Chapter 06 - Efficient Diversification
CHAPTER 06
EFFICIENT DIVERSIFICATION
1. So long as the correlation coefficient is below 1.0, the portfolio will benefit from
diversification because returns on component securities will not move in perfect
lockstep. The portfolio standard deviation will be less than a weighted average of the
standard deviations of the component securities.
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 have the same impact of increasing the Sharpe ratio from .40 to .45.
4. The expected return of the portfolio will be impacted if the asset allocation is changed.
Since the expected return of the portfolio is the first item in the numerator of the Sharpe
ratio, the ratio will be changed.
5. Total variance = Systematic variance + Residual variance = β2 Var(rM) + Var(e)
When β = 1.5 and σ(e) = .3, variance = 1.52 × .22 + .32 = .18. In the other scenarios:
a. Both will have the same impact. Total variance will increase from .18 to .1989.
b. Even though the increase in the total variability of the stock is the same in either
scenario, the increase in residual risk will have less impact on portfolio
volatility. This is because residual risk is diversifiable. In contrast, the increase
in beta increases systematic risk, which is perfectly correlated with the market-
index portfolio and therefore has a greater impact on portfolio risk.
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 large on both the high and low side. The mean return,
however, should be higher since there is higher probability given to the higher
returns.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
, Chapter 06 - Efficient Diversification
b. Calculation of mean return and variance for the stock fund:
c. Calculation of covariance:
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.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
CHAPTER 06
EFFICIENT DIVERSIFICATION
1. So long as the correlation coefficient is below 1.0, the portfolio will benefit from
diversification because returns on component securities will not move in perfect
lockstep. The portfolio standard deviation will be less than a weighted average of the
standard deviations of the component securities.
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 have the same impact of increasing the Sharpe ratio from .40 to .45.
4. The expected return of the portfolio will be impacted if the asset allocation is changed.
Since the expected return of the portfolio is the first item in the numerator of the Sharpe
ratio, the ratio will be changed.
5. Total variance = Systematic variance + Residual variance = β2 Var(rM) + Var(e)
When β = 1.5 and σ(e) = .3, variance = 1.52 × .22 + .32 = .18. In the other scenarios:
a. Both will have the same impact. Total variance will increase from .18 to .1989.
b. Even though the increase in the total variability of the stock is the same in either
scenario, the increase in residual risk will have less impact on portfolio
volatility. This is because residual risk is diversifiable. In contrast, the increase
in beta increases systematic risk, which is perfectly correlated with the market-
index portfolio and therefore has a greater impact on portfolio risk.
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 large on both the high and low side. The mean return,
however, should be higher since there is higher probability given to the higher
returns.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
, Chapter 06 - Efficient Diversification
b. Calculation of mean return and variance for the stock fund:
c. Calculation of covariance:
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.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
