Review of Quantitative Finance and Accounting, 16, 117–130, 2001
2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
An Examination of Alternative Factor Models
in UK Stock Returns
Department of Accounting and Finance,UniversityofStrathclyde,CurranBuilding, 100 Cathedral Street, Glasgow
G4 0LN, United Kingdom
Abstract. This paper examines the mean-variance efﬁciency of a number of factor models in UK stock returns.
The paper also explores, using the approach of MacKinlay (1995), whether missing risk factors or nonrisk-based
explanations best explain the pricing errors of the different factor models. The evidence in the paper suggests that
the mean-variance efﬁciency of each factor model is rejected and missing risk factors are unable to explain the
pricing errors of any of the models. Some nonrisk-based explanations, which posit a wide spread in abnormal
returns, may be a more plausible source of explaining the pricing errors of the factor models.
Key words: multifactor models, CAPM
JEL Classiﬁcation: G12
The Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965) and Mossin
(1966) has been one of the central models in Finance over the past thirty ﬁve years. It has
wide practical applications in areas such as performance measurement (Jensen (1968)) and
cost of equity capital estimation.
However, the model has come under sustained attack with
a large body of evidence which rejects the predictions of the model whenever a stock market
index is used as a proxy for the market portfolio. A number of studies document that other
variables in addition to beta help explain cross-sectional returns. This includes size (Banz
(1981), book to market ratio (Fama and French (1992) and momentum (Jegadeesh and
Likewise the mean-variance efﬁciency of standard stock market indices
are frequently rejected.
This evidence has led to multifactor models being increasingly used in applications such
as performance evaluation and cost of capital estimation. This includes Fama and French
(1997), Pastor and Stambaugh (1999) and Davies, Draper, Paudyal and Unni (1999) in the
cost of equity capital estimation and Carhart (1997) and Pastor and Stambaugh (2000) in
performance evaluation. Much of the recent interest in multifactor models are the empirical
factor models such as Fama and French (1993) and Carhart (1997) which add additional
factors to the stock market index return on the basis of security characteristics that capture
the cross-sectional variation in stock returns.
The issue as to whether multifactor models should replace the single factor model in
practical uses depends on, as MacKinlay (1995) points out, why the single factor model