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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)