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Investors who use prospect theory to evaluate stocks according to their historical return distributions may excessively bid up stocks with high historical mean returns, low volatilities, and positive skewness. The authors find a negative relationship between stocks’ prospect theory values and their future returns in the cross section.

How Is This Research Useful to Practitioners?

Practitioners involved in long–short equity strategies and statistical arbitrage will find a wealth of new potential alpha signals derived from the pioneering work of Kahneman and Tversky (Econometrica 1979) on prospect theory (PT).
PT differs from standard expected-utility analysis in that subjects think in terms of gains and losses around reference points and overweight the tails of probability distributions. This approach leads to PT values that are increasing in a stock’s historical mean, decreasing in its historical volatility, and increasing in its historical skewness. Historical skewness is often thought of as a preference for lottery-type outcomes.
The authors propose that if at least some proportion of market participants judge the value of a stock in PT terms using its historical return distribution, those participants will drive up the prices of stocks with high PT values and drive down the prices of stocks with low PT values—leading to a negative relationship between historical PT values and future returns. Investors might make the judgment by examining the five-year distribution of monthly returns—the kind of default visual representation provided by standard charting packages.
The authors provide a useful review of the main techniques used in cross-sectional returns analysis, including factor sorts, the two-step Fama–MacBeth procedure, and the use of international markets for out-of-sample testing.

How Did the Authors Conduct This Research?

The data on US equities from 1926 through 2010 are from CRSP and Compustat. The international market data are from Datastream. Coverage includes all stocks (in each month) that have the requisite five-year return history.
The authors use two methodologies to test their hypothesis: factor sorts and the Fama–MacBeth two-step procedure. A typical factor sort ranks the universe of stocks by the PT factor and divides the ranked universe into deciles. The (negative) return to the historical PT factor is then constructed as the difference between the returns to the top decile and the bottom decile, whereby decile returns are either equal-weighted or market-capitalization-weighted returns.
According to the authors, the initial PT factor sort is likely to include exposure to small-cap stocks in the top decile, because retail investors are more likely to exhibit the behavior prescribed by prospect theory and institutional investors are less focused on small-cap stocks. Thus, the authors use double-factor sorts to allow a more finely tuned analysis; the result is that the PT value retains its predictive ability.
The second methodology is the Fama–MacBeth two-step procedure, in which a cross-sectional regression is run on the PT value and various explanatory variables from common asset-pricing models, which include the book-to-market ratio, momentum, idiosyncratic volatility, and liquidity. Time-series averages of the coefficients of the PT variable and the various controls are computed. The advantage of this approach is that the independent contribution of the PT variable to expected returns can be calculated. The authors find that the well-known short-term reversion property of stock returns accounts for some proportion of the PT factor returns, but those returns are unaffected by the other controls.
Finally, the authors use data from 46 international equity markets for a substantive out-of-sample exercise. The international evidence is consistent with profitable returns to long–short portfolios formed on the basis of the PT variable.

Abstractor’s Viewpoint

In addition to testing their main hypothesis that a stock’s PT value from its historical return distribution is inversely related to its future returns, the authors provide an impressive guide to the vast factor-based equity literature.
This article can be used as a starting point for constructing new statistical arbitrage strategies based on the state of the art in decision science. For example, a fruitful area to investigate is the probability-weighting scheme that attaches more weight to the tails of the historical return distribution. Various trade-offs between the mean, standard deviation, and skewness of returns can be explored. Researchers are encouraged to use international markets as valuable data sources for out-of-sample tests.
The authors acknowledge that the areas most likely to spur future research are the ways in which investors “represent” historical returns and the ways in which they “evaluate” them. Do the results from the five-year distribution of monthly returns hold at higher frequencies or under alternative specifications? What are the implications for stock price predictability? It will be fascinating to see the answers to these questions unfold.

About the Author(s)

Antony Jackson CFA

Antony Jackson, CFA, is at the University of East Anglia.