Style investing is an investment approach in which rotation among different "styles" is supposed to be important for successful investing. As opposed to investing in individual securities, style investors can decide to make portfolio allocation decisions by placing their money in broad categories of assets, such as "large-cap", "growth", "international", or "emerging markets".
Style investing is of interest to economists because it serves as a useful framework for identifying anomalous price movements in stocks, such as those observed when a stock is added or removed from the S&P 500 index.
Style investing is the study of asset prices in an economy where some investors classify risky assets into different styles and move funds back and forth between these styles depending on their relative performance.
The fundamental basis for this trading method comes from classification: the grouping of objects into categories. “Categorization simplifies our thinking, and enables us to process vast amounts of information reasonably efficiently. Mullainathan (2000) provides an innovative analysis of the implications of categorization for decision making.”
Classification of large numbers of stocks into categories is widespread in financial markets. Traders classify assets as liquid securities such as stocks and bonds. They may also do the same with illiquid securities, such as real estate and venture capital. Stocks may be classified as domestic or international, small or large, growth or value, “old economy" or “new economy", cyclical or non-cyclical. Such groups of securities are often called “asset classes" or “styles”. Portfolio allocation based on selection among styles rather than among individual securities is known as “style investing."
The focus on styles enables institutional investors to organize and simplify their portfolio allocation decisions, as well as to measure and evaluate the performance of professional managers relative to standardized style benchmarks.
The investment problem faced by traders when they allocate our money across individual stocks is complex. They need a method to split their wealth across the thousands of different stocks out there. Investors often make decisions at the level of asset categories. They can split stocks into categories of small-cap, mid-cap, large-cap, value, growth, technology stocks, utility stocks, and so on, and then allocate their money across these different categories. Investment categories are sometimes called “styles”.
“When classifying securities into styles, investors group together assets that appear to be similar, in the sense that they are perceived to have a common characteristic.” A characteristic can be an obvious one such as “the country in which the security is traded, the industry in which the firm operates, or a permanent legal characteristic.” Other times, a less obvious characteristic is used as the basis for a style, such as securities with that characteristic are found to have performed well historically. “Value investing" in equities emerged as a distinctive style over the last century following the work of Graham and Dodd (1934) on high dividend yield stocks, and the spectacular performance of some of the investors who followed their advice.”
Other characteristics used to define styles are based on fundamental values. For example, “U.S. government bonds are backed by the full faith and credit of the U.S. government, and hence as an asset class provide a good guarantee against financial trauma.” 
Comovement and Returns
Style investing generates co-movement between individual assets and their styles. The momentum and reversals in both style and asset returns. “High co-movement winner (loser) portfolios have significantly higher (lower) future returns than low co-movement winner (loser) portfolios. Long-horizon reversals are also larger for high co-movement portfolios.”  “The magnitude of the improvement in three-factor alphas from traditional momentum strategies is large, almost 5 percent per year.” These results suggest that style investing plays an important role in the predictability of returns.
Barberis and Shleifer present a model where investors allocate funds based on the relative performance of investment styles. This model generates a rich set of predictions. “They show that style investing generates excess (too little) co-movement of assets within (across) styles than warranted by fundamentals, implying that reclassification of assets into a new style raises co-movement with respect to that style.” When a stock is added to the S&P 500 index, its co-movement with the index increases while its co-movement with stocks outside of the index declines.
Style-based investing can “generate momentum in individual asset returns at intermediate horizons and reversals at longer horizons.” In their words, “If an asset performed well last period, there is a good chance that the outperformance was due to the asset’s being a member of a “hot” style…If so, the style is likely to keep attracting inflows from switchers next period, making it likely that the asset itself also does well next period” 
- "Style Investing" (PDF). Harvard Institute of Economic Research.
- Barberis; Shleifer. "Style Investing" (PDF).
- Wahal, Sunil; M. Deniz Yavuz. "Style Investing, Comovement and Return Predictability" (PDF).
- Barberis, Nicholas and Shleifer, Andrei, Style Investing, 2003, J. Financial Econ., 68, 161-199.