Shiller CAPE, philosophically speaking

Solution: don’t read books

In this post, I will describe how I produce an analog of the Shiller P/E or CAPE, which is meant to be a measure of equity market valuation that is roughly invariant to the position of the business cycle.

I would not say this is scintillating reading. It is more a technical appendix, to which I may refer occasionally over time, when using the main outputs. The bottom line is that equities look priced to generate poor returns, but that is different from saying they are egregiously expensive and need to reprice lower. Also, valuation can get you only so far. The cycle usually dominates.


Regarding the logic of CAPE, valuing equities on current earnings can be misleading when earnings are well above trend in the late cycle or well below trend in recession and early recovery. This is familiar stuff.

Despite its advantages, Shiller’s CAPE suffers from a couple technical weaknesses that inclined it to give an unduly bearish signal during the recovery from the global financial crisis. And I suspect it may soon begin to give an unduly bullish signal, at least on a rate of change basis, as those technical issues unwind.

So I implement a couple tweaks to Shiller’s CAPE, which are motivated in large part by some excellent work I saw over at Philosophical Economics. That site is run by a fellow who goes by the pen name, Jesse Livermore.

My own valuation measure is not identical with Jesse’s, although it is very close.  Separately, Jesse has a more-complicated measure of equity valuation that controls for distortions caused by changes of dividend payouts and buybacks.  I think that is very clever stuff, although a bit mind numbing too. For now I will leave it aside, except to say that the controls he offers do not typically generate a qualitatively different valuation signal from what a Shillerized P/E or earnings yield provides.

I assume you know how the CAPE is produced and how to calculate it.  Briefly, it is just the real value of the index level divided by a ten-year moving average of associated real earnings.  By calculating the ratio in real terms, we avoid having equities look misleadingly rich in inflationary environments and misleadingly cheap in low-inflation environments. Again, familiar stuff – I assume.

I make the following tweaks to Shiller’s approach to create an index that is more intuitively familiar and – I hope – less affected by what I would call (admittedly subjectively) “distortions” associated with global financial crisis.

First, I want to use operating earnings rather than reported earnings for all periods over which I have the former.  In the current environment, operating earnings are probably the more meaningful or less misleading, because of the huge write-downs in 2008-09 and 2001.

These artificially depressed Shillerized earnings for a few years after after 2008.  During that period, the Shiller P/E understated the case for equities, as was obvious in real time to anyone paying attention. And in the past couple years, the unwinding of this effects has led to a somewhat misleading (although also predictable) rise of Shillerized reported earnings.  We can partly control for this by using operating earnings where they are available, i.e. after 1985.

Second, I need to adjust the historical reported earnings data so that they may be spliced with the operating earnings I used for all dates after 1985.  Outside recessions, operating earnings tend to be about 10% above reported earnings, as shown in the first panel of the chart at the bottom of this note (1).  Another way to put this is that inflating reported earnings by 10% allows them to sit atop reported earnings for most of that same period (2).

I hasten to add that inflating up the reported earnings for the historical periods introduces a bearish tilt that would otherwise not be there. Or more precisely, it corrects for the bullish tilt that would otherwise be there. Let’s not get that backwards.  A brighter take on the past makes today look less bright by comparison. I have a bull bias, but I am leaning into it here.

Third, I use the PCE deflator rather than the CPI for all periods over which the former is available. Prior to 1947, I use CPI, just as Shiller himself does. This one does not matter that much, but the PCE deflator is a less inaccurate measure of inflation and I rely on it in other contexts.

Fourth, I “center” my Shillerized series by multiplying the entire history by the historical real earnings growth rate, 1.7%, compounded over five years.  This has zero effect on the shape of the P/E series over time or on that of the related earnings yield.  It does, however, make the scale of P/E more intuitively compelling.  That is you can compare the outputs with more conventional metrics, such as price to one-year trailing earnings.

So with those tweaks in place, what are we looking at here? A few things stand out.

Operating earnings are not even running above their Shillerized value, because the latter has surged, somewhat predictably, on base effects (3). This is interesting to me because it implies that mere Shillerization does not make current period earnings look particularly inflated cyclically. Rather, you get that result only with Shillerization and use of reported earnings. Bears relying on the Shiller CAPE leave every impression of not being aware of this. But at this point, that is water under the bridge. The rally has happened and that technical issue is going to dissipate.

