The Vagaries of Using CAPE to Forecast Returns
The cyclically adjusted price/earnings (CAPE) ratio is one of the most reliable indicators of prospective long-term stock market returns. First proposed by Benjamin Graham and popularized by John Campbell and Robert Shiller, the formula is deceptively simple, dividing the current price of a stock market or single stock by the average earnings of the last 10 years — both adjusted for inflation.
Historically the CAPE ratio has worked well in predicting the future real returns of stock markets. But as is often the case with simple indicators, people love to poke holes in it, especially if the forecasts are not in line with recent market reality — or their own opinions.
Recently, the earnings side of the CAPE ratio has come under increased scrutiny. For example, Jeremy Siegel theorized that because of accounting changes since the 1990s, the earnings of current listed companies are not comparable to historical norms, and are systematically lower than in the past due to mark-to-market requirements that depress asset prices in times of crisis. These artificially low earnings lead to artificially high CAPE ratios, creating unwarranted pessimism about future stock market returns.
Siegel and others suggest that rather than comparing current CAPE levels to long-term averages going back to 1871, as is often done, compare them instead to the early 1990s, when these accounting changes were initially introduced. Still others contend that comparisons should go back to the World War II era, because after 1945 earnings growth seems to have gone through a lasting regime change. With these changes in time frame, they maintain, the CAPE becomes more predictive, and expected returns for the coming years are higher than those anticipated if long-term historic averages are used.
The theories in favor of changes in historical time frames are troublesome. In the following table, I calculated the CAPE for the US stock market and estimated a regression of beginning CAPE on subsequent five-year real returns (the reason for trying to predict five-year real returns instead of the more standard 10-year returns is to start the regressions at a later stage and do not necessarily require 20 years of data to make one forecast). Beginning in January 1910, the regression results in an annual real return forecast of 1.9% for the next five years — an abysmally low number. The fit of the regression as measured by the R2 is a mere 0.21.
If the regression begins in 1945, after World War II, things look different. While the fit between forecast and realized return is still low with an R2 of 0.23, the predicted return for the next five years is much higher at 3.6% per annum. If started in 1990, however, the return forecast increases to 6.3%, and the fit is much better with an impressive R2 of 0.58.
So far, so good, but what happens if the historic time period is shortened some more? Starting in 1995 results in a return forecast of 4.9% (R2 of 0.61), starting in 2000 yields 4.0% (R2 of 0.64), and starting in 2005 yields 3.6% with a fantastic R2 of 0.83. Thus as the period for the regression moves closer, the fit improves but return expectations drop from more than 6% to figures that are more in line with long-term historic averages. Similar effects can be seen in the United Kingdom, Switzerland, and Germany.
Expected Five-Year Return in Local Currency (R2 in Brackets)
This exercise illustrates an important lesson that is too often forgotten in market predictions: Forecasts depend not only on the kind of variable, but also on the time frame used to calibrate the model. So far this discussion has focused mainly on how to calculate the CAPE, and all readers should review Laurence Siegel’s take on the benefits and drawbacks of different approaches.
The bigger uncertainty, however, stems from the time period used to calibrate the model and run the regressions. In order to provide a reasonable idea of expected returns for the coming five years, I have calculated the expected real returns in local currencies for 38 different countries for the longest historical time period possible, in addition to the starting points given in the table above. The two tables below show the predicted return for the full time series going back as far as possible, as well as the fit of the regression given by the R2. The last column shows the range of return predictions if the different starting points are used. This allows us to summarize the good, the bad, and the ugly truths about the current long-term market outlook.
The Good: Using CAPE as a forecasting tool for long-term stock market returns works in international markets as well as in the United States. The highest return forecasts currently come out of emerging markets, which seem to be the best value.
The Bad: The US market is poised to underperform European and Asian stock markets over the next five years in local currency terms.
The Ugly: It is impossible to say by how much the US market is likely to underperform or if it is going to underperform at all, since the estimation errors around these return forecasts are considerable.
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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.
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