Predicted Factor/Smart Beta Alphas

Which equity factors have high and low expected returns? In their February 2017 paper entitled “Forecasting Factor and Smart Beta Returns (Hint: History Is Worse than Useless)”, Robert Arnott, Noah Beck and Vitali Kalesnik evaluate attractiveness of eight widely used stock factors. They measure alpha for each factor conventionally via a portfolio that is long (short) stocks with factor values having high (low) expected returns, reformed systematically. They compare factor alpha forecasting abilities of six models:

1. Factor return for the last five years.
2. Past return over the very long term (multiple decades), a conventionally used assumption.
3. Simple relative valuation (average valuation of long-side stocks divided by average valuation of short-side stocks), comparing current level to its past average.
4. Relative valuation with shrunk parameters to moderate forecasts by dampening overfitting to past data.
5. Relative valuation with shrunk parameters and variance reduction, further moderating Model 4 by halving its outputs.
6. Relative valuation with look-ahead full-sample calibration to assess limits of predictability. 

They employ simple benchmark forecasts of zero factor alphas. Using 24 years of specified stock data (January 1967 – December 1990) for model calibrations, about 20 years of data (January 1991 – October 2011) to generate forecasts and the balance of data (through December 2016) to complete forecast accuracy measurements, they find that:

• Model 1 generates forecasts with the largest mean squared error (MSE). In fact, its forecasts have negative correlation with subsequent factor alphas and are 127% less accurate than the benchmark forecast of zero factor alphas.
• Model 2 is more accurate than Model 1, but its forecasts also have negative correlation with subsequent factor alphas and are 21% less accurate than the benchmark forecasts.
• Models 3-6 all generate forecasts that have moderately positive correlations with subsequent factor alphas, and…
  • Model 3 is still 8% less accurate than the benchmark assumption of zero factor alphas.
  • Model 4 is 9% more accurate than the benchmark.
  • Model 5 is 14% more accurate than the benchmark, but less like subsequent factor alphas in terms of variability.
  • Model 6, with perfect foresight of actual factor alphas, is 27% more accurate than the benchmark.
• Applying Model 4 to forecast factor gross alphas over the next five years both for the U.S. market (see the chart below) and for international developed and emerging markets:
  • Forecasted gross alphas for the low beta factor, and for corresponding low beta and low-volatility smart beta strategies relative to their benchmarks, are negative in all markets.
  • Forecasted gross alphas for the size factor, and for corresponding size and equal weight smart beta strategies relative to their benchmarks, are negative in all markets.
  • Forecasted gross alphas for the value factor, and for corresponding fundamental indexing and income smart beta strategies relative to their benchmarks, are attractive in all markets.
  • Forecasted gross alphas for the momentum factor are slightly above historical norms in all markets, but momentum forecasts can change quickly.
  • Forecasted gross alphas for the gross profitability factor, and for corresponding quality smart beta strategies relative to their benchmarks, are attractive in the U.S. market.
• Portfolio maintenance costs are particularly high for momentum and low-volatility strategies, such that net outlooks are much weaker than gross outlooks.

The following chart, taken from the paper, depicts 5-year expected gross returns versus volatilities based on Model 4 above for eight U.S. stock market factors (long-short hedge portfolios) as of the end of 2016. Value Composite combines several value metrics, while Value P/B uses only price-to-book value ratios. Results show that Value Composite, Momentum and Gross Profitability factors are attractive, and Low Beta and Size are not, on a gross basis.

In summary, evidence from relative valuation analysis suggests that composite value and gross profitability factors may be the most attractive on a net basis over the next few years.

Cautions regarding findings include:

• Definition of “short-term” as 5-year past return is at odds with conventional momentum research, which typically uses one or a few months as short-term, three to 12 months as intermediate-term and multi-year as long term. Such research generally also finds reversion for 3-year to 5-year lookbacks.
• Discussion of portfolio maintenance costs are for institution-sized investors. Individuals may experience materially higher impacts.
• Calculations of factor/smart beta relative valuations is beyond the reach of most investors, who would bear fees for delegating the calculations to an advisor.
• Testing many forecasting models on the same data introduces model snooping bias, such that the best-performing model impounds lucky processing of sample noise and therefore overstates expected forecast accuracy.