Are the returns of factors widely used to predict the cross-section of stock returns themselves predictable? In the January 2016 draft of his paper entitled “Equity Factor Predictability”, Ulrich Carl analyzes predictability of market, size (market capitalization), value (book-to-market ratio), momentum (returns from 12 months ago to one month ago), low beta (betting against beta) and quality factor returns. All factor returns derive from hedge portfolios that are long (short) stocks with high (low) expected returns based on their factor values. He employs a broad range of economic and financial variables in four sets and multiple ways of testing predictability to ensure robustness of findings and limit model/data snooping bias. Predictability tests he applies include: combinations of simple forecasts (mean or median of single-variable regression forecasts); principal component analysis to distill forecasting variables into a few independent predictive factors; and, methods that adjust variable emphasis according to their respective past performances. He considers several predictability evaluation metrics, including: mean squared error compared to that of the historical average return; utility gain of timing based on predictability; and, information ratio (difference in return divided by difference in risk) relative to the historical average return. He mostly examines next-month forecasts with a one-month gap between predictive variable measurement and forecasted return over two test periods: 1975-2013 and 1950-2013. Using monthly returns for the six factors (start dates ranging from 1928 to 1958), a large set of financial variables since 1928 and a large set of economic variables since 1962, all through November 2013, he finds that:
- Regarding predictability of factor returns:
- Market factor returns (market return in excess of the risk-free rate) exhibit no significant predictability during 1975-2013. Predictability is significantly better for 1950-2013, especially based on financial variables.
- Size factor returns exhibit some significant predictability during 1975-2013, based mostly on economic variables (the business cycle) and concentrating during economic expansions. Predictability is stronger for 1950-2013 based on a stronger role for financial variables.
- Low beta factor returns are the most predictable of the six factors, but results vary across groupings of predictive variables. Predictability derives mostly from lagged returns. Results are similar for 1975-2013 and 1950-2013.
- Value factor returns exhibit no significant predictability during 1975-2013 and moderate predictability for most methods that is strongest during economic expansions during 1950-2013 (but no utility gain from timing the value factor).
- Momentum factor returns exhibit some significant predictability during both 1975-2013 and 1950-2013, mostly during economic contractions based on simple forecasting methods applied to financial variables. Returns exhibit steady gains punctuated by crashes when the broad market rebounds from a large correction, so regime switching models are likely appropriate.
- Quality factor returns exhibit no predictability, and attempting to time this factor results in utility losses.
- Regarding interactions of factor return series with the economy and among themselves:
- Market, size and value factors are anti-cyclical, with high (low) predicted returns during economic recessions (expansions). In contrast, the momentum factor is mirror-image pro-cyclical. The low beta factor is not very cyclical, but its predicted returns mostly decrease (increase) before/at the beginning of recessions (towards the end/shortly after recessions). The quality factor exhibits no cyclicality.
- Market, size and value factor returns exhibit positive monthly correlations among themselves and negative correlations with momentum and low beta factor returns. Correspondingly, momentum and low beta factor returns relate positively. However, low beta factor return correlations are the weakest and often uncorrelated with returns of other factors.
- The first principal component often loads positively on market, size and value, and negatively on momentum, suggesting a common underlying driver for these four factors.
In summary, evidence indicates that low beta and (less so) size factor returns are predictable, momentum factor returns are somewhat predictable, and market, value and especially quality factor returns are not predictable.
Cautions regarding findings include:
- Factor returns are gross, not net. Analyses do not account for the trading frictions from periodic portfolio rebalancing, shorting costs and shorting constraints. Accounting for these costs, which vary considerably over time and across factors, may affect findings (in particular, utility gains/losses).
- As noted in the paper, the one-month gap between predictor variable measurement and forecasted return may not be necessary for some financial data (but may not be enough for some economic data).
- Economic data series may include retroactive revisions (look-ahead biases) that disrupt usefulness in backtests.
