Which economic and market variables are most effective in predicting U.S. stock market returns? In his October 2018 paper entitled “Forecasting US Stock Returns”, David McMillan tests 10-year rolling and recursive (inception-to-date) one-quarter-ahead forecasts of S&P 500 Index capital gains and total returns using 18 economic and market variables, as follows: dividend-price ratio; price-earnings ratio; cyclically adjusted price-earnings ratio; payout ratio; Fed model; size premium; value premium; momentum premium; quarterly change in GDP, consumption, investment and CPI; 10-year Treasury note yield minus 3-month Treasury bill yield (term structure); Tobin’s q-ratio; purchasing managers index (PMI); equity allocation; federal government consumption and investment; and, a short moving average. He tests individual variables, four multivariate combinations and and six equal-weighted combinations of individual variable forecasts. He employs both conventional linear statistics and non-linear economic measures of accuracy based on sign and magnitude of forecast errors. He uses the historical mean return as a forecast benchmark. Using quarterly S&P 500 Index returns and data for the above-listed variables during January 1960 through February 2017, *he finds that:*

- Full-period in-sample tests indicate that Fed model, value premium, PMI and equity allocation are significant predictors of S&P 500 Index returns (plus dividend-price ratio and q-ratio for total returns only).
- For out-of-sample tests based on mean squared error, (whether rolling window or inception-to-date) only PMI beats the historical mean. However, several variables, multivariate combinations and equal-weighted combinations have lower average forecast errors and lower variance forecast errors than the benchmark.
- For out-of-sample tests based on sign of forecast:
- Among rolling window forecasts, eight of 18 individual variables beat the 60% success rate of the historical mean, with PMI highest at 66%. All multivariate and equal-weighted combinations match or beat the benchmark.
- Among inception-to-date forecasts, only two of 18 individual variables and two combinations beat the 67% success rate of the historical mean.

- For out-of-sample tests based on Sharpe ratio of return forecasts:
- Among rolling window forecasts, 14 of 18 individual variables beat the historical mean, as do two of four multivariate combinations and all equal-weighted combinations. Ten of 28 variables/combinations have Sharpe ratios more than double that of the historical mean.
- Among inception-to-date forecasts, only four variables/combinations (same as those for sign of forecast) beat the historical mean, most notably term structure and PMI.

- Poor predictive performance across variables comes from large unsystematic errors, not steady underperformance of the historical mean.
- Forecasts are generally more accurate during bear markets and economic contractions than during good times.
- Short-selling restrictions generally improve forecast accuracies.
- Overall, results suggest that:
- The term structure offers the best set of out-of-sample forecasts, with PMI in second place.
- Based on Sharpe ratio of return forecasts, the most important for investors, the rolling window term structure is optimal.
- Results are very similar for S&P 500 Index capital gains and total returns.

In summary, *evidence indicates that U.S. stock market forecasts based on the term structure of interest rates (first) and PMI (second) are consistently superior to those based on historical mean return.*

Cautions regarding findings include:

- Forecasted Sharpe ratios are gross, not net. Accounting for trading frictions and shorting costs, which vary considerably over the sample period, would reduce Sharpe ratios.
- Testing many variables, combinations of variables, prediction methods and prediction success measures on the same dataset introduces considerable data snooping bias, such that the best-performing predictors overstate accuracy.

For other perspectives, see: