Building a Better CAPE Ratio

October 5, 2022 – After a bit of a hiatus from the blog – thanks to our ambitious summer travel schedule – it’s time for another post. Over the years, I’ve gotten a lot of questions about the Shiller CAPE Ratio and if it’s still relevant. If you’re a regular reader of my blog, you’ll likely be familiar with the CAPE concept, but just as a refresher, Prof. Robert Shiller, economist and Nobel Laureate, came up with the cool idea of calculating a Price-Earnings (PE) ratio based not just on 1-year trailing earnings, which can be very volatile, but on a longer-term average to iron out the corporate earnings fluctuations over the business cycle. Hence the name Cyclically-Adjusted Price Earnings (CAPE) Ratio. If we use a 10-year moving average of inflation-adjusted earnings as the denominator in the PE ratio, we get a measure of market valuations that’s more informative in many instances. For example, historically, the CAPE ratio has been significantly negatively correlated with subsequent equity returns. It’s not useful for the very short-term equity outlook, but over longer horizons, say 10+ years, the CAPE ratio has been highly informative. Especially retirees should take notice because your retirement success hinges a lot on those first 10 or so retirement years due to Sequence of Return Risk. In fact, all failures of the 4% Rule occurred when the CAPE was above 20! A high initial CAPE ratio signals that retirees should probably be more cautious with their withdrawal rate!

But the CAPE has been elevated for such a long time, people wonder if this measure is still relevant. In the comments section, people ask me all the time what kind of adjustments I would perform to “fix” the CAPE. Can we make the Shiller CAPE more comparable over time, to account for different corporate tax environments and stock buybacks and/or dividend payout ratios over the decades? Yes, I will present my ideas here today. And even better, I will post regular updates (potentially daily!) in my Google Drive for everyone to access for free.

So, what do I find? The adjustments certainly lower the CAPE, but don’t get your hopes too high. Even after the adjustments, the CAPE is still a bit elevated today! Let’s take a look at the details…

Before we even get started with the tax and dividend payout ratios, here are two additional and crucial adjustments I always like to perform when calculating the Shiller CAPE. I might have mentioned these adjustments in a previous post, but never delved much into the details. But today is a good excuse to do so…

Fixing Shiller’s data lags

First, Shiller operates with woefully outdated data, especially earnings data. That may not be too much of a problem in typical macroeconomic research projects studying many decades worth of data. But the average retiree likes to have a timely and accurate estimate of the CAPE Ratio. Below is a screenshot from the Shiller Excel Sheet posted on his website. I downloaded this file on October 3, 2022. The first thing we notice is that the data are crazy outdated. The rows only go to July 2022 and the index level not even the month-end but July 5, so almost 3 months outdated. Of course, we can still derive a pretty decent estimate of the October 3 Shiller CAPE. For example, if we use an SPX quote of 3678.43 (=index level as of 10/3/2022, market close) and we rescale the 28.90 CAPE to 28.90/3831.39*3678.43 we get a CAPE of 27.75. But that’s not really precise because the July 2022 CAPE ratio uses the average real earnings over the 120 months of July 2012 to June 2022. But for the October 2022 CAPE, we have to use October 2012 to September 2022 average real earnings. We are using 3 months of data we shouldn’t use and are missing 3 months worth of data that we should be using.

But the data lag problem is even worse. Shiller’s earnings data go only up to March 2022. So, even back in July, he was 3 months short of earnings data. So, we are inadvertently underestimating the “E” part of the CAPE calculation because we’re putting a weight of 1/117 instead of 1/120 on the (significantly lower) earnings numbers from ten years ago. And using Shiller’s data for an October 2022 CAPE ratio estimate we’re now missing 6 months’ worth of earnings data. Excuse me for being pedantic, but that’s not acceptable.

So, how do I deal with the missing data in the Shiller Sheet? The first problem is easy to solve: I simply download the additional SPX index data for the other months. But what about the earnings data? The problem is that even as of October 3, 2022, the earnings for Q2 are not 100% finalized. According to the index provider, DJ SP Global, that Q2 number is “only” 99.8% final, so there are still 0.2% of the index members that haven’t finalized their number (link to their Excel Sheet).

Well, 99.8% is obviously good enough. And remember, the 99.8% refers to the current quarter. Shiller uses the 4-quarter moving average, so the estimate for the annual trailing earnings per share (EPS) is really 99.95% finalized as of 10/3/2022. So, I can certainly use the $192.26 estimate for June 2022. (also notice that, just as a quick check, the 197.91 and 197.87 figures for 2022Q1 and 2021Q4 exactly match the Shiller numbers, so he’s getting his numbers from the same source.)

