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. The smaller the correlation, the bigger
the gains from diversification. The upper limit of these gains occurs when the
correlation coefficient hits its lower bound of -1.0.
2. The covariance with the other assets is more important. Diversification is accomplished
via correlation with other assets and covariance is a function of correlation. Note that
covariance is based on the assets’ standard deviations as well as correlation (e.g.,
Cov(rs , rB ) = rSB ´ s S ´ s B ), but the contribution to decreased risk comes from the
correlation component, not the standard deviations.
3. a and b will have the same impact of increasing the Sharpe ratio from .40 to .45.
SP =
rP - rf
sP
=
.12 - .04
= .40
.20
.13 - .04
= .45
.20
.12 - .03
b. S P =
= .45
.20
.12 - .04
c. S P =
= .42
.19
a. S P =
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:
sM
s(e)
b
0.2
0.2
0.3
0.33
1.65
1.5
Total Correlation
Variance Coefficient
0.1989
0.1989
0.7399
0.6727
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Chapter 06 - Efficient Diversification
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 marketindex portfolio, is non-diversifiable, 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.
b. Calculation of mean return and variance for the stock fund:
(A)
(B)
(C)
Rate of
Scenario
Probability Return
Severe recession
0.05
-40
Mild recession
0.25
-14
Normal growth
0.40
17
Boom
0.30
33
Expected Return =
(D)
Col. B
×
Col. C
-2.0
-3.5
6.8
9.9
11.2
(E)
(F)
Deviation
from
Expected Squared
Return
Deviation
-51.2 2621.44
-25.2
635.04
5.8
33.64
21.8
475.24
Variance =
Standard Deviation =
(G)
Col. B
´
Col. F
131.07
158.76
13.46
142.57
445.86
21.12
c. Calculation of covariance:
(A)
Scenario
Severe recession
Mild recession
Normal growth
Boom
(B)
Probability
0.05
0.25
0.40
0.30
(C)
(D)
Deviation from
Mean Return
Stock
Fund
-51.2
-25.2
5.8
21.8
Bond
Fund
-14
10
3
-10
(E)
Col. C
´
Col. D
716.8
-252
17.4
-218
Covariance =
(F)
Col. B
´
Col. E
35.84
-63.00
6.96
-65.40
-85.6
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Chapter 06 - Efficient Diversification
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:
Scenario
Severe recession
Mild recession
Normal growth
Boom
Stock
Col. B
Rate of
´
Probability Return Col. C
0.10
-0.37 -0.037
0.20
-0.11 -0.022
0.35
0.14
0.049
0.35
0.30
0.105
Expected Return =
0.095
Deviation
from
Col. B
Expected Squared
´
Return Deviation Col. F
-0.465
0.2162 0.0216
-0.205
0.0420 0.0084
0.045
0.0020 0.0007
0.205
0.0420 0.0147
Variance = 0.0454
Standard Deviation = 0.2132
c. Calculation of covariance
Deviation from
Mean Return
Scenario
Severe recession
Mild recession
Normal growth
Boom
Stock
Probability Fund
0.1
-0.465
0.2
-0.205
0.35
0.045
0.35
0.205
Expected return =
Bond
Fund
-0.122
0.119
0.049
-0.082
-0.036
Col. C
´
Col. D
0.05673
-0.024395
0.002205
-0.01681
Covariance =
Col. B
´
Col. E
0.00567
-0.0049
0.00077
-0.0059
-0.0043
Covariance has decreased because the probabilities of the more extreme returns
in the recession and boom periods are now higher. This gives more weight to
the extremes in the mean calculation, thus making their deviation from the mean
less pronounced.
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Chapter 06 - Efficient Diversification
8.
