Is it possible to test factor models of stock returns directly on individual stocks rather than on portfolios of stocks sorted per preconceived notions of factor importance. In their November 2015 paper entitled “Tests of Alternative Asset Pricing Models Using Individual Security Returns and a New Multivariate F-Test”, Shafiqur Rahman, Matthew Schneider and Gary Antonacci apply a statistical method that allows testing of equity factor models directly on individual stocks. Results are therefore free from the information loss and data snooping bias associated with sorting stocks based on some factor into portfolios. They test several recently proposed multi-factor models based on five or six of market, size, value (different definitions), momentum, liquidity (based on turnover), profitability and investment factors. They compare alternative models via 100,000 Monte Carlo simulations each in terms of ability to eliminate average alpha and appraisal ratio (absolute alpha divided by residual variance) across individual stocks. Using monthly returns and stock/firm characteristics for the 407 Russell 3000 Index stocks with no missing monthly returns during January 1990 through December 2014 (300 months), they find that:
- A five-factor model including market, size, conventional book-to-market ratio (value), momentum, and liquidity outperforms other proposed five-factor and six-factor models in explaining excess returns of individual stocks. This best model is a natural candidate to replace the widely used four-factor model that includes all the factors except liquidity.
- Within this best model, liquidity contributes as much to explanatory power as momentum.
- Tests suggest that (1) profitability and momentum factors and (2) investment and conventional book-to-market factors play similar roles in asset pricing models.
In summary, evidence from testing directly on individual stock returns suggests pre-eminence for a five-factor model encompassing market, size, book-to-market, momentum and liquidity factors.
Cautions regarding findings include:
- As noted (but discounted) in the paper, the 407 stocks with continuous data for testing may not be representative of the many more disqualified stocks.
- As shown in the paper, testing focuses on relative model performance. The authors note that none of the factor models tested appear useful for identifying stocks with idiosyncratic positive alpha.
- Analyses use gross, not net, returns. Accounting for portfolio formation/rebalancing frictions and shorting costs/feasibility to exploit factor premiums would work against premium capture. Capture of the liquidity premium is especially suspect since trading frictions for a stock likely vary inversely with liquidity.
- To the extent that randomness is present in stock returns, examination of many factor models and alternative factor definitions introduces snooping bias, such that the best-performing model incorporates luck. See “Taming the Factor Zoo?” and “Stock Return Model Snooping”.
- Many investors may not be able to hold enough stocks to ensure statistical reliability of factor premium capture (or they pay a fee to a fund manager who can hold many stocks).
- The kinds of statistical tests used impound assumptions about asset return distributions that may be materially incorrect.
See also “Equity Investing Based on Liquidity”.
