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IAPM

PGP17

1

Day

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TwopartargumentofAPT

Tellsushowtogofromthemultifactormodeltoriskpremiums

Twowelldiversifiedportfolioswiththesameshouldhavethesameexpectedreturn

Arbitrage: Exploitation of asset mispricing in such a waythat risk-free rofits can be earned

Conclusion:Expectedreturnonwelldiversifiedportfoliosmustlieonthestraightlinefromtheriskfreeasset(SML)

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APTTheriskreturnrelationcanbeextendedfromwell

diversifiedportfoliostoindividualassets.

AsimilarargumentisusedtoestablishthemultifactorSML.

TheriskpremiumsinamultifactorSMLarecomingfromfactorportfolios.

Connections between the two equations in the first slide: Is

the airline stock over priced or under priced?

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Fama and

French

and

the

three

factor

model

ResearchersEu eneFama andKenFrenchhavedoneextensiveresearchinthisarea

Foundfactorsdescribingvalueandsizetobethemostsignificantfactors,outsideofmarketrisk,forexplainingtherealizedreturnsofpubliclytradedstocks(1992)

To represent these risks, they constructed two factors: SMB Small Minus Big (firm size) to address size risk and HML High Minus Low (book-to-market ratio) to address value risk

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Fama FrenchSMBisdesi nedtomeasuretheadditionalreturn

investorshavehistoricallyreceivedbyinvestinginstocksofcompanieswithrelativelysmallmarketcapitalization.Thisadditionalreturnisoftenreferredtoasthesizepremium.

In practice, the SMB monthly factor is computed as the

average return of the largest 30% of stocks in that month.

A positive SMB in a month indicates that small cap stocksoutperformed large cap stocks in that month.

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HML

HMLwhichisshortforHi hMinusLow hasbeenconstructedtomeasurethevaluepremiumprovidedtoinvestorsforinvestingincompanieswithhighbooktomarketvalues

Constructed in a fashion similar to that of SMB, HML is

computed as the average return for the 50% of stocks with

stocks with the lowest B/M ratio each month.

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Fama French

re eser s ac ors

Whatdoesthe3factorSMLlooklike?

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ClassifyingFundsintoStyleBuckets The3factormodelprovidesawaytocategorizemutualfundsbythe

sizeandvalueriskstowhichitsportfolioisexposed,andthusthereturnpremiumsexpected.

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Fund

evaluation

in

practice

(using

CAPM)

Isa iven erformancehi herthanthebenchmark?

TheLMVPfundreturned27.3%annuallyfromSeptember1998toDecember2002whilethemarketonlyreturned21.6%.

The fund manager might claim the excess returns were due toher exceptional ability at picking stocks.

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UseofSCL

Usin historicalmonthl valuesforr r and r wecandeterminethevaluesof and usingtheSCL.

Using rArf for the y-values and rMrf for the x-values in aregression, the following coefficients are returned:

= 0.93

= 0.46% per month

i.e. the fund manager was able to add 46 basis points to thefunds return on a monthly basis or about 5.5% per year abovethe return expected from a portfolio with a beta of .93.

Is this higher than benchmark return?

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Thetstatisticassociatedwithal hais2. indicatin thatachievingsuchreturnswithoutskillwouldbeextremelyunlikely

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Fund

evaluation

in

practice

(using

Fama

French)

Wenowhaveanothertoolwithwhichtoscrutinizethemanagersclaim

Utilize historic monthly values to build a regression usingrA,rM, rf, SMB, and HML . Regress rArf against rM rf, SMBand HML to determine the estimates of, M, S and V

In this particular case, the following coefficients result:

= .M= 0.99

S = 0.36

V = 0.22

t-statistic for = 1.112

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Fund

evaluation

in

practice Therelativelylowtstatisticof1.1,however,underminesthe

managersclaimandindicatesthatthealphawasmorelikelytohavehappenedbychance(i.e.itisnotstatisticallydifferentfromzero) A high R2(0.92 in this case) tells us that the three factors explain all

but 8% of the variation in historical returns, further lendingcredence to the findings.

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Upshot:ApositivealphaobservedinaCAPMregression

couldmerelybearesultofexposuretoeitherHMLorSMBfactors,ratherthanactualmanagerperformance.

(Courtesy:KentWomacksteachingnote)