Linear Factor Models in Finance
Combining actual quantitative finance experience with analytical research, this book covers the science of asset pricing by concentrating on the most widely used modelling technique called linear factor modelling.
TABLE OF CONTENTS Linear Factor Models in Finance
Chapter 3: Misspecification in the Linear Pricing Model
Ka-Man Lo [*]
Abstract
This chapter compares the performance of multivariate F test and average F test under misspecification. In particular, two misspecifications with autocorrelated factors and time-varying factor loadings are considered. The linear factor pricing literature uses a noncentral F distribution to evaluate the extent of misspecification. However, one central finding in this chapter that under the two forms of misspecification considered, the test statistic does not follow a noncentral F distribution. A simulation study is conducted to gauge the extent of the misspecification. Another finding is that the average F test is more sensitive to misspecification than the multivariate F test.
[*] I am indebted to my thesis advisors, John Knight and Stephen Sapp, for their help.
3.1 Introduction
Linear factor models are at the heart of asset management. Knowing the effect of misspecifying the linear factor pricing model is of paramount importance. Arbitrage pricing theory states that the expected return of an asset is a linear function of k factors. However, the theory itself, unlike the CAPM theory, does not state which k factors should be included. Thus empirical researchers have little theoretical guidance as to what factors to include in the linear factor model. In this context, it is important to ask the question What is the potential damage if the model is misspecified? The standard practice in the literature is to evaluate the distortion in the size and the power of the multivariate F under misspecification. The multivariate F test was proposed...
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