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E¢ cient Semiparametric Estimation of the Fama-French Model and Extensions

Gregory Connor The London School of Economics Matthias Hagmann Concordia Advisors and Swiss Finance Institute Oliver Linton The London School of Economics May 16, 2007

Abstract This paper develops a new estimation procedure for characteristic-based factor models of stock returns. We treat the factor model as a weighted additive nonparametric regression model, with the factor returns serving as time-varying weights, and a set of univariate nonparametric functions relating security characteristic to the associated factor betas. We use a time-series and cross-sectional pooled weighted additive nonparametric regression methodology to simultaneously estimate the factor returns and characteristic-beta functions. By avoiding the curse of dimensionality our methodology allows for a larger number of factors than existing semiparametric methods. We apply the technique to the three-factor Fama-French model, Carhart’ four-factor extension of it adding a momentum factor, and a …ve-factor extension s adding an own-volatility factor. We …nd that momentum and own-volatility factors are at least as important if not more important than size and value in explaining equity return comovements. We test the multifactor beta pricing theory against the Capital Asset Pricing model using a standard test, and against a general alternative using a new nonparametric test.

Connor: Department of Finance, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom, E-mail g.connor@lse.ac.uk.; Hagmann: Concordia Advisors, Unit 112 Harbour Yard, Chelsea Harbour, London SW10 0XD, United Kingdom. E-mail: mhagmann@concordiafunds.com. Linton: Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom. E-mail: o.linton@lse.ac.uk.

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Keywords: Additive Models; Arbitrage pricing theory; Characteristic-based factor model; Kernel estimation; Nonparametric...