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IAPM
PGP17
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Day6
FromCAPMtoindexmodels
Wh factormodel?
CAPM says everything in terms of expected returns, which we
dont see. We see only the actual returns.
TheregressioncanbeusedtoestimatetheCAPM
The definition of regression (sample version)matches the
defn of CAPM (population version)
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Usefulnessof
the
index
model
SFmodelenablesthebreaku intos stematicriskandunsystematicrisk.
Notonlythat; isareasonablemeasureofsystematicrisk.
Waitaminute!Excessmarketreturns?
Single factor model to single index model: Using a market
index as a proxy for the market portfolio
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SecurityCharacteristicLine
tetRtRHPPSHPHPHP
500&
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Relationbetween
betas
and
std
deviations
Ifthesim leCAPMisvalid isthefollowin situationpossible?
Portfolio Expreturn Stdev
A 30 35
B 0 2
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Usingarisk
return
model
for
evaluating
investments
Twoinvestmentadvisorsarecom arin erformance.Oneaverageda19%rateofreturnandtheothera16%return.Howeverthebetaofthefirstinvestorwas1.5,
whereasthatofthesecondwas1.
Which one is a better selector of individual stocks?
If risk-free rate were 6% and market returned 14% during the
a ove per o , w o s etter
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Understandingthe
index
model
Considertheout utfromasin leindexmodel
Stock Beta Meanexcessreturn stdev
A 1.7 17% 50%
B 1.0 10% 40%
Thestdev ofthemarketindexportf is25%.
. systematiccomponents?
b. Supposeyouformanequallyweightedportf ofAandB.Whatwillbethenonsystematicstdev ofthatportfolio?
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MultiFactormodels
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BeyondCAPM
Motivationforamultifactormodelissameaswesawbeforeforanyriskreturnmodel
Needformorefactors
The same news item can be good for one firm, but bad for
another. For e.g. on a particular day, an important
announcement suggests that economy will expand. GDP is
expec e o ncrease an so are n eres ra es.
A single factor model cannot capture such differential
responses.
Howaretheyconstructed?
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AnExample
r=1 . +1.2 GDP . IR +e in ercenta es
How is it interpreted?
GoingfromheretomultifactorSML
Factor Risk premium
GDP 6%
IR -7%
Vehiclethatisusedtomakethistransition:ArbitragePricingTheory(APT)
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Twopart
argument
of
APT
1. Welldiversified ortfolioshaveonl factorrisk
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TwopartargumentofAPT
Wherearetheriskpremiumscomingfrom?
2. Twowelldiversifiedportfolioswiththesameshouldhavethesameexpectedreturn
Arbitrage: Exploitation of asset mispricing in such a way
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Conclusion:Expectedreturnonwelldiversifiedportfoliosmustlieonthestraightlinefromtheriskfreeasset(SML)
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WhereShould
We
Look
for
Factors?
Needim ortants stematicriskfactors
Chen, Roll, and Ross used industrial production, expected
inflation, unanticipated inflation, excess return on corporate
bonds, and excess return on government bonds.
Fama and French used firm characteristics that proxy for
systematic risk factors.
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Problems
Ch.10 P P P8 P10 P11
Reading:Chapter10(sections2and4)
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