Transcript No Slide Title

CHAPTER 6
Efficient Diversification
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
6.1 DIVERSIFICATION AND
PORTFOLIO RISK
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Figure 6.2 Portfolio Risk as a
Function of Number of Securities
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6.2 ASSET ALLOCATION WITH
TWO RISKY ASSETS
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Covariance and Correlation
Portfolio risk depends on the correlation or
covariance between the returns of the
assets in the portfolio
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Two Asset Portfolio Return
rp

rP
 Portfolio Return
w r
B
B
 wS r S
wB  Bond Weight
rB
 Bond Return
wS  Stock Weig ht
rS
 Stock Return
6-6
Covariance and Correlation
Coefficient
Covariance:
S
Cov(rS , rB )   p(i) rS (i)  rS  rB (i)  rB 
i 1
Correlation Coefficient:
 SB 
Cov(rS , rB )
 S B
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Correlation Coefficients:
Possible Values
Range of values for S,B
-1.0 <  < 1.0
If  = 1.0, the securities would be
perfectly positively correlated
If  = - 1.0, the securities would be
perfectly negatively correlated
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Two Asset Portfolio St Dev
  w   w   2w w   
  Portfolio Variance

Portfolio
Standard
Deviation

2
2
2
2
2
p
B
B
S
S
B
S
S
B
B,S
2
p
2
p
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Three Rules of Two-Asset Portfolio
Rate of return on the portfolio:
rP  wB rB  wS rS
Expected rate of return on the portfolio:
E(rP )  wB E(rB )  wS E(rS )
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Three Rules of Two-Asset Portfolio
Variance of the rate of return on
the portfolio:
  (wB B )  (wS S )  2(wB B )(wS S ) BS
2
P
2
2
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Numerical Text Example: Bond and
Stock (Page 158)
Returns
Bond = 6% Stock = 10%
Standard Deviation
Bond = 12% Stock = 25%
Weights
Bond = .5
Stock = .5
Correlation Coefficient
(Bonds and Stock) = 0
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Numerical Text Example: Bond and
Stock Returns (Page 158)
Return = 8%
.5(6) + .5 (10)
Standard Deviation = 13.87%
[(.5)2 (12)2 + (.5)2 (25)2 + …
2 (.5) (.5) (12) (25) (0)] ½
[192.25] ½ = 13.87
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Investment Opportunity Set (Page 159)
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Figure 6.3 Investment Opportunity
Set for Stocks and Bonds
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Figure 6.4 Investment Opportunity Set
for Stocks and Bonds with Various
Correlations
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6.3 THE OPTIMAL RISKY PORTFOLIO
WITH A RISK-FREE ASSET
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Extending to Include Riskless Asset
The optimal combination
becomes linear
A single combination of risky and
riskless assets will dominate
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Figure 6.5 Opportunity Set Using Stocks
and Bonds and Two Capital Allocation Lines
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Figure 6.6 Optimal Capital Allocation Line
for Bonds, Stocks and T-Bills
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Dominant CAL with a Risk-Free
Investment (F)
• CAL(FO) dominates other lines -- it
has the best risk/return or the
largest slope
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Figure 6.7 The Complete Portfolio
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6.4 EFFICIENT DIVERSIFICATION WITH
MANY RISKY ASSETS
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Figure 6.10 The Efficient Frontier of Risky
Assets and Individual Assets
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6.5 A SINGLE-FACTOR ASSET MARKET
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Specification of a Single-Index Model of
Security Returns
Use the S&P 500 as a market proxy
Excess return can now be stated as:
Ri    i RM  e
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Figure 6.11 Scatter Diagram for Dell
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Figure 6.12 Various Scatter Diagrams
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Components of Risk
Market or systematic risk: risk related to the
macro economic factor or market index
Unsystematic or firm specific risk: risk not
related to the macro factor or market index
Total risk = Systematic Risk + Unsystematic
Risk
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Measuring Components of Risk
i2 = i2 m2 + 2(ei)
where;
i2 = total variance
i2 m2 = systematic variance
2(ei) = unsystematic variance
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Examining Percentage of Variance
Total Risk = Systematic Risk +
Unsystematic Risk
Systematic Risk/Total Risk = 2
ßi2  m2 / 2 = 2
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Advantages of the Single Index Model
Reduces the number of inputs for
diversification
Easier for security analysts to specialize
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