Testing the CAPE Ratio: Cyclically Adjusted P/E
Introduction
The Price-to-Earnings (PE) Ratio is perhaps the simplest and most classic measure of a stock’s value. This method for valuing a company measures its current share price relative to its earnings per share (EPS). P/E ratios are commonly used by investors and analysts to determine the relative value of a company’s shares and provides a basis for making an “apples-to-apples” comparison.
As of September 2021 the 10-Year, Cyclically Adjusted PE Ratio for the S&P 500 is 38.34. By this measure, the cyclically adjusted PE ratio is approaching highs not seen since the days of the Dotcom Bubble in the late 90’s. This suggests that the market is significantly overvalued compared to underlying profit generation. As the below chart demonstrates, we are swiftly approaching historically dangerous territory:
Price multiples are popular valuation criteria among professional and retail investors alike; with the PE ratio being key among them. However, as any good analyst knows one metric cannot alone tell the full story. The analysis to follow has four objectives:
- Review the theory of financial ratios and why you might use them.
- Describe the data and construction used for the analysis.
- Quantify what the CAPE ratio says about potential future returns.
- Offer critiques and counterpoints.
The Theory of Financial Ratios
Financial ratios like Price/Earnings (PE), Price/Book (PB), and Enterprise Value/EBITDA ( EV/EBITDA) are commonly used by financial analysts to gauge the relative value of a stock. For example, a PE ratio of 15 tells us that we are required to pay $15 up front in order to access $1 of earnings. A high PE ratio might imply that a company is expected to grow aggressively while a low PE might tell us that a company is attractively valued.
Financial ratios can be expressed on either a trailing or forward-looking basis. The Forward PE is calculated by taking the current price and dividing it by an estimate for earnings over the next 12-months. More commonly the PE is expressed on a trailing basis which takes the current price divided by earnings over the previous 12-months.
The PE for the S&P 500 has averaged about 16 over its 100+ year history but in any one year can deviate significantly. Take a look at the below graph of the PE ratio for 1891–2000. The average might be 16, but the ratio has rarely stayed there for very long and can be quite volatile year to year (or quarter to quarter).
I excluded the 2010’s in the previous graph for a reason. The ’08 Financial Crisis and Great Recession were so severe that for a period of time the trailing 12-month earnings for the S&P were actually negative which had the perverse effect of making stocks look wildly expensive when, in reality, they were historically very cheap. You can see this dynamic in the graph for the PE from 1926–2020. The long run dynamics of the PE are distorted during this period of time and confound our understanding of what relative valuations mean for stocks.
In order to smooth out the fluctuations in corporate profits that are part of the business cycle and reduce the volatility of valuations, Noble winning economist Robert Shiller developed the Cyclically Adjusted Price-Earnings (CAPE) Ratio. Professor Shiller first introduced the CAPE in a series of provocative papers in 1998 and 2001 which concluded that the stock market was historically overvalued and that the ensuing 10 years would produce very poor returns indeed. This god-like call on the markets solidified the CAPE Ratio as a critical metric when discussing market valuation.
Unlike the simple PE ratio, the CAPE ratio takes as the denominator an average of the previous 10-years earnings adjusted for inflation and is defined as follows:
You can see the effect this adjustment has in the below graph which depicts the CAPE ratio for 1891–2021. The volatility of the ratio is significantly reduced and the oddness of 2010’s is replaced by the behavior we would expect (i.e. cheap valuations coming out of recession). One feature about the CAPE chart that is of particular interest is that it suggests valuations are stable.
Stability, Mean Reversion and Valuation
It’s imperative to understand what the stability of a valuation ratio implies about mean reversion. If we accept the premise that valuation ratios (like CAPE) are, in fact, stable and will continue to fluctuate within their historical range and not move permanently outside or “get stuck” at historically extreme levels, then we are claiming that valuations are stationary or mean reverting. It follows that when a valuation ratio is at an extreme level, then eventually something must happen to restore a long run equilibrium. In the case of a CAPE ratio that is historically high, either the numerator (i.e. Price) must decline or the denominator (i.e. Average 10-Year Earnings) must grow to bring the ratio back to a normal level.
If this is the case, then surely something must be forecastable based on the CAPE; either the numerator or the denominator. If we are using the P/E ratio, then the P/E must be able to forecast either the future trajectory of prices (the ‘P’) or the future path of earnings (the ‘E’). The Shiller studies I referenced and my own work (see Stock Market Valuation and the 2020’s in R) demonstrate that valuations imply nothing about future earnings growth in either the short or long term. While empirically important, valuations have only limited relevance for predicting returns in the short-run. It is over the long run that valuations demonstrate their utility and become a major factor for predicting the future direction of markets.
Now that we are properly armed with theory and historical context, let us now proceed to examine the current state of the CAPE ratio and what is can tell us about the prospects of future returns.
Current Analysis
The plot above depicts the CAPE ratio from 1891–2021. Over this 130 year history the CAPE ratio has averaged 17.3, but often differs from this average significantly. The CAPE reached a nadir of 4.78 in December 1920 (literally the eve of the Roaring ‘20’s) and a zenith of 44.2 in December 1999 at the crest of the Tech Bubble.
