Cross-Sectional Dispersion in Economic Forecasts and Expected Stock Returns

Bali, Turin G., Stephen J. Brown, and Yi Tang, “Cross-Sectional Dispersion in Economic Forecasts and Expected Stock Returns,” The American Finance Association 75th Annual Meeting, Boston (2015).

Purpose:  To show that economic uncertainty is an economically and statistically significant driver of the cross-section of stock returns.

Motivation:  In the ICAPM world, investors care not only about the expected payoff of their investments, but also about their portfolios’ covariances with state variables affecting both future consumption and opportunities for investment.

Data/Methods:

  • Measure economic uncertainty using
    • the dispersion of forecasts from the Survey of Professional Forecasters
      • real GDP growth and real GDP level
      • log (75th pctl forecast / 25th pctl forecast) * 100
    • cross-sectional dispersion in forecasts for output, inflation, and unemployment
  • Fama-MacBeth regressions
    • Sort into deciles based on market beta.
    • Find time-varying “uncertainty betas” of stocks using rolling regressions of stock excess returns on the uncertainty measure, and sort into subdeciles.
  • Economic Uncertainty Index
    • Use Principal Component Analysis to find the common component among seven different proxies for economic uncertainty.

Results:

  • Covariance with economic uncertainty is significantly negatively correlated with higher returns, after controlling for market beta, size, book-to-market, momentum, short-term reversal, illiquidity, co-skewness, idiosyncratic volatility, and the dispersion of analyst forecasts.
  • The beta of the proposed “uncertainty index” appears able to significantly predict future stock returns.

The Cross-Section of Expected Stock Returns

Fama, Eugene F. and Kenneth R. French, 1992, “The Cross-Section of Expected Stock Returns,” The Journal of Finance 47 (2), 427-465.

Purpose:  This paper evaluates the joint effect of market beta, firm size, E/P ratio, leverage, and book-to-market equity in explaining the cross-section of average stock returns on NYSE, AMEX, and NASDAQ.

Findings:  Beta does not explain the cross-section of average returns.  Size and book-to-market equity each have explanative power both when used alone and in the presence of other variables.

Motivation:  The Sharpe, Lintner, and Black asset pricing model (beta) has been very influential, but there are notable exceptions to its premises.  Banz (1981) finds a significant size effect.  Bhandari (1988) finds a leverage effect.  Others have argued for effects of the book-to-market equity ratio and the earnings-to-price ratio.  Furthermore, Reinganum (1981) and Lakonishok and Shapiro (1986) find that the beta-return relationship disappears after 1963.

Data/Methods:

  • Data:  Nonfinancial NYSE, AMEX, and NASDAQ firms from 1962-1989
    • Monthly return data from CRSP
    • Annual accounting data from COMPUSTAT
  • Create portfolios based on size and pre-ranked beta (using trailing data)
  • Calculate the beta for each portfolio-year and assign it to each stock in that portfolio-year
  • Fama-MacBeth Regressions
    • Beta-size portfolios
      • For each month, for the entire cross-section, regress average return on beta, ln(ME), ln(BE/ME), ln(A/ME), ln(A/BE), and E/P
      • Sort stocks into 10 size deciles and then into 100 sub-deciles on “pre-ranking” beta
        • pre-ranking beta is each security’s beta for the 60 months prior to portfolio creation (requiring at least 24 months of data for inclusion in any portfolio)
        • Pre-ranking beta cutoffs are established using only NYSE stocks
    • Book-to-market portfolios and E/P portfolios
      • formed in a similar manner, with stocks sorted on either BE/ME or E/P
    • Size & book-to-market portfolios
      • Match accounting data for fiscal year-ends in calendar year t-1 to returns for the period starting in July of year t and ending in June of year t+1.
      • Use market equity in December of year t-1 to calculate leverage, book-to-market, and E/P ratios.
      • Use market equity in June of year t to measure size.
      • sort stocks into 10 market equity deciles, then into 100 book-to-market sub-deciles.

Conclusions:

  • Controlling for size, there is no relationship between beta and average return
  • Size is significant in predicting average returns
  • Book-to-market equity is also significant in predicting average returns, and has an even bigger effect than size
  • The effects of leverage and E/P are captured by size and book-to-market equity