Robert Shillers The cyclically adjusted price-earnings ratio (CAPE) is approaching historically high levels. In fact, the present value of CAPE has only been exceeded twice since 1900. But must you care?
Investment professionals know that despite the historical tendency to anticipate stock market returns, CAPE isn’t a reliable market management tool. The evidence discussed here offers a possible explanation for this.
As shown in Figure 1, CAPE was largely trendless within the post-1900 period, with increases typically followed by “compression.” For most of its history, it might have been natural to assume that periods of high CAPE can be followed by periods of low CAPE.
Figure 1: KAP, 1900-2024
And there’s a well-recognized, if troubling, empirical regularity linking CAPE and future stock market returns. Figure 2 shows the 10-year annualized returns for the Ibbotson Large Cap Stock Index®. The points are populated by the CAPE starting value (red = high, blue = low). As is evident from the descending pattern, CAPE values are strongly negatively correlated with future returns (correlation coefficient = -0.7). In the long run the connection is weaker but still negative. The correlation between the initial CAPE and the following 20-year annual returns is -0.3.
Taken together, Figures 1 and a couple of suggest that episodes of rising CAPE are followed by episodes of shrinking CAPE and subdued stock market returns.
Figure 2: CAPE (horizontal axis) and the subsequent 10 years annual return, 1926-2024.
Could this time be different?
The query is whether or not CAPE’s current period of expansion shall be followed by a period of contraction and low stock market returns may rely upon the steadiness of CAPE in a time series sense. My own work suggests that CAPE isn’t “stationary” and subsequently shouldn’t be expected to mean a return. See “A time series evaluation and forecast of Cape” in . I’ll explore this query again on this blog.
Testing for a CAPE break
Since the expansion rate of P (price) divided by E (earnings) is just the difference between the expansion rates of P and E, the concept that CAPE could rise indefinitely could make investment professionals uneasy.
To avoid this discomfort, it is useful to assume CAPE as a single quantity and consider how that quantity has behaved over time and whether the method that drives it has modified. That’s the approach I’m taking here.
From an informal visual inspection of Figure 1, it is evident that CAPE has modified a minimum of once in its long history. CAPE has been increased for the reason that Nineteen Nineties. Before 1990, the mean CAPE was 14.1. Since then, the common has been 26.6. At 34, today’s CAPE is 95Th Percentile of observations since 1900.
A critical query for practitioners is subsequently: Did CAPE “change” within the Nineteen Nineties in order that its behavior was less relevant before than after? A statistical test of a change in a time series over a spread of dates Quandt likelihood ratio test (QLR).may help answer this query.
Estimating a break date using this test requires a regression of the CAPE on time and possible but unknown break dates (on this case months) that fall inside a particular time window. I selected the window 1980 to 1999.
By including a possible break-date interval as a right-hand side dummy variable within the regression model together with their interaction with time, a straightforward test of the joint significance of a series of regressions (one for every date) may help to account for changes over time discover -series process. (R code for this test and other results cited on this blog will be found here Here.)
Figure 3 shows the resulting test statistics (technically F-statistics). The highest test statistic value is the perfect candidate for a break within the CAPE. This date, marked with a red dot in Figure 3, is August 1991. It agrees well with the date seen by visual inspection of Figure 2.
Figure 3: Date break test in CAPE, 1980 to 1999.
Given a candidate’s exit date, we will then test whether CAPE’s behavior modified after that time. In particular, we wish to know whether CAPE’s mean-revert tendency was more pronounced before 1991. To test this, I used a definition of mean revert common in empirical finance: existence of a negative serial correlation.
A serial correlation test is easy. Changes in CAPE over a period are attributed to the change in an immediately preceding period of the identical length. If the estimated coefficient is negative and significant, CAPE could also be mean reversion.
To estimate the serial correlation of CAPE, I regressed the five-year change in CAPE against the previous five-year change. The results confirm a change within the behavior of CAPE after 1991. Before 1991, the estimated relationship between the change in CAPE in successive five-year periods was actually negative (coefficient = -0.19) and significant (t = 5.8). However, after the estimated break 12 months (1991), the estimated coefficient increases to a much less meaningful -0.06 and is insignificant (t = 1.4). In particular, the outcomes of tests over longer periods of time are less convincing, but additionally less reliable.
The potential change in serial correlation is usually recommended by the scatterplots in Figure 4. The relationship in the best panel, showing the more moderen period, is weaker than within the precedent days, shown within the left panel. This is highlighted by the flatter slopes of the linear regression fit lines drawn through each set of points within the later period.
Figure 4: Serial correlation of 5-year change in CAPE, 1900-91 (left panel) and 1992-2024 (right panel)
Implications
Most practitioners probably agree that CAPE modified within the Nineteen Nineties. Since the beginning of this decade, it has been above its mean of 14.1 from 1900 to 1989 a remarkable 99.8% of the time. That increased CAPE is empirically related to lower returns is troubling. But empirical regularities will not be reliable for prediction if the underlying relationships are unstable.
My easy evaluation provides evidence that CAPE modified within the Nineteen Nineties and that concerns about mean reversion could also be misplaced. Even though CAPE modified three many years ago, there’s nothing stopping it from changing again.
Should you are concerned that CAPE is high? That depends upon whether you think that CAPE will change again.
CAPE has been a well-liked topic for years. You may also like these archive posts: “The Case for Further Stock Market Gains” and “The Vagaries of Using CAPE to Forecast Returns.”
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