My measure of the Shillerized P/E is 21 ½ vs 27 for the Shiller CAPE.  About 1/3 of this is just due to the centering and is therefore uninteresting, if both series are measured relative to their own history. The rest is due to the other differences in the calculations.

Even with my adjustments, the Shillerized P/E still looks fairly high (4).  At 21 ½, it is 1 ¼ standard deviations above its average for the entire history after 1909. If we look at the period since 1985, roughly the price stability regime, the PE looks a bit less inflated at ¼ standard deviation above average.  This is largely due to the heavy influence of the equity bubble in the late 1990s when the PE rose exponentially.

A fairer way to look at this is to consider the earnings yield, whose distribution is closer to normal. Right now, the earnings yield is 1 standard deviation below its full-same average and ½ standard deviation below its average sine 1985.  This is rich, but not egregiously so.

The low earnings yield is arguably offset to some extent by the low real yield offered in Treasury securities (5).  The real yield on the 10-year note is just 30 bps, which is 1 ½ standard deviations below its post-1985 average.  As a result, the equity spread (defined as the Shillerized earnings yield less the real bond yield) is just ½ of a standard deviation below its all-sample average and ¾ of a standard deviation above its average since 1985 (6).

How to interpret that last point is a matter of great controversy, which totally trumps any quibbling over how to calculate a CAPE.  If the bond yield decline is just a function of an equivalent decline in the corporate sector’s real growth prospect, then the two influences are a wash and it would be wrong to say that lower bond yields support “high” P/E multiples. (Another way to put that is that my equity “spread” does not approximate a proper equity premium.) Alternatively, if bond yields are low for reasons unrelated to growth, then equities are cheap at current prices, particularly relative to bonds.

Goldman’s equity strategists get around this issue by modeling the outlook for earnings directly, rather than using a Shilerization process (merely) to take out the influence of the cycle. Their proper equity premium that has roughly the same shape as my simple yield spread metric, although it is less volatile, I assume because there is information about growth prospects in asset prices. Not every price move is noise. On their work, stocks are somewhat cheap, even taking direct account of this slow-growth environment. I am not sure if that is what the GS strategists are emphasizing now, but it is my reading of that particular indicator.

So what is the net net here? I would say two things.  First, valuation in equities is not yet egregious, so it is hard to pound the table.  I don’t get why the perma bears continue to place such heavy emphasis on the ideas the Shiller CAPE needs to mean revert. That has been quite wrong-footing.

Second, as I have mentioned before, it is possible for equities to be priced roughly fairly, but to to deliver well-below-average returns.  If low bond yields largely reflect slow growth, and if low economic volatility favors a low equity premium (properly construed), then equities may just drift higher, irritating the hell out of all of us — until the next recession.

The return prospect it too dim to be that bullish, particularly if you consider the entire distribution of possible results, including the extreme pain associated with being wrong at these levels. But the heroic bear call does not seem to be there either.  Full disclosure: with me it never is, because it is hard to pay the risk premium.  One needs to avoid base rate neglect, particularly if one is not that bright.  If I were smarter, I could occasionally be bearish.

That is reading a heck of a lot into some pretty crude valuation metrics, but that is the context in which I interpret these charts.  It is subjective. You may have a different interpretation.

Changing subjects radically here, the pseudonymous Jess Livermore reminds me of the real Jesse Livermore, whose fictionalized biography, Reminiscences of a Stock Operator, came off copyright in 2013.  That allowed Tom Rubython to publish Jesse Livermore, Boy Plunger, The Man Who Sold America Short in 1929The new book contains the same trading aphorisms (about which I know nothing) as Reminiscences but also provides a more accurate account of Livermore’s life.  The guy was self-aware, which is always admirable. But what a sad life he led. At the end, he was financially down on the year and down on the life.  And he took that to be all that mattered, the total measure of himself.

One way the real Jesse relates to the fake Jesse and his valuation work is that the former always warned never to commit to the bull or bear side of the market.  As real Livermore would say, using terms irritating to the modern ear, “a man” need not be wed to either perspective.

Yup.  I somehow managed unwittingly to apply that in 2000, at least as a lowly analyst.  But the more books I read, the harder it became for me to pay the equity premium. So the most bearish I can do these days is out.  Solution: don’t read books!