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
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
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.
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.