### Combining and Exploiting Stock Market Forecasting Variables

**August 26, 2015** - Equity Premium

Does the set of variables that have the strongest correlations with subsequent U.S. stock market returns over the prior decade usefully predict market returns out-of-sample? In the July 2015 draft of their paper entitled “A Practitioner’s Defense of Return Predictability”, Blair Hull and Xiao Qiao apply this correlation screening approach to a set of 20 published stock market forecasting variables encompassing technical indicators, macroeconomic variables, return-based predictors, price ratios and commodity prices. Their horizon for historical daily correlation measurements and out-of-sample forecasts is 130 trading days (about six months). Every 20 days just before the market close, they employ regressions using the most recent ten years of data to: (1) determine the form of each forecasting variable (raw value, exponentially-weighted moving average or log value minus exponentially-weight moving average) that maximizes its daily correlation with 130-day returns; and, (2) estimate variable coefficients to predict the return for the next 130 days. For the next 20 days, they then use the estimated coefficients to generate expected returns and take a (market on close) position in SPDR S&P 500 (SPY) eight times the expected return in excess of the risk-free rate (capped at 150% long and 50% short). They consider three expected return models:

- Kitchen sink – employing regression coefficients for all 20 forecasting variables (but with four of the variables compressed into a composite).
- Correlation Screening – employing regression coefficients only for forecasting variables having absolute correlations with subsequent 130-day market returns at least 0.10 over the past ten years.
- Real-time Correlation Screening – same as Correlation Screening, but excluding any forecasting variables not yet discovered (published).

They assume: trading frictions of two cents per share of SPY bought or sold; daily return on cash of the three-month U.S. Treasury bill yield minus 0.3%; and, interest on borrowed shares of the Federal Funds Rate plus 0.3%. To limit trading frictions, they adjust positions only when changes in expected market return reach a threshold of 10%. They ignore tax implications of trading. Using daily total returns for SPY, the 3-month Treasury bill yield and vintage (as-released) values of the 20 forecast variables during 6/8/1990 through 5/4/2015, *they find that:* Keep Reading