The parameters of the opportunity set are:
E(rS) = 15%, E(rB) = 9%, sS = 32%, sB = 23%, r = 0.15, rf = 5.5%
From the standard deviations and the correlation coefficient we generate the covariance
matrix [note that Cov(rS, rB) = rsSsB]:
Bonds Stocks
529.0
110.4
Bonds
110.4
1024.0
Stocks
The minimum-variance portfolio proportions are:
wMin(S) =
sB2 － Cov(rS, rB)
529 － 110.4
=
= .3142
2
2
sS + sB － 2Cov(rS, rB) 1,024 + 529 － (2 ×110.4)
wMin(B) = 1 – .3142 = .6858
The mean and standard deviation of the minimum variance portfolio are:
E(rMin) = ( .3142 ´ 15%) + ( .6858 ´ 9%) = 10.89%
sMin = [w! s! + w" s" + 2 wS wB Cov(rS, rB)]1/2
2
2
2
2
= [( .31422 ´ 1024) + ( .68582 ´ 529) + (2 ´ .3142 ´ .6858 ´ 110.4)]1/2 = 19.94%
% in bonds Exp. Return
1.00
0.09
0.80
0.10
0.6858
0.1089
0.60
0.11
0.40
0.13
0.3534
0.1288
0.20
0.14
0.00
0.15
Std dev. Sharpe Ratio
0.23
0.15
0.20
0.23
0.1994
0.2701 Min. Var. Portfolio
0.20
0.29
0.23
0.3155
0.233382
0.3162 Tangency Portfolio
0.27
0.31
0.32
0.30
Investment Opportunity Set
Expected Return (%)
20
15
10
5
0
0
10
20
30
40
Standard Deviation (%)
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Chapter 06 - Efficient Diversification
9.
Expected Return (%)
Investment Opportunity Set
20
18
16
14
12
10
8
6
4
2
0
0
10
20
30
40
Standard Deviation (%)
The graph approximates the points:
Minimum variance portfolio
Tangency portfolio
E(r)
10.89%
12.88%
s
19.94%
23.3382%
10. The Sharpe ratio of the optimal CAL is:
E(rP) － rf 12.88% － 5.50%
sP
=
23.34%
= .3162
11.
a. The equation for the CAL is:
E(rC) = rf +
E(rP) － rf
sP
sC = 5.50% + .3162sC
Setting E(rC) equal to 12% yields a standard deviation of 20.56%.
b. The mean of the complete portfolio as a function of the proportion invested in
the risky portfolio (y) is:
E(rC) = rf + y × [E(rP) - rf] = 5.50% + y × (12.88% - 5.50%)
Setting E(rC) = 12% Þ y = .8808 (88.08% in the risky portfolio)
1 - y = .1192 (11.92% in T-bills)
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Chapter 06 - Efficient Diversification
To prevent rounding error, we use the spreadsheet with the calculation of the
previous parts of the problem to compute the proportion in each asset in the
complete portfolio:
s(c)
0.205559955 = (12% - 5.5%)/Sharpe ratio(risky portfolio)
W(risky portfolio) 0.880786822 = s(c)/s(risky portfolio)
Proportion of stocks in complete portfolio
W(s) = W(risky portfolio)*% in stock of the risky portfolio
=
0.569541021
Proportion of bonds in complete portfolio
W(b) = W(risky portfolio)*% in bonds of the risky portfolio
=
0.311245801
12. Using only the stock and bond funds to achieve a mean of 12%, we solve:
12% = 15% × wS + 9% × (1 - wS) = 9% + 6% × wS Þ wS = .5
Investing 50% in stocks and 50% in bonds yields a mean of 12% and standard deviation
of: sP = [( .502 ´ 1,024) + ( .502 ´ 529) + (2 ´ .50 ´ .50 ´ 110.4)] 1/2 = 21.06%
The efficient portfolio with a mean of 12% has a standard deviation of only 20.61%.
Using the CAL reduces the standard deviation by 45 basis points.
13.
a. Although it appears that gold is dominated by stocks, gold can still be an
attractive diversification asset. If the correlation between gold and stocks is
sufficiently low, gold will be held as a component in the optimal portfolio.
Return
12%
Stock
10%
0.2, 0.1
Corr = -1
8%
Corr = -0.5
6%
Gold
0.25, 0.05
4%
Corr = 0
Corr = 0.5
Corr = 1
2%
0%
0%
10%
20%
30%
Standard
Deviation
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Chapter 06 - Efficient Diversification
b. If gold had a perfectly positive correlation with stocks, gold would not be a part
of efficient portfolios. The set of risk/return combinations of stocks and gold
would plot as a straight line with a negative slope. (Refer to the above graph
when correlation is 1.) The graph shows that when the correlation coefficient is
1, holding gold provides no benefit of diversification. The stock-only portfolio
dominates any portfolio containing gold. This cannot be an equilibrium; the
price of gold must fall and its expected return must rise.
14. Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can
be created and the rate of return for this portfolio in equilibrium will always be the riskfree rate. To find the proportions of this portfolio [with wA invested in Stock A and wB
= (1 –wA ) invested in Stock B], set the standard deviation equal to zero. With perfect
negative correlation, the portfolio standard deviation reduces to:
sP = ABS[wAsA -wBsB]
0 = 40 × wA - 60 × (1 –wA) Þ wA = .60
The expected rate of return on this risk-free portfolio is:
E(r) = (.60 ´ .08) + (.40 ´ .13) = 10.0%
Therefore, the risk-free rate must also be 10.0%.
15. Since these are annual rates and the risk-free rate was quite variable during the sample
period of the recent 20 years, the analysis uses continuously compounded rates in
excess of T-bill rates. Convert percentage to decimal to calculate continuously
compounded rates. The decimal continuously compounded rate, ln(1+percentage
rate/100), can then be multiplied by 100 to return to percentage rates. Excess returns are
just the difference between total returns and the risk-free (T-bill) rates.
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Chapter 06 - Efficient Diversification
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Min-Var
Annual returns from Table 2
LongLarge
Term TStock
Bonds
T-Bills
-11.71
14.49
5.89
-11.42
4.03
3.78
-21.13
14.66
1.63
31.77
1.28
1.02
11.92
5.19
1.20
6.05
3.10
2.96
15.39
2.27
4.79
5.71
9.64
4.67
-36.87
17.67
1.47
28.36
-5.83
0.10
17.49
7.45
0.12
0.48
16.60
0.04
16.34
3.59
0.06
35.23
-6.90
0.03
11.72
10.15
0.02
0.08
1.07
0.01
13.49
0.70
0.1886
22.29
2.80
0.7914
-5.22
0.04
1.7066
30.43
8.2622
2.15
Weights in
Stocks
Bonds
0.0
1
0.1
0.9
0.2
0.8
0.3
0.7
0.4
0.6
0.5
0.5
0.6
0.4
0.7
0.3
0.8
0.2
0.9
0.1
1.0
0
0.1938
0.8062
Continuously compounded rates
LongLarge
Term TStock
Bonds
T-Bills
-12.45
13.53
5.72
-12.13
3.95
3.71
-23.73
13.68
1.62
27.59
1.27
1.01
11.26
5.06
1.19
5.88
3.06
2.92
14.31
2.25
4.67
5.56
9.21
4.57
-45.99
16.27
1.46
24.96
-6.00
0.10
16.12
7.18
0.12
0.48
15.36
0.04
15.13
3.52
0.06
30.18
-7.15
0.03
11.08
9.67
0.02
0.08
1.06
0.01
12.65
0.70
0.19
20.12
2.76
0.79
-5.36
0.04
1.69
26.56
7.94
2.12
Average
SD
Corr(stocks,bonds)
Excess returns
LongLarge
Term TStock
Bonds
-18.18
7.81
-15.84
0.24
-25.35
12.06
26.57
0.26
10.07
3.86
2.96
0.14
9.64
-2.43
0.99
4.64
-47.45
14.80
24.87
-6.10
16.00
7.06
0.44
15.32
15.08
3.47
30.15
-7.18
11.06
9.65
0.07
1.05
12.46
0.51
19.34
1.98
-7.06
-1.65
24.44
5.81
4.51
3.57
19.59
6.22
-0.58
Portfolio
Mean
SD
3.57
6.22
3.66
4.74
3.75
4.18
3.85
4.88
3.94
6.44
4.04
8.38
4.13
10.51
4.23
12.72
4.32
14.98
4.42
17.27
4.51
19.59
3.75
4.18
The bond portfolio is less risky as represented by its lower standard deviation. Yet, as
the portfolio table shows,81% bonds and 19% stocks produces a portfolio less risky
than bonds.
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Chapter 06 - Efficient Diversification
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.
However, if the borrowing and lending rates are not equal, then borrowers (who are
relatively risk averse) and lenders (who are relatively risk tolerant) will have different
optimal risky portfolios.
17. No, it is not possible to get such a diagram. Even if the correlation between A and B
were 1.0, the frontier would be a straight line connecting 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
deviations. Otherwise, as the formula for portfolio variance (Equation 6.6) shows, the
portfolio standard deviation is less than the weighted average of the component-asset
standard deviations. The portfolio variance is a weighted sum of the elements in the
covariance matrix, with the products of the portfolio proportions as weights.
19. The probability distribution is:
Probability
.7
.3
Rate of Return
100%
-50%
Expected return = (.7 ´ 1) + .3 ´ (- .5) = 0.55 or 55%
Variance = [ .7 ´ (1 - 0.55)2] + [ .3 ´ (-0.50 - 0.55)2] = 0.4725
Standard Deviation =√0.4725 = 0.6874 or 68.74%
20. The expected rate of return on the stock will change by beta times the unanticipated
change in the market return: 1.2 ´ (.08 – .10) = –2.4%
Therefore, the expected rate of return on the stock should be revised to:
.120 – .024 = .096 = 9.6%
21.
a. The risk of the diversified portfolio consists primarily of systematic risk. Beta
measures systematic risk, which is the slope of the security characteristic line (SCL).
The two figures depict the stocks' SCLs. Stock B's SCL is steeper, and hence Stock
B's systematic risk is greater. The slope of the SCL, and hence the systematic risk, of
Stock A is lower. Thus, for this investor, stock B is the riskiest.
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Chapter 06 - Efficient Diversification
b. The undiversified investor is exposed primarily to firm-specific risk. Stock A
has higher firm-specific risk because the deviations of the observations from the
SCL are larger for Stock A than for Stock B. Deviations are measured by the
vertical distance of each observation from the SCL. Stock A is therefore riskiest
to this investor.
22. Using “Regression” command from Excel’s Data Analysis menu, we can run a
regression of Apple’s excess returns (rAAPL – rT-bill) against those of S&P 500 (rSP500 –
rT-bill), and obtain the following data. The Beta of Apple is 1.04.
SUMMARY
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.80
0.64
0.64
0.06
72
Coefficients
Standard Error
t Stat
0.00
1.04
0.01
0.09
1.74
11.18
Intercept
S&P 500
P-value
0.09
0.00
23. A scatter plot results in the following diagram. The slope of the regression line is 2.0
and intercept is 1.0.
4
Generic
Return,
Percent
y = 1.0 + 2.0 x
3
2
1
0
-1
-0.5
0
-1
0.5
1
Market Return, Percent
-2
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Chapter 06 - Efficient Diversification
24.
a. Regression of Google’s excess monthly returns on the S&P 500’s excess
monthly returns (both using 3-Month T-Bill annualized returns converted to
monthly returns as the risk-free rate) produces the following output:
α = .9314, β = 1.0606, Residual Standard Deviation = 4.6596
Regression Statistics
Multiple R
0.6299
R Square
0.3968
Adjusted R Square
0.3864
Standard Error
4.6596
Observations
60
Coefficients
0.9314
1.0606
Intercept
S&P 500
b. Sharpe Ratio of S&P =
E(rS&P) － rf
Alpha
S&P
Google
Standard Error
0.6031
0.1717
0.9314
t Stat
1.5445
6.1772
P-value
0.1279
0.0000
sS&P
= 8.6926/11.9638 = .7266
Beta
E(r) - rf
8.6926
19.6898
1.0606
VAR
143.1323
404.4227
SD
11.9638
20.1103
c. Information Ratio = αG/s(eG) = 0.9314/4.6596 = .1999
O
d. We use Equation 6.16 to compute wG
αG /s2(eG) 0.9314/(4.65962)
wG =
=
= 70.64%
RS&P/s2S&P 8.6926/(11.96382)
O
O
Then, plug wG into Equation 6.17 to compute the optimal position of Google in
the optimal risky portfolio and the weight in the market index:
wG∗ = .7064 / [1 + (.7064 ´ (1 – 1.0606)] = .7380 = 73.80%
wM∗ = 1– wG∗ = 26.20%
e. Rearrange Equation 6.18 to solve for S0
αG 2
0.9314 2
SO = !"
# + (SM)2 = !"
# + (.7266)2 = .7536
s (eG )
4.6596
Sharpe ratio increases from .7266 to .7536.
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Chapter 06 - Efficient Diversification
25.
a.
Payout
Outcome A: No Fire
$110
Outcome B: Fire!
$
(99,890)
b.
Expected Return
$10.00
Variance
9990000
Standard Deviation
3161
c.
Payout
Probability
Outcome: No Fire
$ 220
99.8001%
Outcome: One Fire
$ (99,780)
0.1998%
Outcome: Two Fires
$ (199,780)
0.0001%
d.
Expected Return
$20.00
Variance
11466315
Standard Deviation
3386
e. Risk pooling increased the total variance of profit.
f.
Payout
Probability
Outcome: No Fire
$ 110
99.8001%
Outcome: One Fire
$ (49,890)
0.1998%
Outcome: Two Fires
$ (99,890)
0.0001%
g.
Expected Return
$10.00
Variance
2,866,579
Standard Deviation
1,693
h. Risk has dropped significantly while the expected profit is the same as (b). This
demonstrates the power of Risk Sharing as a necessary complement to Risk Pooling.
(g) is a superior outcome to (b) [Same Expected Reward, Lower Risk]
i. Risk Pooling builds both expected payout and variance. Risk Sharing implies profit
sharing so expected payout is halved, but so has standard deviation
CFA 1
Answer:
E(rP) = ( .5 ´ 15) + ( .4 ´ 10) + ( .10 ´ 6) = 12.1%
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Chapter 06 - Efficient Diversification
CFA 2
Answer:
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 (+ .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.
CFA 3
Answer:
a. Subscript OP refers to the original portfolio, ABC to the new stock, and NP
to the new portfolio.
i. E(rNP) = wOP E(rOP ) + wABC E(rABC ) = ( .9 ´ .67) + ( .1 ´ 1.25) = .7280%
ii. CovOP , ABC = CorrOP , ABC ´ sOP ´ sABC = .40 ´ 2.37 ´ 2.95 = 2.7966
iii.
sNP = [wOP 2 sOP 2 + wABC 2 sABC 2 + 2 wOP wABC (CovOP , ABC)]1/2
= [( .92 ´ 2.372) + ( .12 ´ 2.952) + (2 ´ .9 ´ .1 ´ 2.7966)]1/2
= 2.2672%
b. Subscript OP refers to the original portfolio, GS to government securities, and
NP to the new portfolio.
i. E(rNP) = wOP E(rOP ) + wGS E(rGS ) = ( .9 ´ .67) + ( .1 ´ .42) = .6450%
ii. CovOP , GS = CorrOP , GS ´ sOP ´ sGS = 0 ´ 2.37 ´ 0 = 0
iii.
