Modified Test of P/E10 Usefulness

In response to the U.S. stock market timing backtest in "Usefulness of P/E10 as Stock Market Return Predictor", a subscriber suggested a modification for exploiting P/E10 (or Cyclically Adjusted Price-Earnings ratio, CAPE). Instead of binary signals that buy (sell) stocks when P/E10 crosses below (above) its historical average, employ a scaled allocation to stocks that considers how far P/E10 is from average. Specifically:

• If P/E10 is more than 2 standard deviations below its past average, allocate 100% to the S&P Composite Index.
• If P/E10 is more than 2 standard deviations above its past average, allocate 0% to the S&P Composite Index.
• If P/E10 is between these thresholds, allocate a percentage (ranging from 100% to 0%) to the S&P Composite Index, scaled linearly.

To investigate, we backtest this set of rules. Using monthly data from Robert Shiller, including S&P Composite Index level, associated dividends, 10-year government bond yields and values of P/E10 as available during January 1871 through September 2022, we find that: