Applications of state space models in finance

124 7 A Kalman filter based conditional multifactor pricing model
switching framework. In this thesis, time-varying sensitivities will be modeled directly
as continuous stochastic random walk processes based on the state space framework
introduced in Chapter 3.
The research goal of this chapter is to study the practical relevance of time-varying
factor loadings in a multifactor pricing framework. Based on the conditional multiple
beta series to be estimated via the Kalman filter, it will be analyzed whether an explicit
consideration of the time-varying impact of macroeconomics and fundamentals on
European industry portfolios can be exploited in a profitable way, either from a risk
management or from a portfolio management perspective. The present chapter contributes
to the literature a synthesis of the classical cross-sectional regression approach
by Fama and MacBeth (1973) and conditional factor loadings.
The chapter is organized as follows. After briefly summarizing the concept of factor
modeling, Section 7.1 reviews the anomalies literature with a focus on macroeconomic
and fundamental factors. Section 7.2 outlines the conditional multifactor methodology.
It will be differentiated between time series and cross-sectional regressions. Section 7.3
introduces the set of common risk factors. Section 7.4 discusses the empirical results
and evaluates the relative out-of-sample forecasting ability of the proposed conditional
multifactor specification. It will be analyzed whether the statistical superiority of the
Kalman filter based model can be exploited in practice. Section 7.5 concludes.
7.1 Factor modeling
As outlined in ¢ 6.1 the most widely used factor model is the CAPM, in which the excess
return of the overall market is chosen as the single common factor. The measure of
systematic risk is referred to as market beta. Despite the CAPM’s popularity, various
studies over the last three decades have suggested that a single beta model, while describing
a large portion of the common variation in returns, may not be sufficient to explain
the cross-section of returns. The biggest challenge to the CAPM includes the empirical
evidence that macroeconomic sources of risk and company-specific characteristics are
priced beyond market risk. In accordance with these well-documented findings, the empirical
deficiencies of the CAPM are most commonly explained by missing risk factors or
by a misapproximation of the total wealth portfolio. 22 This leads to multifactor pricing
models as motivated by the Intertemporal Capital Asset Pricing Model (ICAPM), introduced
by Merton (1973), or the Arbitrage Pricing Theory (APT), developed by Ross
(1976). The basic idea of a multifactor pricing model is that the common variation in
asset returns can be accounted for by multiple common components, or risk factors. 23
Without explicitly differentiating between the ICAPM and the APT in the following,
22 Alternatively, instead of explaining the violations of the CAPM using risk-based arguments,
nonrisk-based explanations have been proposed. They include, among others, data-snooping
biases, the existence of market frictions, transaction costs and liquidity effects. As nonriskbased
explanations will not find any consideration in this chapter, the reader is referred to
MacKinlay (1995) for more details.
23 An introduction to the basic conception of asset pricing theory is provided in Appendix A.
As the theory on multifactor models is well-established, it is not intended to derive the underlying
assumptions of the various multifactor pricing models in this thesis; for any details and