Also presented are standard deviation bands showing +/-1 and +/- 2 standard deviations, respectively. Again, we need to make a crucial assumption, namely that the data is normally distributed. This assumption is probably not justifiable on empirical grounds, BUT if we are willing to make it, then generally speaking ~68% of the data should lie within 1 standard deviation of the mean (i.e., fairly valued) and ~95% of the data should lie within 2 standard deviations. A value for the CAPE Ratio greater than/less than 2 standard deviations should be regarded as a market that is significantly over/under-valued.
A possible critique of this analysis may be that 130 years is a long time. The economy today is dramatically different from what it was in the last 1800’s. Back-then, industry primarily relying on steam power and didn’t have cars or planes let alone the internet and smart phones. Perhaps the relationship should be assessed over a shorter period of time to capture current dynamics and valuation trends. In Structural Change in Stock Market Valuations I find evidence to suggest that valuations were structurally lower from 1926–1940 and again from 1969–1977 than they were over other periods. Therefore we may refine our analysis by considering valuation trends during the “modern era” 1980-Present. The below graph plots the CAPE over this more recent period.
Over this abbreviated 30 year history the CAPE averaged 22.69, had a high of 44.2 and a low of 6.64. Presently at 38.34, the CAPE might be considered “high” but not yet extreme if recent history is any guide.
Predictive Value of the CAPE Ratio
The salient question for any investor studying valuation is “what does this model say about the prospects for future returns?”. Predicting the stock market is fraught with difficulty, but using data to examine how the market performed following periods of excessive high/low valuation is easy. For the analysis to follow I present a series of regressions to help us quantify what today’s valuations say about future returns.
Full Period, 5-Year Forward Returns
In the previous section we reviewed how the current CAPE ratio compares to its full history (1891-Present) and an abbreviated history (1980-Present). I argued that structural change may make recent history more representative than valuations seen far back in the past. For the time being, let us assume I am wrong: full history is better at predicting future outcomes than recent history.
The below plot depicts monthly datapoints beginning in January 1891. The explanatory variable (i.e. x-axis) is the CAPE ratio for that month and the dependent variable (i.e. y-axis) is the 5-year forward annualized return. The objective is to determine if a relationship exists between the CAPE ratio and subsequent returns. A regression line, confidence and prediction interval are also depicted.
The results of the accompanying regression model follow. Standard Errors are corrected for heteroscedasticity and autocorrelation.
The results are reasonable and consistent with what we expected a priori. The coefficient of the CAPE is negative and highly statistically significant. This suggests that market valuation as measured by the Cyclically-Adjusted PE Ratio is important for explaining future expected return. Crucially, the coefficient is negative which tells us that (on average) higher valuation is associated with lower future return.
The adjusted-R-Squared of .1472 suggests that approximately 15% of variation in future 5-year returns is explained by the CAPE ratio. Not bad for a single variable model, but it tells us that there are many other factors at work that our model does not capture.
Some other casual observations stand out. The data is clearly heteroscedastic. Essentially, this means that the variability of ‘y’ depends on ‘x’. For example, future returns are much more dispersed when the CAPE is close to 17 (i.e. the long run average) v. at the extremes. Around 17, the mean annualized return is ~10% as we might have guessed. This is right in line with the long run historical average annual return for large cap stocks. However, around 17, annualized returns have historically ranged from approximately -10% to 20%. This is a wide range and not very helpful information if you’re an investor.
The extremes tell a different story. For “high” valuations (those greater than 30), the data is clustered quite tightly to the regression line. At high valuations, forward annualized returns have quite reliably been around 0 or slightly negative. Let us label these points with their corresponding date.
As you may have guessed these points correspond the the years that followed the bust of 1929 and the Tech Bubble. Given that today’s CAPE is higher than that observed in 1929 and swiftly approaching the heady Dotcom days, then this graph should give you pause.
Let us now use the regression line we derived to develop a forecast for future returns. We can do this simply by plugging in today’s CAPE of 38.34 into the regression equation as follows:
E(5-Year Forward Annualized Rtn.) = .1465 — .0046(38.34) = -.03 or -3%
The output from the regression tells us that investors should expect an approximately -3% annualized return over the next 5 years which is…uninspiring to say the least.
1980-Present, 5-Year Forward Annualized Returns
Having examined what the full history of valuation has to say about annualized returns let us now turn our attention to the “modern era”. If I am correct and valuations today are structurally different from the distant past, then perhaps our expectations for future returns should be as well.
Below is the plot and accompanying regression results:
Visual evidence from the plot suggests a tighter degree of fit than the full history plot; forward returns decline more uniformly with increased valuation.
The regression results are also rather encouraging. The coefficient for the CAPE ratio is, once again, highly statistically significant. Moreover, it is negative which comports to our expectations. To assess “fit-ness” we can turn to R-Squared. At .41 the R-Squared for this abbreviated period is substantially higher than that observed for the full history. Approximately 41% of the variance of forward returns in the “modern era” is explained by current valuations which is quite high for a single variable model. This lends considerable credence to the “structural change” hypothesis.
Armed with these results let us now compute the expected 5-year forward return:
E(5-Year Forward Annualized Rtn) = .21 — .0057(38.34) = -.0085 or -.85%
The output from the regression tells us that investors should expect an approximately -.85% annualized return over the next 5 years. It would appear that even if today’s valuation environment is different from what we have observed in the past investors are still likely facing an world of paltry returns in the years to come.
Originally published at https://lightfinance.blog.
