Testing CAPMTesting CAPM

EFM 2006/7EFM 2006/7 22

NES

Plan Plan

Up to now: analysis of return Up to now: analysis of return predictabilitypredictability– Main conclusion: need a better risk model Main conclusion: need a better risk model

explaining cross-sectional differences in explaining cross-sectional differences in returns returns

Today: is CAPM beta a sufficient Today: is CAPM beta a sufficient description of risks?description of risks?– Time-series testsTime-series tests– Cross-sectional testsCross-sectional tests– Anomalies and their interpretationAnomalies and their interpretation

EFM 2006/7EFM 2006/7 33

NES

CAPMCAPM

Sharpe-Lintner CAPM: Sharpe-Lintner CAPM:

EEt-1t-1[R[Ri,ti,t] = R] = RFF + β + βii (E (Et-1t-1[R[RM,tM,t] – R] – RFF)) Black (zero-beta) CAPM: Black (zero-beta) CAPM:

EEt-1t-1[R[Ri,ti,t] = E] = Et-1t-1[R[RZ,tZ,t] + β] + βii (E (Et-1t-1[R[RM,tM,t] – E] – Et-1t-1[R[RZ,tZ,t])]) Single-period model for expected returns, Single-period model for expected returns,

implying thatimplying that– The intercept is zeroThe intercept is zero– Beta fully captures cross-sectional variation in Beta fully captures cross-sectional variation in

expected returnsexpected returns Testing CAPM = checking that market portfolio Testing CAPM = checking that market portfolio

is on the mean-variance frontieris on the mean-variance frontier– ‘‘Mean-variance efficiencyMean-variance efficiency’ tests’ tests

EFM 2006/7EFM 2006/7 44

NES

Testing Testing CAPMCAPM

Standard assumptions for testing CAPMStandard assumptions for testing CAPM– Rational expectations for Rational expectations for RRi,ti,t, R, RM,tM,t, R, RZ,tZ,t: :

Ex ante Ex ante → → ex postex post E.g., RE.g., Ri,ti,t = E = Et-1t-1RRi,ti,t + e + ei,ti,t, where e is white noise, where e is white noise

– Constant betaConstant beta Testable equations:Testable equations:

RRi,ti,t-R-RFF = β = βii(R(RM,tM,t-R-RFF) + ε) + εi,ti,t,,

RRi,ti,t = (1-β = (1-βii)R)RZ,tZ,t + β + βiiRRM,tM,t + ε + εi,ti,t,,– where Ewhere Et-1t-1(ε(εi,ti,t)=0, E)=0, Et-1t-1(R(RM,tM,tεεi,ti,t)=0, E)=0, Et-1t-1(R(RZ,tZ,tεεi,ti,t)=0, )=0,

EEt-1t-1(ε(εi,ti,t, ε, εi,t+ji,t+j)=0 (j≠0))=0 (j≠0)

EFM 2006/7EFM 2006/7 55

NES

Time-series testsTime-series tests

Sharpe-Lintner CAPM:Sharpe-Lintner CAPM:RRi,ti,t-R-RFF = α = αii + β + βii(R(RM,tM,t-R-RFF) + ε) + εi,ti,t (+ δ (+ δiiXXi,t-1i,t-1))– HH00: α: αii=0 for any i=1,…,N (δ=0 for any i=1,…,N (δii=0)=0)

Strong assumptions: RStrong assumptions: Ri,ti,t ~ IID Normal ~ IID Normal– Estimate by ML, same as OLSEstimate by ML, same as OLS

Finite-sample F-test, which can be rewritten in terms Finite-sample F-test, which can be rewritten in terms of Sharpe ratiosof Sharpe ratios

– Alternatively: Wald test or LR testAlternatively: Wald test or LR test Weaker assumptions: allow non-normality, Weaker assumptions: allow non-normality,

heteroscedasticity, auto-correlation of heteroscedasticity, auto-correlation of returnsreturns– Test by GMMTest by GMM

EFM 2006/7EFM 2006/7 66

NES

Time-series testsTime-series tests (cont.)(cont.) Black (zero-beta) CAPM:Black (zero-beta) CAPM:

RRi,ti,t = α = αii + β + βiiRRM,tM,t + ε + εi,ti,t,,– HH00: there exists γ s.t. α: there exists γ s.t. αii=(1-β=(1-βii)γ for any )γ for any

i=1,…,Ni=1,…,N Strong assumptions: RStrong assumptions: Ri,ti,t ~ IID Normal ~ IID Normal

– LR test with finite-sample adjustmentLR test with finite-sample adjustment Performance of tests:Performance of tests:

– The size is correct after the finite-sample The size is correct after the finite-sample adjustmentadjustment

– The power is fine for small N relative to TThe power is fine for small N relative to T

EFM 2006/7EFM 2006/7 77

NES

ResultsResults

Early tests: did not reject CAPMEarly tests: did not reject CAPM Gibbons, Ross, and Shanken (1989)Gibbons, Ross, and Shanken (1989)

– Data: US, 1926-1982, monthly returns of 11 Data: US, 1926-1982, monthly returns of 11 industry portfolios, VW-CRSP market indexindustry portfolios, VW-CRSP market index

– For each individual portfolio, standard For each individual portfolio, standard CAPM is not rejectedCAPM is not rejected

– Joint test rejects CAPMJoint test rejects CAPM CLM, Table 5.3CLM, Table 5.3

– Data: US, 1965-1994, monthly returns of 10 Data: US, 1965-1994, monthly returns of 10 size portfolios, VW-CRSP market indexsize portfolios, VW-CRSP market index

– Joint test rejects CAPM, esp. in the earlier Joint test rejects CAPM, esp. in the earlier part of the sample periodpart of the sample period

EFM 2006/7EFM 2006/7 88

NES

Cross-sectional testsCross-sectional tests

Main idea: Main idea: RRi,ti,t = γ = γ00 + γ + γ11ββii + ε + εi,ti,t (+γ (+γ22XXi,ti,t))

HH00: asset returns lie on the security : asset returns lie on the security market linemarket line– γγ00 = R = RFF, , – γγ11 = mean(R = mean(RMM-R-RFF) > 0, ) > 0, – γγ22 = 0 = 0

Two-stage procedure (Fama-MacBeth, Two-stage procedure (Fama-MacBeth, 1973):1973):– Time-series Time-series regressionsregressions to estimate betato estimate beta– Cross-sectional Cross-sectional regressions period-by-periodregressions period-by-period

EFM 2006/7EFM 2006/7 99

NES

Time-series Time-series regressionsregressions

RRi,ti,t = α = αii + β + βiiRRM,tM,t + ε + εi,ti,t First 5y period: First 5y period:

– Estimate betas for individual stocks, form Estimate betas for individual stocks, form 20 beta-sorted portfolios with equal number 20 beta-sorted portfolios with equal number of stocksof stocks

Second 5y period: Second 5y period: – Recalculate betas of the stocks, assign Recalculate betas of the stocks, assign

average stock betas to the portfoliosaverage stock betas to the portfolios Third 5y period: Third 5y period:

– Each month, run cross-sectional regressionsEach month, run cross-sectional regressions

EFM 2006/7EFM 2006/7 1010

NES

Cross-sectional Cross-sectional regressionsregressions

RRi,ti,t-R-RFF = γ = γ00 + γ + γ11ββii + γ + γ22ββ22ii + γ + γ33σσii + ε + εi,ti,t

Running this regression for each month Running this regression for each month tt, , one gets the time series of coefficients one gets the time series of coefficients γγ0,t0,t, γ, γ1,t1,t, …, …

