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:
