Factor models are often used to explain the cross section of equity returns. Over time and through different stages of the business cycle, the factor loadings of stocks in the context of a four-factor equity model vary considerably. A modeling approach that incorporates investor learning can lead to a better understanding of these fluctuations.
The authors use an approach based on the time-varying Kalman filter (TVK) to illustrate the variation of factor loadings and abnormal returns that occurs in the US equity market over time. The factor loadings and abnormal returns are tested by using a simple, industry-based four-factor model. The authors find that the time-varying modeling approach produces more intuitive results than those based on other methods.
How Is This Research Useful to Practitioners?
The authors confirm that stocks’ risk loadings on common equity factors fluctuate over time and vary among different industry groups. They also find that risk loadings on factors do not necessarily mean revert; macroeconomic shocks can lead to long-term changes that do not quickly reverse. The TVK learning-based approach produces better results than earlier methods that required either stricter time/frequency assumptions or linear modeling of time-based parameters. The TVK approach also confirms the development and concentration of systematic risks leading up to the global financial crisis. Interestingly, the authors illustrate that the exposure of stocks to fundamental risk factors has significantly increased over the past two decades.
This research is particularly useful for portfolio managers and analysts running portfolios that are based on quantitative models because the techniques that are used may lead to further refinements of existing factor-timing models.
How Did the Authors Conduct This Research?
The authors base their research on a four-factor equity model that models excess stock returns (measured with reference to one-month Treasury bills) against such factors as excess market returns, size, value, and momentum. Stocks on the NYSE, Amex, and NASDAQ exchanges are used. Annual returns over the period from 1926 to 2012 are calculated. The authors use a TVK-based approach to incorporate investor learning as stock returns are observed. The TVK allows for a recursive modeling approach that produces a weighted average result based on observed results and future predictions. One output of a TVK-based approach is estimates of the conditional variance of forecast errors. The authors show that these estimates account for uncertainty arising from the time variation in the factor loadings and also from idiosyncratic risk.
They perform a regression for 10 high-level industry groupings with the resulting regression parameters representing factor loadings on the underlying factors. Variations of the model are used to test whether it produces a more consistent result under the assumption that factor loadings are stationary or that they follow a random walk. The results suggest that parameter volatility is reduced under the assumption of nonstationary coefficients.
Finally, the authors test the TVK approach to determine whether it improves the investment opportunity set for investors.
The use of time-varying parameters and a learning-based approach appears to provide useful insight into the evolution of factor loadings over the course of the business cycle. The approach aligns with how institutional investors seem to be constantly modifying their investment processes to account for changing investment conditions. Certainly, this research has received greater emphasis since the global financial crisis, when a number of quantitative investors were dismayed to find that their so-called diversified factor models did not deliver the diversification they were seeking.