Compute mean and std of γ’s from these Compute mean and std of γ’s from these time series:time series:– No need for s.e. of coefficients in the cross-No need for s.e. of coefficients in the cross-

sectional regressions!sectional regressions!– Shanken’s correction for the ‘Shanken’s correction for the ‘error-in-error-in-

variablesvariables’ problem’ problem

Assuming normal IID returns, t-testAssuming normal IID returns, t-test

EFM 2006/7EFM 2006/7 1111

NES

Why is Fama-MacBeth Why is Fama-MacBeth approach popular in approach popular in finance?finance? Period-by-period cross-sectional regressions Period-by-period cross-sectional regressions

instead of one panel regressioninstead of one panel regression– The time series of coefficients => can estimate the The time series of coefficients => can estimate the

mean value of the coefficient and its s.e. over the mean value of the coefficient and its s.e. over the full period or subperiodsfull period or subperiods

– If coefficients are constant over time, this is If coefficients are constant over time, this is equivalent to FE panel regressionequivalent to FE panel regression

Simple: Simple: – Avoids estimation of s.e. in the cross-sectional Avoids estimation of s.e. in the cross-sectional

regressionsregressions– Esp. valuable in presence of cross-correlationEsp. valuable in presence of cross-correlation

Flexible:Flexible:– Easy to accommodate additional regressorsEasy to accommodate additional regressors– Easy to generalize to Black CAPMEasy to generalize to Black CAPM

EFM 2006/7EFM 2006/7 1212

NES

ResultsResults

Until late 1970s: CAPM is not rejectedUntil late 1970s: CAPM is not rejected– But: betas are unstable over timeBut: betas are unstable over time

Since late 70s: multiple anomalies, Since late 70s: multiple anomalies, ““fishing licensefishing license” on CAPM” on CAPM– Standard Fama-MacBeth procedure for a Standard Fama-MacBeth procedure for a

given stock characteristic X:given stock characteristic X: Estimate betas of portfolios of stocks sorted by XEstimate betas of portfolios of stocks sorted by X Cross-sectional regressions of the ptf excess Cross-sectional regressions of the ptf excess

returns on estimated betas and Xreturns on estimated betas and X Reinganum (1981): Reinganum (1981):

– No relation between betas and average No relation between betas and average returns for beta-sorted portfolios in 1964-returns for beta-sorted portfolios in 1964-1979 in the US1979 in the US

EFM 2006/7EFM 2006/7 1313

NES

Asset pricing Asset pricing anomaliesanomalies

Variable Premium's sign

Reinganum (1983) January dummy +

French (1980) Monday dummy -

Basu (1977, 1983) E/P +

Stattman (1980) Book-to-market: BE/ME +

Banz (1981) Size: ME -

Bhandari (1988) Leverage: D/E +

Jegadeesh & Titman (1993) Momentum: 6m-1y return +

De Bondt & Thaler (1985) Contrarian: 3y-5y return -

Brennan et al. (1996) Liquidity: trading volume -

EFM 2006/7EFM 2006/7 1414

NES

Interpretation of Interpretation of anomaliesanomalies Technical explanationsTechnical explanations

– There are no real anomaliesThere are no real anomalies Multiple risk factorsMultiple risk factors

– Anomalous variables proxy Anomalous variables proxy additional risk factorsadditional risk factors

Irrational investor behaviorIrrational investor behavior

EFM 2006/7EFM 2006/7 1515

NES

Technical Technical explanations: Roll’s explanations: Roll’s critique critique For any ex post MVE portfolio, pricing equations For any ex post MVE portfolio, pricing equations

suffice automaticallysuffice automatically It is impossible to test CAPM, since any market It is impossible to test CAPM, since any market

index index is not completeis not complete Response to Roll’s critiqueResponse to Roll’s critique

– Stambaugh (1982): similar results if add to stock index Stambaugh (1982): similar results if add to stock index bonds and real estate: unable to reject zero-beta CAPMbonds and real estate: unable to reject zero-beta CAPM

– Shanken (1987): if correlation between stock index and Shanken (1987): if correlation between stock index and true global index exceeds 0.7-0.8, CAPM is rejectedtrue global index exceeds 0.7-0.8, CAPM is rejected

Counter-argument:Counter-argument:– Roll and Ross (1994): even when stock market index is Roll and Ross (1994): even when stock market index is

not far from the frontier, CAPM can be rejectednot far from the frontier, CAPM can be rejected

EFM 2006/7EFM 2006/7 1616

NES

Technical Technical explanations: Data explanations: Data snooping bias snooping bias Only the successful results (out of many Only the successful results (out of many

investigated variables) are publishedinvestigated variables) are published– Subsequent studies using variables correlated with Subsequent studies using variables correlated with

those that were found significant before are also those that were found significant before are also likely to reject CAPMlikely to reject CAPM

Out-of-sample evidence:Out-of-sample evidence:– Post-publication performance in US: premiums get Post-publication performance in US: premiums get

smaller (size, turn of the year effects) or disappear smaller (size, turn of the year effects) or disappear (the week-end, dividend yield effects)(the week-end, dividend yield effects)

– Pre-1963 performance in US (Davis, Fama, and Pre-1963 performance in US (Davis, Fama, and French, 2001): similar value premium, which French, 2001): similar value premium, which subsumes the size effectsubsumes the size effect

– Other countries (Fama&French, 1998): value Other countries (Fama&French, 1998): value premium in 13 developed countriespremium in 13 developed countries

EFM 2006/7EFM 2006/7 1717

NES

Technical explanations Technical explanations (cont.)(cont.) Error-in-variables problem: Error-in-variables problem:

– Betas are measured impreciselyBetas are measured imprecisely– Anomalous variables are correlated with true betasAnomalous variables are correlated with true betas

Sample selection problemSample selection problem– Survivor bias: the smallest stocks with low returns Survivor bias: the smallest stocks with low returns

are excludedare excluded Sensitivity to the data frequency: Sensitivity to the data frequency:

– CAPM not rejected with annual dataCAPM not rejected with annual data Mechanical relation between prices and Mechanical relation between prices and

returns (Berk, 1995)returns (Berk, 1995)– Purely random cross-variation in the current prices Purely random cross-variation in the current prices

(P(Ptt) automatically implies higher returns ) automatically implies higher returns (R(Rtt=P=Pt+1t+1/P/Ptt) for low-price stocks and vice versa) for low-price stocks and vice versa

EFM 2006/7EFM 2006/7 1818

NES

Multiple risk factorsMultiple risk factors

Some anomalies are correlated with Some anomalies are correlated with each other: each other: – E.g., size and January effectsE.g., size and January effects

Ball (1978): Ball (1978): – The value effect indicates a fault in The value effect indicates a fault in

CAPM rather than market inefficiency, CAPM rather than market inefficiency, since the value characteristics are since the value characteristics are stable and easy to observe => low info stable and easy to observe => low info costs and turnovercosts and turnover

EFM 2006/7EFM 2006/7 1919

NES

Multiple risk factors Multiple risk factors (cont.)(cont.) Chan and Chen (1991): Chan and Chen (1991):

– Small firms bear a higher risk of Small firms bear a higher risk of distressdistress, , since they are more sensitive to since they are more sensitive to macroeconomic changes and are less likely macroeconomic changes and are less likely to survive adverse economic conditionsto survive adverse economic conditions

Lewellen (2002): Lewellen (2002): – The momentum effect exists for large The momentum effect exists for large

diversified portfolios of stocks sorted by diversified portfolios of stocks sorted by size and BE/ME => can’t be explained by size and BE/ME => can’t be explained by behavioral biases in info processingbehavioral biases in info processing

EFM 2006/7EFM 2006/7 2020

NES

Irrational investor Irrational investor behaviorbehavior Investors overreact to bad Investors overreact to bad

earnings => temporary earnings => temporary undervaluation of undervaluation of value value firmsfirms

La Porta et al. (1987): La Porta et al. (1987): – The size premium is the highest The size premium is the highest

after bad earnings announcementsafter bad earnings announcements

Testing CAPM:Testing CAPM:is beta dead ?is beta dead ?

