Is stock price momentum an imperfect proxy for sensitivity of individual stocks to past dispersion of returns across stocks (zeta risk, or return dispersion)? In their November 2018 paper entitled “Market Risk and the Momentum Mystery”, James Kolari and Wei Liu investigate relationships between momentum and return dispersion as predictors of individual U.S. stock returns. They employ both portfolio comparisons and regression tests. For the former, their momentum portfolio is long (short) the equally weighted top (bottom) tenth, or decile, of stocks ranked on past 12-month minus one skip-week returns, reformed monthly. Their main return dispersion portfolio is long (short) the equally weighted decile of stocks with the most positive (negative) sensitivities to the dispersion of all individual daily stock returns over the past 12 months minus one skip-week, reformed monthly. Using daily and monthly returns for a broad sample of U.S. stocks priced over $5 since January 1964, and contemporaneous 1-month U.S. Treasury bill yields and monthly returns of selected stock return model factors since January 1965, all through December 2017, they find that:
- Regression tests for the full sample over the full period indicate stock returns exhibit similar sensitivities to past momentum and past return dispersion.
- For the full sample over the full period:
- The momentum (return dispersion) portfolio generates average monthly gross return 0.94% (1.50%), much higher than those generated by size, book-to-market, profitability and investment factors.
- Volatility of monthly returns for the momentum (return dispersion) portfolio is 6.24% (6.08%), also much higher than those for other factors.
- Lowest monthly returns are similar for momentum and return dispersion portfolios, but highest monthly returns are higher for the latter (gains are more a driver of volatility for return dispersion).
- Maximum drawdown for the momentum (return dispersion) portfolio is -82% (-61%), deeper than those for other factors.
- For a subsample excluding the 20% of stocks with the smallest market capitalizations (to avoid the most severe short-term reversals) over the full period:
- Average monthly gross excess (relative to Treasury bills) return of the market is 0.52%, with monthly volatility 4.44% and maximum drawdown -55%.
- Average monthly gross return of the momentum portfolio is 1.74%, with monthly volatility 7.18% and maximum drawdown -76%.
- The adjusted R-squared statistic for regression of monthly return dispersion portfolio returns versus momentum portfolio monthly returns is 0.61, indicating a close relationship.
- A combined portfolio that is long (short) the equally weighted intersection of stocks in the highest (lowest) momentum and return dispersion deciles generates average monthly gross return 1.81%, with monthly volatility 7.35% and maximum drawdown -78%.
- A combined portfolio that weights selected stocks by sensitivity to return dispersion rather than equally generates average monthly gross return 1.91%, with monthly volatility 7.82% and maximum drawdown -81%.
- A combined sensitivity-weighted portfolio that further switches to the market portfolio whenever the difference in returns between the top and bottom return dispersion deciles is in the lowest fifth of past values generates average monthly gross return 2.03%, with monthly volatility 7.22% and maximum drawdown -71%.
In summary, evidence indicates that stock price momentum is an inferior proxy for stock sensitivity to overall return dispersion across stocks.
Cautions regarding findings include:
- Reported returns are gross, not net. Including reasonable trading frictions and shorting costs would reduce reported returns. Moreover:
- Momentum portfolios, and likely zeta risk portfolios likely have high turnovers (not addressed in the paper).
- Stocks with the highest momentum and zeta risk may be the least liquid. Equal weighting of portfolios exacerbates this concern.
- Shorting of all stocks as specified may not be feasible due to lack of shares to borrow, with this concern also exacerbated by equal weighting.
- Cumulative returns or Sharpe ratios of portfolios, not reported in the paper, would be useful to expose the joint effects of high average monthly returns and high monthly volatilities of momentum and return dispersion portfolios.
- Maximum drawdowns of momentum, return dispersion and combination portfolios are very deep and perhaps disqualifying for many investors.
- Return dispersion measurement (based on daily data) is computationally intense and beyond the reach of most investors, who would bear fees for delegating to a fund manager).
- Testing multiple portfolios on the same data introduces snooping bias, such that the best combination likely overstates reasonable out-of-sample expectations. There may be further bias in selection of stock sorting parameters.
- The paper includes no subperiod tests to examine consistencies of/trends in momentum and return dispersion portfolio performances over time. Nor does it include tests on other asset classes.
For additional background on zeta risk, see “Zeta Risk and Future Stock Returns”.
