The body of U.S. stock market research offers hundreds of factors (the factor zoo) to explain and predict return differences across stocks. Is there a reduced set of factors that most accurately and consistently captures fundamental equity risks? In their March 2018 paper entitled “Searching the Factor Zoo”, Soosung Hwang and Alexandre Rubesam employ Bayesian inference to test all possible multi-factor linear models of stock returns and identify the best models. This approach enables testing of thousands of individual assets in combination with hundreds of candidate factors. They consider a universe of 83 candidate factors: the market return in excess of the risk-free rate, plus 82 factors measured as the difference in value-weighted average returns between extreme tenths (deciles) of stocks sorted on stock/firm characteristics. Their stock universe consists of all U.S. listed stocks excluding financial stocks, stocks with market capitalizations less than the NYSE 20th percentile (microcaps) and stocks priced less than $1. They test microcaps separately. They further test 20 sets of test portfolios (300 total portfolios). The overall sample period is January 1980 through December 2016. To assess factor model performance consistency, they break this sample period into three or five equal subperiods. Using the specified data as available over the 36-year sample period, they find that:
- Across three subperiods:
- The best models of stock returns mostly have fewer than five factors and never more than seven, with only 13 ever selected.
- The only factor consistently selected in these best models is market excess return. The only other factor selected in more than one subperiod is short-term (1-month) reversal.
- Other factors selected during specific subperiods are not those in widely used multi-factor models, but rather include such factors as change in 6-month momentum, change in number of analysts following and industry concentration.
- Across five subperiods:
- The best models of stock returns never have more than four factors, with only 10 ever selected. Results suggest that picking the best model becomes easier as the sample period shrinks.
- Again, the only factor consistently selected in these best models is market excess return. Other factors selected in more than one subperiod are short-term reversal, change in 6-month momentum and unexpected quarterly earnings.
- Among factors selected in just one subperiod, only size and book-to-market ratio appear in widely used factor models.
- Among microcaps, the best models have no more than six factors in any subperiod. Only three factors are clearly influential: market excess return, abnormal earnings announcement volume and earnings announcement return.
- For portfolios of stocks:
- Best models usually include the factor related to the factor portfolio sorting characteristic/variable.
- Again, the one most important factor is market excess return.
- Other factors selected are mostly different from those for individual stocks.
In summary, evidence from Bayesian inference generally undermines belief in a stable linear factor model of equity returns and specifically undermines acceptance of widely used 3-factor, 4-factor and 5-factor models of stock returns.
Findings thereby undermine belief in consistent efficacy of specific factor (smart beta) portfolios.
Cautions regarding findings include:
- The analysis involves gross, not net, stock and stock portfolio returns. Specifically:
- Accounting for turnover and shorting costs for stocks in factor measurement portfolios would reduce factor returns. Shorting may not always be feasible as specified due to lack of shares to borrow.
- Some factors may involve higher turnovers and/or shorting costs than other factors, such that factors are not equal in terms of implementation costs. Said differently, net analysis may select different models from gross analysis.
- Analyses are statistical rather than economic. In other words, there are no tests of the value of forming smart beta portfolios based on findings.
For related research, see:
