**CAPE Values are Looking Toppy**

According to Professor Shiller's data (available on YCharts or through Professor Shiller's own website) recent values of the cyclically-adjusted price-to-earnings ratio or CAPE (also sometimes known as the "Shiller PE" or "PE10") has been inching up recently and is now (at 25.96) close to the 2007 pre-crash value and well above the historical average value of 16.6.

Figure 1. Source: Robert Shiller

**How Not to Interpret the CAPE**

Unlike Professor Shiller, who draws a nuanced, measured conclusion from his study of the index CAPE numbers, Wall Street is not known for nuance, measured prognostication, or appropriate use of statistics. As such, various pundits look at Figure 1 and make the following argument without hint of reservation or doubt:

While this syllogism is valid, it might not be true. Financial ratios do not reflect constants of nature, so simply because the present value of a given ratio is higher or lower than an historical value of that ratio or a measure of its historical central tendency, holds little meaning.

To assess the importance of the present CAPE level, we must take a closer look at the basic concept of the PE Ratio to see what it is telling us about how market participants view the world.

**A Smarter Interpretation of the CAPE**

According to financial theory and common sense, the price of an asset should be directly related to the profit the asset creates for its owners over its entire economic life. That economic life is perpetual for all companies assumed to be "going concerns." To find the present value of the future earnings of a company in perpetuity, financial theorists use the Gordon Growth Model.

Where *P* = Price, *E* = Earnings, *r* = the discount rate of the asset, and *g* = the growth rate of the earnings.

Rearranging this equation, we can use the P/E ratio to solve for the growth term:

We know the PE ratio of a stock, so to find the implied growth rate, we simply have to know what discount rate (*r*) to use. There are various ways of determining what a reasonable discount rate should be, but this author's personal rule of thumb is to discount large capitalization stocks (or the index as a whole in this case) at a rate of 10%.[1]

With the assumption of a 10% discount rate, all of the terms on the right side of equation 2 are known, so can easily see what future earnings growth rate is implied by a given PE ratio.

This table means that if a stock has a PE ratio of 15, the market as a whole expects its earnings to grow at 3% per year in perpetuity. Since the CAPE uses average earnings over the previous 10 years, a CAPE of 15 means that the market expects that a company (or the index in the case of the S&P 500) will be able to expand its average earnings of the last 10 years at a rate of 3% in perpetuity.

Now that we have a sense for what the CAPE is telling us about future expected growth, let's go back to the question of whether we should worry about present CAPE readings.

**What the CAPE Is Saying about Future Earnings Growth**

Using the equation and logic above[2], we find that the market is presently pricing in a growth expectation for S&P stocks of 6.5% in perpetuity (compared to an average implied growth expectation of 4.5% for the entire series since 1881).

The 6.5% implied growth figure should seem familiar to you. It is, in fact, the average annual growth in nominal GDP in the post-War period (1Q47 - 1Q14) as shown by the slope of the black dotted trend line in Figure 3 below.

Figure 2. Source: Bureau of Economic Analysis, YCharts Research analysis

In short, considering the nominal GDP growth rate shown Figure 3, we can frame the present value of the CAPE as a sign that market participants are-using their capital as voting chits-predicting that the U.S. economy will perpetually grow at about the same rate it has in the post-War period.

**The Big Question**

Looking at present value of the CAPE through the lens of projected future earnings growth is a more intelligent way of analyzing the data than the simple syllogism above. However, it still does not answer the question of how concerned you should be with present CAPE levels.

How concerned (or indeed how happy) you should be depends ultimately on your outlook for future growth. The U.S. economy's growth rate has been below the post-War trend level since 2001, and dramatically so since 2008. Graphically, the three possible scenarios for economic growth over the next 10 years is shown in Figure 7 below.

Figure 3. Source: Bureau of Economic Analysis, YCharts Research analysis

Let's start with the "Bad" scenario, which we have picked as nominal economic growth over the next ten years of 5%-PIMCO's "New Normal" outlook, in other words. If the market comes to perceive this scenario as likely, present CAPE values are inappropriately high. This perception would likely force a revaluation of stocks downward and if this revaluation was perfect, its magnitude would be on the order of 25%.[3]

In the "Steady" scenario, economic growth follows the post-War trend and expands at roughly 6.5%. If market participants continue to believe this scenario is most likely in the future, growth rates implied by the CAPE are appropriate and the doom-and-gloom crew's refrain that the sky is falling will not come true.

In the "Good" scenario, economic growth accelerates faster than the historical trend-at a rate of 8% per year.[4] If the market believes this is the most likely future course of the economy, the present CAPE is radically too low and market participants are making the same mistake that we have shown the majority of their post-War predecessors have made. A general shift toward this view would lead to a revaluation of stocks upward by roughly 25%.

**Conclusion**

While pundits may shriek about the impending market crash on cable business channels, it is clear that the CAPE is not implying unreasonable earnings growth rates vis-à-vis recent historical earnings growth. In fact, present levels of the CAPE indicate that most market participants believe that S&P earnings will continue to grow at about the rate they have over the entire post-War period.

While reasonable people may disagree as to whether this is a rational assumption (and if not, what catalyst will force the market to come to the correct conclusion), it is clear that the CAPE is not signaling a precipitous market fall simply because of its present value vis-à-vis its historical mean.

[1] Read our full report to find out why we think this simplifying rule of thumb makes sense.

[2] We also translate Shiller's numbers into nominal rather than real values. This change shifts the Shiller chart and generates an average CAPE value 18.2, but does not change the peaks and troughs of the image. For the nominal CAPE series, we use Shiller's data.

[3] This is just the approximate percentage difference between 6.5% and 5%. Note, though, that "corrections" often overshoot, so actual declines might be greater.

[4] This rapid increase in economic output would lead to a situation similar to that pictured in Figure 3, where the actual economic growth line "wraps around" a persistently increasing trend line. This image is reminiscent of the dynamics between productivity-based economic increases (which are fairly stable) and debt-fueled cycles (which move from boom to bust and back again) that Bridgewater founder Ray Dalio talks about in his popular video and associated white paper.

**Disclosure: **The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it. The author has no business relationship with any company whose stock is mentioned in this article.