Empirical
Finance: Testing equilibrium models of returns: CAPM and the 3
factor model.
Module Leader: Dr Stuart Fraser
stuart.fraser@wbs.ac.uk
Room D1.18 (
Social Studies)Warwick Business School 2
Introduction
Last time…
Looked at the Martingale Model and relationship with EMH.
留学生论文代写Found evidence for return predictability in FTSE250 indicating rejection of MM/EMH (compare evidence for SP500 –see seminars 1 and 2)
But this need not imply that the EMH doesn’t hold –could be that the MM is a poor model of equilibrium returns (Joint Hypo
thesis Problem).
Today…
Testing CAPM and multi-factor models.
Testing the assumptions of the Classical Linear Regression Model (OLS) –misspecification testing: are the observed data consistent with the statistical model?Warwick Business School 3
Capital Asset Pricing Model (CAPM)
So far we’ve been working with models of the formwith no structure given to equilibrium returns. Review of CAPM(see e.g., CuthbertsonChp5):1. All investors (regardless of preferences) hold the market portfolio (M) which is mean variance efficient. M lies at the point of tangency between the capital market line and the efficient frontier. 2. Investors hold portfolios of the risk free asset and the market portfolio which maximize their utility. The more (less) risk averse the investor the lower (higher) the proportion of wealth held in the market portfolio.3. The return on an individual asseti reflects its relative contribution to the risk of the market portfolio as measured by its beta()rprrEft+≡=μ()()()()()MtMtitiftMtiftitrrrrrErrEvar,cov=−+=ββWarwick Business School 4
Testing CAPM
If we assume that risk adjusted returns are fair games(EMH assumption) then the ex-post (observable) form of CAPM iswhere Stochastic processis a martingale difference ⇒error terms are linearly independent over time.⇒but error terms could be heteroscedasticover time and across stocks (⇒but OLS standard errors are incorrect) ⇒and errors could be non-normal (⇒but coefficients won’t follow t-distributions in small samples⇒invalidinferences in small samples)()itftMtiitftitrrrrεβα+−+=−()[]()MtMtiitititrErrEr−−−=βε{}itε()0=itEεWarwick Business School 5
Testable implications of CAPMThere are both time-series and cross-sectional components to the CAPM with testable implications.For a given stock and beta:The time-seriesvariation in the excess return on stock i depends solely on variation in the excess returns on the market portfolio.⇒Test intercept=0, no effect of variables other than excess return on the market portfolio, linear independence of error terms (EMH) and constancy/stability of OLS estimate of beta (see misspecification testing below).Across stocksfor a given risk-return trade-off:The cross sectionalvariation in excess stock returns depends solely on variations in betas.⇒Test intercept=0, no effect of variables other than betaand that the risk-return trade-off is positive.Should also test for heteroscedasticity(and non-normality) in both time-series and cross-section regressions if OLS inferences on coefficients are being made (see misspecification testing below). ()0>−fMrrEWarwick Business School 6
Basic procedure for testing CAPM
A simple way to test CAPM involves a two-stage procedure.STAGE 1: Estimate a first pass time seriesregression (for eachsecurity) on a sub-sample of the dataNeed a long enough sample to
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