P/E10 and Future Stock Returns
Posted in Fundamental Valuation
September 23, 2009
A reader asked: “Have you looked at P/E10 as to the value of the markets?” The definitive P/E10 is perhaps that implied by the publicly available Robert Shiller data set, which calculates P/E10 monthly as the ratio of the inflation-adjusted S&P Composite Index level to the average monthly inflation-adjusted 12-month trailing earnings of the index companies over the previous ten years. Inflation adjustments approximately cancel in this calculation. To test the predictive power and usefulness of P/E10, we employ regression, ranking and cumulative value tests. Using the monthly value of P/E10 and the level of the S&P Composite Index as calculated by Robert Shiller over the period January 1881 through August 2009, we find that:
The following scatter plot relates the 10-year future return for the S&P Composite Index to initial P/E10 using monthly data over the entire sample period (through August 1999 as constrained by the future return calculation). In general, the higher the P/E10, the lower the 10-year future return. The Pearson correlation for the relationship is -0.38, and the R-squared statistic is 0.15, indicating that variation in P/E10 explains 15% of 10-year future returns.
Given the large number of low and negative 10-year returns at fairly low values of P/E10, it appears that using P/E10 as a valuation indicator does not preclude poor outcomes.
The clumpiness of the data is a symptom of the large month-to-month overlap of the the earnings data used in the P/E10 calculations. This overlap means that the effective sample size is much smaller than indicated by the number of data points on the plot. There are only about 13 completely independent 10-year intervals in the sample.
To test for non-linearity in the results, we try a ranking.
The following chart summarizes S&P Composite Index average 10-year future returns by quintile of initial P/E10 over the entire sample period. Results indicate a fairly systematic relationship between P/E10 and future stock market returns: the lower the initial P/E10, the stronger the average future return.
However, even for the highest quintile of initial P/E10s, the average 10-year future return is substantially positive, so it is not obvious that exiting the stock market after high values of P/E10 beats a buy-and-hold strategy.
Is there a level of P/E10 that unequivocally avoids poor future returns?
The next chart summarizes the average monthly P/E10 by quintile of S&P Composite Index 10-year future returns over the entire sample period. While there is a reasonably consistent progression in the relationship, the differences among P/E10s for the three lowest-return quintiles are not large, confirming the observation above that P/E10 as a valuation indicator may be substantially unable to avoid poor outcomes.
How might an investor apply P/E10 in a simple investment strategy?
One approach to applying P/E10 as a valuation indicator is to buy (sell) when P/E10 crosses below (above) some threshold related to its average over the long term. To avoid look-ahead bias, it is essential to establish such a threshold using only data that an investor could know when making decisions. For example, an investor making a decision in early 1971 knows the average P/E10 for 1881-1970, but not the average P/E10 for 1881-2009. (The small bias of the earnings release schedule does not matter much for long-term analyses.)
Suppose an investor adopts a strategy at the end of January 1901 of buying (selling) the S&P Composite Index when P/E10 crosses below (above) its cumulative average since 1881. The following chart shows when the investor would be in stocks (orange) and out of stocks (white) through August 2009, along with the behavior of the S&P Composite Index over the entire period (log scale). The investor would be out of stocks for all of the 1960s and nearly all of the last two decades. It is not obvious from this chart that the strategy outperforms a buy-and-hold benchmark.
For a closer look, we calculate cumulative returns for this strategy and for buy-and-hold with the following simplistic assumptions:
- The S&P Composite Index is readily investable since the beginning of 1901 with no trading frictions.
- There is some constant monthly return on cash while out of stocks.
- Tax consequences of trading are negligible.
Based on these assumptions, we find that:
- The P/E10 threshold strategy generates 16 round-trip trades.
- The strategy is in stocks 52% of the time.
- The S&P Composite Index average monthly return while the strategy is in (out of) stocks is 0.72% (0.55%).
- The strategy’s cumulative return through August 2009 matches or exceeds that for a buy-and-hold benchmark as long as the monthly return on cash is at least 0.36% (4.4% annualized).
It is not obvious from these results that the P/E10 threshold strategy could beat a buy-and-hold benchmark.
What about a floating interval for calculation of a P/E10 trading threshold?
Suppose the investor instead wants to discard very old data and adopts a strategy at the end of January 1921 of buying (selling) the S&P Composite Index when P/E10 crosses below (above) its 40-year lagged average since 1881. The following chart shows when the investor would be in stocks (brown) and out of stocks (white) through August 2009, along with the behavior of the S&P Composite Index over the period (log scale). The investor would have been out of stocks for much of the 1950s-1960s and nearly all of the last two decades. It is not obvious from this chart that the strategy outperforms a buy-and-hold benchmark.
Based on the same simplifying assumptions used above, we find that:
- This P/E10 threshold strategy generates 19.5 round-trip trades.
- The strategy is in stocks 58% of the time.
- The S&P Composite Index average monthly return while the strategy is in (out of) stocks is 1.00% (0.56%).
- The strategy’s cumulative return through August 2009 matches or exceeds that for a buy-and-hold benchmark as long as the monthly return on cash is at least 0.27% (3.3% annualized).
Again, it is not obvious that the P/E10 threshold strategy can earn a large enough return on cash while out of stocks to materially best a buy-and-hold benchmark.
In summary, evidence from simple tests on long-run data indicates that P/E10 has some predictive power for long-term future returns, but this predictive power does not convincingly translate into an outperforming investment strategy.
As noted above, the intervals used in calculating P/E10 and measuring its power to predict stock market returns are long, so the available sample (1871-2009) is modest in duration for purposes of statistical inference.