sNP = [wOP 2 sOP 2 + wGS 2 sGS 2 + 2 wOP wGS (CovOP , GS)]1/2
= [( .92 ´ 2.372) + ( .12 ´ 0) + (2 ´ .9 ´ .1 ´ 0)]1/2
= 2.1330%
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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.
d. The comment is not correct. Although the respective standard deviations and
expected returns for the two securities under consideration are identical, the
correlation coefficients between each security and the original portfolio are
unknown, making it impossible to draw the conclusion stated. For instance, if the
correlation between the original portfolio and XYZ stock is smaller than that
between the original portfolio and ABC stock, replacing ABC stocks with XYZ
stocks would result in a lower standard deviation for the portfolio as a whole. In
such a case, XYZ socks would be the preferred investment, assuming all other
factors are equal.
e. Grace clearly expressed the sentiment that the risk of loss was more important to
her than the opportunity for return. Using variance (or standard deviation) as a
measure of risk in her case has a serious limitation because standard deviation
does not distinguish between positive and negative price movements.
CFA 4
Answer:
a. Restricting the portfolio to 30 stocks, rather than 40 to 50, will very likely
increase the risk of the portfolio, due to the reduction in diversification. Such an
increase might be acceptable if the expected return is increased sufficiently.
b. Hennessy could contain the increase in risk by making sure that he maintains
reasonable diversification among the 30 stocks that remain in his portfolio. This
entails maintaining a low correlation among the remaining stocks. As a practical
matter, this means that Hennessy would need to spread his portfolio among
many industries, rather than concentrating in just a few.
CFA 5
Answer:
Risk reduction benefits from diversification are not a linear function of the number of
issues in the portfolio. (See Figures 6.1 and 6.2 in the text.) Rather, the incremental
benefits from additional diversification are most important when the portfolio is least
diversified. Restricting Hennessy to 10 issues, instead of 30 issues, would increase the
risk of his portfolio by a greater amount than reducing the size of the portfolio from 30
to 20 stocks.
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consent of McGraw-Hill Education.
Chapter 06 - Efficient Diversification
CFA 6
Answer:
The point is well taken because the committee should be concerned with the volatility
of the entire fund. Since Hennessy's portfolio is only one of six well-diversified
portfolios, and is smaller than the average, the concentration in fewer issues might have
a minimal effect on the diversification of the total fund. Hence, unleashing Hennessy to
do stock picking may be advantageous.
CFA 7
Answer:
a. Systematic risk refers to fluctuations in asset prices caused by macroeconomic
factors that are common to all risky assets; hence systematic risk is often
referred to as market risk. Examples of systematic risk factors include the
business cycle, inflation, monetary policy, and technological changes.
Firm-specific risk refers to fluctuations in asset prices caused by factors that are
independent of the market, such as industry characteristics or firm
characteristics. Examples of firm-specific risk factors include litigation, patents,
management, and financial leverage.
b. Trudy should explain to the client that picking only the five best ideas would
most likely result in the client holding a much more risky portfolio. The total
risk of a portfolio, or portfolio variance, is the combination of systematic risk
and firm-specific risk.
The systematic component depends on the sensitivity of the individual assets to
market movements, as measured by beta. Assuming the portfolio is welldiversified, the number of assets will not affect the systematic risk component
of portfolio variance. The portfolio beta depends on the individual security betas
and the portfolio weights of those securities.
On the other hand, the components of firm-specific risk (sometimes called
nonsystematic risk) are not perfectly positively correlated with each other and,
as more assets are added to the portfolio, those additional assets tend to reduce
portfolio risk. Hence, increasing the number of securities in a portfolio reduces
firm-specific risk. For example, a patent expiration for one company would not
affect the other securities in the portfolio. An increase in oil prices might hurt an
airline stock but aid an energy stock. As the number of randomly selected
securities increases, the total risk (variance) of the portfolio approaches its
systematic variance.
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consent of McGraw-Hill Education.