EFM 2006/7EFM 2006/7 2222

NES

Fama and FrenchFama and French (1992)(1992)

""The cross-section of expected The cross-section of expected stock returnsstock returns", ", a.k.a. a.k.a. "Beta is "Beta is dead“ articledead“ article

Evaluate joint roles of market Evaluate joint roles of market beta, size, E/P, leverage, and beta, size, E/P, leverage, and BE/ME in explaining cross-BE/ME in explaining cross-sectional variation in US stock sectional variation in US stock returnsreturns

EFM 2006/7EFM 2006/7 2323

NES

DataData

All non-financial firms in NYSE, AMEX, All non-financial firms in NYSE, AMEX, and (after 1972) NASDAQ in 1963-1990and (after 1972) NASDAQ in 1963-1990

Monthly return data (CRSP)Monthly return data (CRSP) Annual financial statement data Annual financial statement data

(COMPUSTAT)(COMPUSTAT)– Used with a 6m gapUsed with a 6m gap

Market index: the CRSP value-wtd Market index: the CRSP value-wtd portfolio of stocks in the three exchangesportfolio of stocks in the three exchanges– Alternatively: EW and VW portfolio of NYSE Alternatively: EW and VW portfolio of NYSE

stocks, similar results (unreported)stocks, similar results (unreported)

EFM 2006/7EFM 2006/7 2424

NES

Data (cont.)Data (cont.)

‘‘Anomaly’ variables:Anomaly’ variables:– Size: ln(ME)Size: ln(ME)– Book-to-market: ln(BE/ME)Book-to-market: ln(BE/ME)– Leverage: ln(A/ME) or ln(A/BE)Leverage: ln(A/ME) or ln(A/BE)– Earnings-to-price: E/P dummy (1 if Earnings-to-price: E/P dummy (1 if

E<0) or E(+)/PE<0) or E(+)/P E/P is a proxy for future earnings only E/P is a proxy for future earnings only

when E>0when E>0

EFM 2006/7EFM 2006/7 2525

NES

MethodologyMethodology

Each year Each year tt, in June:, in June:– Determine the NYSE decile breakpoints for size (ME), Determine the NYSE decile breakpoints for size (ME),

divide all stocks to 10 size portfoliosdivide all stocks to 10 size portfolios– Divide each size portfolio into 10 portfolios based on Divide each size portfolio into 10 portfolios based on

pre-ranking pre-ranking betas estimated over 60 past monthsbetas estimated over 60 past months– Measure Measure post-ranking post-ranking monthly returns of 100 size-beta monthly returns of 100 size-beta

EW portfolios for the next 12 monthsEW portfolios for the next 12 months Measure full-period betas of 100 size-beta Measure full-period betas of 100 size-beta

portfoliosportfolios Run Fama-MacBeth (month-by-month) CS Run Fama-MacBeth (month-by-month) CS

regressions of the regressions of the individual stock individual stock excess excess returns on betas, size, etc.returns on betas, size, etc.– Assign to each stock a post-ranking beta of its portfolioAssign to each stock a post-ranking beta of its portfolio

EFM 2006/7EFM 2006/7 2626

NES

ResultsResults

Table 1: characteristics of 100 size-beta Table 1: characteristics of 100 size-beta portfoliosportfolios– Panel A: enough variation in returns, small Panel A: enough variation in returns, small

(but not high-beta) stocks earn higher (but not high-beta) stocks earn higher returnsreturns

– Panel B: enough variation in post-ranking Panel B: enough variation in post-ranking betas, strong negative correlation (on betas, strong negative correlation (on average, -0.988) between size and beta; in average, -0.988) between size and beta; in each size decile, post-ranking betas capture each size decile, post-ranking betas capture the ordering of pre-ranking betasthe ordering of pre-ranking betas

– Panel C: in any size decile, the average size Panel C: in any size decile, the average size is similar across beta-sorted portfoliosis similar across beta-sorted portfolios

EFM 2006/7EFM 2006/7 2727

NES

Results (cont.)Results (cont.)

Table 2: characteristics of Table 2: characteristics of portfolios sorted by size or by pre-portfolios sorted by size or by pre-ranking betaranking beta– When sorted by size alone: strong When sorted by size alone: strong

negative relation between size and negative relation between size and returns, strong positive relation returns, strong positive relation between betas and returnsbetween betas and returns

– When sorted by betas alone: no When sorted by betas alone: no clear relation between betas and clear relation between betas and returns!returns!

EFM 2006/7EFM 2006/7 2828

NES

Results (cont.)Results (cont.)

Table 3: Fama-MacBeth regressions Table 3: Fama-MacBeth regressions – Even when alone, beta fails to explain returns!Even when alone, beta fails to explain returns!– Size has reliable negative relation with returnsSize has reliable negative relation with returns– Book-to-market has even stronger (positive) Book-to-market has even stronger (positive)

relationrelation– Market and book leverage have significant, Market and book leverage have significant,

but opposite effect on returns (+/-)but opposite effect on returns (+/-) Since coefficients are close in absolute value, this is Since coefficients are close in absolute value, this is

just another manifestation of book-to-market effect!just another manifestation of book-to-market effect!

– Earnings-to-price: U-shape, but the Earnings-to-price: U-shape, but the significance is killed by size and BE/MEsignificance is killed by size and BE/ME

EFM 2006/7EFM 2006/7 2929

NES

Authors’ conclusionsAuthors’ conclusions

““Beta is dead”: no relation between beta Beta is dead”: no relation between beta and average returns in 1963-1990and average returns in 1963-1990– Other variables correlated with true betas?Other variables correlated with true betas?

But: beta fails even when aloneBut: beta fails even when alone Though: shouldn’t beta be significant because of high Though: shouldn’t beta be significant because of high

negative correlation with size?negative correlation with size?

– Noisy beta estimates?Noisy beta estimates? But: post-ranking betas have low s.e. (most below But: post-ranking betas have low s.e. (most below

0.05)0.05) But: close correspondence between pre- and post-But: close correspondence between pre- and post-

ranking betas for the beta-sorted portfoliosranking betas for the beta-sorted portfolios But: same results if use 5y pre-ranking or 5y post-But: same results if use 5y pre-ranking or 5y post-

ranking betasranking betas

EFM 2006/7EFM 2006/7 3030

NES

Authors’ conclusionsAuthors’ conclusions

Robustness:Robustness:– Similar results in subsamplesSimilar results in subsamples– Similar results for NYSE stocks in 1941-Similar results for NYSE stocks in 1941-

19901990 Suggest a new model for average Suggest a new model for average

returns, with size and book-to-market returns, with size and book-to-market equityequity– This combination explains well CS variation This combination explains well CS variation

in returns and absorbs other anomaliesin returns and absorbs other anomalies

EFM 2006/7EFM 2006/7 3131

NES

DiscussionDiscussion

Hard to separate size effects from CAPMHard to separate size effects from CAPM– Size and beta are highly correlatedSize and beta are highly correlated– Since size is measured precisely, and beta is Since size is measured precisely, and beta is

estimated with large measurement error, size estimated with large measurement error, size may well subsume the role of beta!may well subsume the role of beta!

Once more, Roll and Ross (1994): Once more, Roll and Ross (1994): – Even portfolios deviating only slightly (within Even portfolios deviating only slightly (within

the sampling error) from mean-variance the sampling error) from mean-variance efficiency may produce a flat relation between efficiency may produce a flat relation between expected returns and betaexpected returns and beta

EFM 2006/7EFM 2006/7 3232

NES

Further researchFurther research

Conditional CAPMConditional CAPM– The ‘anomaly’ variables may proxy for time-The ‘anomaly’ variables may proxy for time-

varying market risk exposuresvarying market risk exposures Consumption-based CAPMConsumption-based CAPM

– The ‘anomaly’ variables may proxy for The ‘anomaly’ variables may proxy for consumption betasconsumption betas

Multifactor modelsMultifactor models– The ‘anomaly’ variables may proxy for time-The ‘anomaly’ variables may proxy for time-

varying risk exposures to multiple factorsvarying risk exposures to multiple factors

EFM 2006/7EFM 2006/7 3333

NES

Ferson and HarveyFerson and Harvey (1998)(1998)

"Fundamental determinants of "Fundamental determinants of national equity market returns: national equity market returns: A perspective on conditional A perspective on conditional asset pricingasset pricing""

Conditional tests of CAPM on the Conditional tests of CAPM on the country levelcountry level– Monthly returns on MSCI stock Monthly returns on MSCI stock

indices of 21 developed countries, indices of 21 developed countries, 1970-19931970-1993

EFM 2006/7EFM 2006/7 3434

NES

Time series approachTime series approach

rri,t+1i,t+1=(α=(α0i0i+α’+α’1i1iZZtt+α’+α’2i2iAAi,ti,t) + (β) + (β0i0i+β’+β’1i1iZZtt+β’+β’2i2iAAi,ti,t) ) rrM,t+1M,t+1++εεi,t+1i,t+1

ZZtt are global instruments are global instruments– World market return, dividend yield, FX, interest World market return, dividend yield, FX, interest

ratesrates

AAi,ti,t are local (country-specific) instruments are local (country-specific) instruments– E/P, D/P, 60m volatility, 6m momentum, GDP per E/P, D/P, 60m volatility, 6m momentum, GDP per

capita, inflation, interest ratescapita, inflation, interest rates

HH00: α: αii = 0 = 0

EFM 2006/7EFM 2006/7 3535

NES

Results: for mostResults: for most countriescountries

Betas are time-varying, mostly due Betas are time-varying, mostly due to local variablesto local variables– E/P, inflation, long-term interest rateE/P, inflation, long-term interest rate

Alphas are time-varying, due toAlphas are time-varying, due to– E/P, P/CF, P/BV, volatility, inflation, E/P, P/CF, P/BV, volatility, inflation,

long-term interest rate, and term long-term interest rate, and term spreadspread

– Economic significance: typical Economic significance: typical abnormal return (in response to 1σ abnormal return (in response to 1σ change in X) around 1-2% per monthchange in X) around 1-2% per month

EFM 2006/7EFM 2006/7 3636

NES

Fama-MacBeth Fama-MacBeth approachapproach Each month:Each month: Estimate time-series regression with 60 prior Estimate time-series regression with 60 prior

months using one local instrumentmonths using one local instrument

rri,t+1i,t+1 = ( = (αα0i0i + + αα1i1iAAi,ti,t) + () + (ββ0i0i + + ββ1i1iAAi,ti,t) r) rM,t+1M,t+1 + + εεi,t+1i,t+1

Estimate WLS cross-sectional regression using Estimate WLS cross-sectional regression using the fitted values of alpha and beta and the the fitted values of alpha and beta and the attribute:attribute:

rri,t+1i,t+1 = = γγ0,t+10,t+1++γγ1,t+11,t+1aai,t+1i,t+1++γγ’’2,t+12,t+1bbi,t+1i,t+1++γγ3,t+13,t+1AAi,ti,t+e+ei,t+1i,t+1

EFM 2006/7EFM 2006/7 3737

NES

ResultsResults

The explanatory power of The explanatory power of attributes as instruments for risk attributes as instruments for risk is much greater than for is much greater than for mispricingmispricing

Some attributes enter mainly as Some attributes enter mainly as instruments for beta (e.g., E/P) or instruments for beta (e.g., E/P) or alpha (e.g., momentum)alpha (e.g., momentum)

EFM 2006/7EFM 2006/7 3838

NES

ConclusionsConclusions

Strong support for the conditional asset Strong support for the conditional asset pricing modelpricing model

Local attributes drive out global Local attributes drive out global information variables in models of information variables in models of conditional betasconditional betas

The explanatory power of attributes as The explanatory power of attributes as instruments for risk is much greater than instruments for risk is much greater than for mispricingfor mispricing

The relation of the attributes to expected The relation of the attributes to expected returns and risks is different across returns and risks is different across countriescountries