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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

-

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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