Its time to put the Shiller PE ratio to the test. As mentioned in my previous blog, Shiller calculates a special PE ratio which he calls P/E10. He defines this ratio as price divided by the average of ten years of earnings (a moving average) and adjusted for inflation. Price refers to the index level of the S&P 500 index, and earnings are those of the 500 constituent stocks.

The PE15 trading rule is a contrarian strategy that buys the index when the PE is below 15 and is out of the market when the PE is above 15. It is an *active* strategy compared to the buy-and-hold (BH) strategy. In this blog, I will compare the profitability of the PE15 strategy with that of the passive BH strategy. The winner is the strategy that produces the highest compounded or **terminal value**, starting with an investment of $1.

My data is obtained from Professor Shiller’s website. The full dataset runs from Jan 1881 to Jan 2018, a total of 137 years. While a long dataset is a treasure trove for researchers, no real investors have such long time horizons. Therefore, in addition to the full dataset, I also show results based on a more recent period, from 1970 to 2018.

I implement the PE15 trading rule as follows: every month, I check whether P/E10 was above or below 15 for* each* of the last twelve months. Denote these signals as >15 and <15 respectively. If the signal for a month is < 15, I buy the index, and hold it until a >15 signal appears. When this happens, I cash out of the index. For simplicity, I assume that cash earns a zero rate of interest and exclude dividends from the return calculations. I also ignore trading costs (this will actually skew my results in favor of the PE15 strategy).

Here are the results.

Over the full sample period, one dollar increased to $430.43 for the buy-and-hold (BH) strategy but grew to only $229.98 for the PE15 strategy. As the second row shows, the PE15 strategy is also inferior to the BH strategy in the more recent period. The last column (% Out) shows the percentage of months when the investor is out of the market. For the BH strategy, this is zero. For the PE15 strategy, the investor is 47.5% out of the market over the full sample period and a whopping 60% in the more recent period. Clearly, the investor following the PE15 trading rule paid a high price for being out of the market for so long.

Okay, the PE15 trading rule didn’t quite work out. Maybe, it is too premature to say that the market is overvalued when its PE is above 15. As the famous economist, John Maynard Keynes once said, “*markets can remain irrational longer than you can remain solvent*“. So, let’s raise the bar to a PE of 20.

Here are the results of the new test.

Its the same story – BH beats PE20 hands down. Notice that missing out just 20.7% of number of months in the full sample period was enough to bring the terminal value down from $430 to $363, a difference of 16%.

**Conclusion**: Shiller has given us a rich dataset and a nice chart. But no, 15 is not a magical number for stock traders. And neither is 20.