three funds have shortcomings in terms of either expected return enhancement or volatility reduction through diversification benefits. Fund A offers the potential for increasing the portfolio’s return, but is too highly correlated to provide substantial volatility reduction benefits through diversification. Fund B provides substantial volatility reduction through diversification benefits, but is expected to generate a return well below the current portfolio’s return. Fund C has the greatest potential to increase the portfolio’s return, but is too highly correlated to provide substantial volatility reduction benefits through diversification. 3. a. The mean return should be equal to the value computed in the spreadsheet. The fund's return is 3% lower in a recession, but 3% higher in a boom. However, the variance of returns should be higher, reflecting the greater dispersion of outcomes in the three scenarios. b. Calculation of mean return and variance for the stock fund: (A) (B) (C) (D) (E) (F) (G) Col. B Col. B × × Col. C Col. F Recession 0.3 -14 -4.2 -24 576 172.8 Normal 0.4 13 5.2 3 9 3.6 Boom 0.3 30 9 20 400 120 10 296.4 17.22 Scenario Probability Rate of Return Deviation from Expected Squared Deviation Expected Return = Variance = Standard Deviation = 6-1

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Chapter 06 - Efficient Diversification c. Calculation of covariance: (A) (B) (C) (D) (E) (F) Col. C Col. B Stock Bond × × Fund Fund Col. D Col. E Recession 0.3 -24 10 -240 -72 Normal 0.4 3 0 0 0 Boom 0.3 20 -10 -200 -60 Scenario Probability Covariance = -132 Deviation from Mean Return Covariance has increased because the stock returns are more extreme in the recession and boom periods. This makes the tendency for stock returns to be poor when bond returns are good (and vice versa) even more dramatic. 4. a. One would expect variance to increase because the probabilities of the extreme outcomes are now higher. b. Calculation of mean return and variance for the stock fund: (A) (B) (C) (D) (E) (F) (G) Col. B Col. B × × Col. C Col. F Recession 0.4 -11 -4.4 -20 400 160 Normal 0.2 13 2.6 4 16 3.2 Boom 0.4 27 10.8 18 324 129.6 9 292.8 17.11 Rate of Return Deviation from Expected Squared Deviation Expected Return = Variance = Standard Deviation = 6-2
Chapter 06 - Efficient Diversification c. Calculation of covariance (A) (B) (C) (D) (E) (F) Col. C Col. B × × Col. D Col. E Recession 0.4 -20 10 -200 -80 Normal 0.2 4 0 0 0 Boom 0.4 18 -10 -180 -72 Deviation from Mean Return Scenario Probability Stock Fund Bond Covariance = -152

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## This note was uploaded on 02/25/2011 for the course FIN 3826 taught by Professor Staff during the Fall '08 term at LSU.

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chap006 - Chapter 06 - Efficient Diversification Chapter 6...

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