Chapter 06 – Efficient Diversification
1. So long as the correlation coefficient is below 1.0, the portfolio will benefit from
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.
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:
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
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:
8. The parameters of the opportunity set are:
E(rS) = 15%, E(rB) = 9%, S = 32%, B = 23%, = 0.15, rf = 5.5%
From the standard deviations and the correlation coefficient we generate the covariance
matrix [note that Cov(rS, rB) = SB]:
15 20 25 30 35 40
0
20
Investment Opportunity Set
Standard Deviation (%)
Expected Return (%)
9.
10. The reward-to-variability ratio (Sharpe ratio) of the optimal CAL is:
E( r P) － r f
P
12.88 － 5.5
23 .34
11.
a. The equation for the CAL is:
E(rC) = rf +
E( r P) － r f
P
C = 5.5 + .3162C
12. Using only the stock and bond funds to achieve a mean of 12%, we solve:
6-4
13.
a. Although it appears that gold is dominated by stocks, gold can still be an
Chapter 06 – Efficient Diversification
convert percentage return to decimal. The decimal cc rate, ln(1 + percentage rate/100),
can then be multiplied by 100 to return to percentage rates. Recall also that with cc
rates, excess returns are just the difference between total returns and the risk-free (T–
16. If the lending and borrowing rates are equal and there are no other constraints on
portfolio choice, then the optimal risky portfolios of all investors will be identical.
17. No, it is not possible to get such a diagram. Even if the correlation between A and B
18. In the special case that all assets are perfectly positively correlated, the portfolio
standard deviation is equal to the weighted average of the component-asset standard
19. The probability distribution is:
Probability Rate of Return
23. A scatter plot results in the following diagram. The slope of the regression line is 2.0
and intercept is 1.0.
y = 1.0 + 2.0 x
-2
-1
0
1
2
3
4
-1 -0.5 0 0.5 1
Market Return, Percent
Generic
Return,
Percent
24.
a. Regression output produces the following:
alpha = 3.1792, beta = 1.3916, Residual St Dev = 11.5932
b. Sharpe Ratio of S&P =
E( rS&P ) － r f
S &P
= – .6123/4.0316 = – .1519
6-8
Chapter 06 – Efficient Diversification
αG
2
3.1 792
2
CFA 1
Answer:
CFA 3 Answer:
Chapter 06 – Efficient Diversification
c. Adding the risk-free government securities would result in a lower beta for the
new portfolio. The new portfolio beta will be a weighted average of the individual
security betas in the portfolio; the presence of the risk-free securities would lower
that weighted average.
CFA 4Answer:
a. Restricting the portfolio to 20 stocks, rather than 40 to 50, will very likely
increase the risk of the portfolio, due to the reduction in diversification. Such an
CFA 5 Answer:
Chapter 06 – Efficient Diversification
CFA 7 Answer: