Applications of state space models in finance

126 7 A Kalman filter based conditional multifactor pricing model
testing the validity of the CAPM. Various empirical findings have demonstrated the existence
of factors with explanatory power for the cross-section of returns beyond market
beta risk. This section provides a brief literature review on the different factor types
that can be categorized into macroeconomic, fundamental, momentum and statistical
factors.
7.1.1 Factor taxonomy
Macroeconomic variables constitute the first set of potential risk factors that can be
assumed to be rewarded by the market. They are intended to capture the state of the
economy or to forecast future economic conditions. Commonly employed macroeconomic
factors include interest rates, production growth, consumer confidence, credit spreads,
steepness of the yield curve and shifts in energy prices. Macroeconomic factor models
with multiple betas, where each beta relates an asset to a particular economic risk,
allow fund managers to gain top-down insights into how their portfolios are affected
by different economic scenarios. Alternatively, fundamental factor models assume that
sensitivities to firm characteristics such as the price-earnings ratio (PE), leverage or size
are capable of explaining the cross-section of returns. Although it is not yet clear which
systematic risks are approximated by fundamental factors, this second type of model has
been very successful empirically. Employing the third type of factors, momentum models
are based on the empirical finding that past return patterns may offer an indication of
future returns. In contrast to those factor categories, statistically derived factors are not
observable and have to be inferred from the return data using statistical factor selection
procedures.
7.1.1.1 Macroeconomic factors
The possibility that macroeconomic factors may successfully predict security returns has
spawned a remarkable bulk of literature that analyzes whether stock and bond returns
can be predicted using macroeconomic variables. One of the best known studies is that
of Chen et al. (1986). In an APT framework, the authors implement expected and
unexpected inflation, industrial production, the spread between short- and long-term
interest rates and the default premium, defined as the yield spread between high and
low rated bonds. The chosen risk factors are found to be significantly priced. The
predictive power of the default premium has been confirmed, among others, by Fama
and French (1989) and Keim and Stambaugh (1986). The results presented by Campbell
(1987) imply that excess stock returns are predicted by the state of the term structure
of interest rates. A further indication of the importance of interest rates as well as their
volatility is provided by Shanken (1990). In an analysis of the source of predictability
of monthly stock and bond returns, Ferson and Harvey (1991) look at a set of state
variable proxies: the value-weighted New York Stock Exchange index return less the
1-month Treasury-bill return, per capita growth of personal consumption expenditures,
unanticipated inflation, the yield spread between Baa-rated corporate bonds and a longterm
government bond, the change in the slope of the yield curve, the real 1-month
Treasury-bill return and the dividend yield on the S&P 500. In a later study on risk and