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# Chap006 - Chapter 06 Efficient Diversification CHAPTER 06...

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Chapter 06 - Efficient Diversification CHAPTER 06 EFFICIENT DIVERSIFICATION 1. So long as the correlation coefficient is neither zero nor 1.0, the portfolio will contain diversification benefits. Any other combination will cause a diversification benefit since the standard deviation will fall, relative to the return on the portfolio. Otherwise, the risk and return will change in unison. 2. The covariance with the other assets is more important. Diversification is accomplished via correlation with other assets. Covariance helps determine that number. 3. a. and b. will both have the same impact of increasing the sharpe measure from .40 to . 45. 4. The expected return of the portfolio will be impacted if the asset allocation is changed. But also so will the standard deviation. The Sharpe ratio will remain unchanged along the CML (slope will remain the same), it will be independent of the actual allocation between the optimal risky portfolio and the risk free asset. 5. Impact on total variance Om Os B TOTAL Variance Corr Coeff 0.2 0.3 1.5 0.1800 0.5000 0.2 0.3 1.65 0.1989 0.5475 0.2 0.33 1.5 0.1989 0.4525 a. Both will have the same impact. The total variance will increase from .18 to . 1989 b. An increase in beta, however, increases the correlation coefficient and thus creates more diversification benefit. 6. a. Without doing any math, the severe recession is worse and the boom is better. Thus, there appears to be a higher variance, yet the mean is probably the same since the spread is equally larger on both the high and low side. The mean return, however, should be higher since there is higher probability given to the higher returns. b. Calculation of mean return and variance for the stock fund: 6-1

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Chapter 06 - Efficient Diversification (A) (B) (C) (D) (E) (F) (G) Col. B Col. B × × Col. C Col. F Severe recession 0.05 -40 -2 -51.2 2621.44 131.07 Mild recession 0.25 -14 -3.5 -25.2 635.04 158.76 Normal growth 0.4 17 6.8 5.8 33.64 13.46 Boom 0.3 33 9.9 21.8 475.24 142.57 11.2 445.86 21.12 Expected Return = Variance = Standard Deviation = Scenario Probability Rate of Return Deviation from Expected Squared Deviation c. Calculation of covariance: (A) (B) (C) (D) (E) (F) Col. C Col. B Stock Bond × × Fund Fund Col. D Col. E Severe recession 0.05 -51.2 -14 716.8 35.84 Mild recession 0.25 -25.2 10 -252 -63 Normal growth 0.4 5.8 3 17.4 6.96 Boom 0.3 21.8 -10 -218 -65.4 Covariance = -85.6 Deviation from Mean Return Scenario Probability 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. 7. 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 Severe recession 0.1 -40 -2 -51.2 2621.44 131.07 Mild recession 0.2 -14 -3.5 -25.2 635.04 158.76 Normal growth 0.35 17 6.8 5.8 33.64 13.46 Boom 0.35 33 9.9 21.8 475.24 142.57 11.2 445.86 21.12 Expected Return = Variance = Standard Deviation = Scenario Probability Rate of Return Deviation from Expected Squared Deviation 6-2
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 Severe recession 0.1 -51.2 -14 716.8 71.68 Mild recession 0.2 -25.2

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