Ebook Style Rotation, Momentum, and Multifactor Analysis
The notion of equity styles has been around for decades. An equity style is simply an equity class, a portfolio of stocks that share a common characteristic (e.g., small-cap stocks). A large body of both academic and industry research has been devoted to style investing. In recent years, average return differences between styles, such as the difference between growth and value stocks, have become the focus of many investigations. For example, Rosenberg, Reid, and Lanstein (1985), Fama and French (1992), Lakonishok, Shleifer, and Vishny (1994), and Roll (1997), among many others, have examined the long-term relative performances between growth, value, small-cap, and large-cap stocks. Meanwhile, the potential success of style rotation strategies has also attracted numerous studies (e.g., Beinstein (1995), Fan (1995), Sorensen and Lazzara (1995), Kao and Shumaker (1999), Levis and Liodakis (1999), and Asness et al. (2000)). These studies conclude that various dynamic style strategies are profitable and suggest that relative performances between equity styles are time-varying and predictable. In addition to the attempts to explore investment strategies, the concept of styles has also been utilized in the evaluation of managed portfolios. Most notably, Sharpe (1992) proposes an asset class factor model for performance attribution of mutual funds. Daniel et al. (1997), Fung and Hsieh (1997), and Ibbotson and Kaplan (2000) have extended Sharpe's style analysis in several ways.
In this article, we provide a multifactor analysis of style momentum. Style momentum is a combination of style rotation and momentum strategies. Specifically, we consider a set of size and book-to-market sorted portfolios that represent well-known investment styles, and rank the style portfolios in each month according to their returns over the previous month. A style momentum strategy buys the winner style and short-sells the loser style. This style strategy generates significant profits. Over the period from 1960 to 2001, the average return of the winner is, on an annualized basis, more than 16 percent higher than that of the loser. This return difference is significantly larger than the difference between the average returns of any two style portfolios. More surprisingly, conventional risk adjustment using the Fama and French (1993) three factor model appears to strengthen, rather than explain, the style momentum profits, although the model does capture much of the variation in the returns of the underlying style portfolios. The Fama-French three factor regressions do not provide any evidence that the strategy of buying the winner is any riskier than that of buying the loser. According to the regression intercepts, the risk-adjusted return difference between the winner and loser strategies is even larger than the raw return difference.
The puzzling performance of the style momentum strategy is consistent with several explanations. First, since the Fama-French three factor model is imperfect in pricing the style portfolios, the style momentum profits may arise from pricing errors of the model. On one hand, the pricing errors may result from investor irrationality. For example, Barberis, Shleifer, and Vishny (1998), Daniel, Hirshleifer, and Subrahmanyam (1998), and Hong and Stein (1999) propose theories based on investor cognitive biases that can generate momentum and other anomalies. On the other hand, a rational story can be built on Conrad and Kaul's (1998) argument that the cross-sectional dispersion in average returns may explain momentum. That is, the style momentum profits (raw returns) may be generated by the cross-style differences in average returns, but the Fama-French model fails to accurately capture the cross-section of the average returns. As a result of this mispricing, the three factor model does not explain the performance of style momentum.
Second, the style momentum profits may be due to cycles or non-stationarity in style returns. Barberis and Shleifer (2001) recently provided an interesting theory that irrational trend-chasing investors can generate cyclical investment styles. Their model can generate strong profits for style-level momentum. However, even to generate style non-stationarity, it is not necessary to assume investor irrationality. For example, it su±ces that style returns are generated by a risk-based model with non-stationary time-varying parameters. The pricing errors explanation and the non-stationarity explanation are obviously not mutually exclusive. Both are general enough to be consistent with either investor irrationality or market effciency. Finally, a closely-related alternative explanation is that the style momentum profits may be due to the time-varying risk of the style portfolios. In this story, the style betas with respect to the Fama-French three factors change significantly over time, although both the style betas and the style returns are strictly stationary. In other words, a time-varying beta version of the three factor model may explain the style momentum.
This article offers a different explanation. As the first step, three examples are provided to illustrate the effects of pricing errors. Three sets of excess returns are constructed from the standard Fama-French three factor regressions. The first set is obtained by removing the regression intercepts. These returns are perfectly correlated with the actual style returns, but the cross-section of the average returns is perfectly captured by the three factor model. The second set of excess returns is obtained by removing both the regression intercepts and the regression residuals. These returns are perfectly captured by the constant beta version of the Fama-French model, such that the time series regressions for these returns produce intercepts that are all equal to zero and R2's that are all equal to one. To generate the third set of returns, the sample means of the factors are first subtracted from the factors; then the construction is identical to that for the second set, so that there are no pricing errors with respect to the three factor model. In this case, there is no cross-style difference in average returns. Using each of these three sets of returns, we replicate the style momentum strategy to obtain the strategy's returns and run the conventional risk adjustment regressions.
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