Foundations of Financial Markets 2
Diversification and Portfolio Risk
• Market risk– Systematic or Nondiversifiable
• Firm-specific risk– Diversifiable or nonsystematic
Foundations of Financial Markets 5
A single factor Model
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surprisemarket y tosensitivit is
Surprise micMacroecono-Market is
return excess expected is
return excess is
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M
RE
rrR
Foundations of Financial Markets 6
What is M?
• Anything that can be regarded as a proxy for macroeconomic risk
• Commonly used factor: a broad market index like the S&P500
• Call it Rm
Foundations of Financial Markets 7
Commonly Run Regression
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market overall
in the movements toduereturn ofcomponent is
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Foundations of Financial Markets 10
Coca Cola: another example
-1.5
-1.0
-0.5
0.0
0.5
-0.3 -0.2 -0.1 0.0 0.1 0.2
SP
KO
KO vs. SP
Foundations of Financial Markets 11
Regression statistics
Dependent Variable: KOMethod: Least SquaresSample: 1962:02 2007:10Included observations: 549
Variable Coefficient Std. Error t-Statistic Prob. C -0.005508 0.004206 -1.309559 0.1909SP 0.816898 0.098425 8.299663 0.0000
R2 = 0.111846
Foundations of Financial Markets 12
A more recent sample
Dependent Variable: KOMethod: Least SquaresSample: 1990:01 2007:10Included observations: 214
Variable Coefficient Std. Error t-Statistic Prob. C -0.004975 0.006378 -0.780066 0.4362SP 0.523387 0.158603 3.299976 0.0011
R2 = 0.048858
Foundations of Financial Markets 13
Some Betas of S&P500 companies
Company BetaApple 1.3
Amazon 1.6
Cisco 1.1
Coca Cola 0.8
Countrywide Financial 1.8
Goldman Sachs 1.7
Johnson & Johnson 0.5
McDonald's 0.8
Microsoft 0.9
Foundations of Financial Markets 14
Measuring Components of Risk
i2 = i
2 m2 + 2(ei)
Where:
i2 = total variance
i2 m
2 = systematic variance
2(ei) = unsystematic variance
Foundations of Financial Markets 15
Decomposition of Risk
• Total variability of the rate of return depends on two components
1. The variance attributable to the uncertainty common to the entire market
2. The variance attributable to firm specific risk factors
Foundations of Financial Markets 16
Systematic and idiosyncratic risk with many securities
• Two assets
• Portfolio weights are w1 and (1-w1)
• What is the portfolio ?
• What is the systematic risk of the portfolio?
• What is the idiosyncratic risk of the portfolio?
1111 eRR m 2222 eRR m
Foundations of Financial Markets 17
Portfolio
• because
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wwRwRw
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Foundations of Financial Markets 18
Systematic Risk
• A good strategy would select securities with smallest ’s
222111 1 mww
Foundations of Financial Markets 19
Idiosyncratic Risk
• Benefits from diversification if idiosyncratic risk is less than perfectly correlated
2111 1 ewewVar
Foundations of Financial Markets 20
Advantages of the Single Index Model
• Reduces the number of inputs for diversification
• Easier for security analysts to specialize
Foundations of Financial Markets 21
What risk should be priced?
• What risk should be priced?– Idiosyncratic risk: no– Aggregate risk: yes
• Only aggregate/macro risk commands a premium
Foundations of Financial Markets 22
Why?
Because:
1. idiosyncratic risk can be diversified away
2. Macro risk affects all assets and cannot be diversified
Foundations of Financial Markets 23
Example: two assets
assets twoin the shares portfolio equalInvest
0),cov(
1)()(
1
:Assume
and
:assets Two
21
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ee
eVareVar
eRReRR mm
Foundations of Financial Markets 24
What is the portfolio variance?
2/1)()( 2211 mRVarRwRwVar
Systematic
Risk
Idiosyncratic
Risk
Foundations of Financial Markets 25
Example: three assets
assets threein the shares portfolio equalInvest
0),cov(),cov(),cov(
1)()()(
1
:Assume
3,2,1 ,
:assets Two
323121
321
321
eeeeee
eVareVareVar
ieRR imiii
Foundations of Financial Markets 26
What is the portfolio variance?
3/1)()( 332211 mRVarRwRwRwVar
Systematic
Risk
Idiosyncratic
Risk
•Systematic risk: unchanged
•Idiosyncratic risk: decreased
•Can you guess what would happen if we had an infinite number of assets?
Foundations of Financial Markets 27
Infinite assets
• For a well diversified portfolio
• That is: we got rid of any idiosyncratic shock and we are left only with systematic risk
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mi
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or
,2
Foundations of Financial Markets 28
What lesson did we learn?
• The only source of risk that we are entitled to ask a compensation for is aggregate risk.
• Idiosyncratic risk does not entitle to any compensation because it can be diversified away.
Foundations of Financial Markets 29
Risk compensation
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