And while we’re at it, I am also using the subsequent earnings forecasts for Q3 as the September EPS number in my table. And just like Shiller, I linearly interpolate the EPS for the months in between. And I concede that these are only forecasts, and sure, the forecasts may be off. But not using the SP Global estimates and effectively using the average over the 114 past months as an estimate for the six missing months is also a forecast and likely one with an even greater error!

In any case, I wrote a little Python program to perform the Shiller CAPE calculations, but instead of using the outdated Shiller EPS data, I access the SP Global data and fill in the missing earnings data and use the earnings estimates of the index provider instead. See the output below:

Month-end vs. monthly average index data

One peculiar feature of the data displayed above is that I get different SPX index readings. That’s because Prof. Shiller uses monthly average index levels, while I am using the month-end figure (or the latest available in the current month). In fact, using the month-end index levels is the second change I like to make in the CAPE calculation. Just to be sure, there is no correct or incorrect way. For example, as a macroeconomist, you might indeed be more interested in the average valuation of the S&P 500 during the month of September 2022. However, if you’re a retiree and pondering about what’s the right withdrawal rate today, then you’d be better served using today’s S&P value and not a 31-day moving average. That’s because you will sell your equities at today’s price not an average price over the last month. So, with those two adjustments, the table below is a sample of the most recent CAPE calculations.

Notice how the estimates can be significantly different. For example, in April, my CAPE (31.94) is almost 6% below the Shiller CAPE (33.89). That’s because the index finished significantly below the monthly average. Differences like that will certainly have a meaningful impact on your CAPE-based withdrawal rate. You don’t want to be sloppy about that. Precision is important in retirement planning!

And I want to make one thing really clear: I’m not trying to ding Prof. Shiller’s methodology. It may be correct in another context. But for our specific application, using the most recent index value and padding the EPS data with the currently available estimates makes the most sense.

Sorry about the deep dive into the CAPE methodology. For the three to four readers that haven’t fallen asleep yet, let’s talk about the issues mentioned in the intro now. One criticism of the Shiller methodology is that the CAPE has been elevated for such a long time. It seems that a CAPE ratio in the high-20s in today’s market seems a lot more sustainable than in the 1920s or 30s. What could be responsible for this shift? I found an interesting post by a guy called Damien Klassen on a financial planner website that proposes adjustments for both corporate taxes and share buybacks. I liked the way he models the corporate tax adjustments and I will use his methodology one-for-one. But I will use a slightly different approach for the buybacks, more on that below.

Accounting for the lower corporate tax rate

First, why do we want to adjust for corporate taxes? Imagine there’s a corporation that generated (CPI-adjusted) pre-tax earnings of exactly $100 a year for the last 10 years. During the last five years, corporate taxes were 21%, and thus the corporation earned $79 after-tax. The five years before that, corporate taxes were 35% and the company earned $65. Your average 10-year rolling earnings were $72. But $72 is a really poor estimate for the earnings trend. Your tax rate today isn’t 28% but 21%. Thus, the Klassen adjustment takes all past earnings and divides them by 1.0 minus the then-prevailing tax rate to get a sense of the pre-tax earnings. And then you apply the current corporate tax rate to all past earnings. Klassen thus calculates the 10-year after-tax rolling earnings per share (EPS) as if today’s corporate tax rates had been in effect for the entire past 10 years. The reason for this adjustment is that it would take an entire 10 years for a tax cut like the 2018 corporate tax reduction (from 35% to 21%) to work itself through Shiller’s CAPE calculations. The Klassen adjustment applies the tax impact instantaneously, exactly when the tax cut happens.

Thus, whenever corporate tax rates have decreased, our adjustment will increase the rolling average EPS used in the denominator and thus lower the CAPE, increasing the valuation-based attractiveness of stocks. And by the way, if the corporate tax rate were to rise again, and there are some rumblings in Washington D.C. right now, then this effect reverses and the adjusted Shiller CAPE will look unattractive again.

Accounting for share buybacks

The second adjustment has to do with share buybacks. Mr. Klassen doesn’t spend a lot of time explaining the rationale behind his adjustment. So here’s my take. Imagine we have two very similar corporations: Corporation A and Corporation B. They each have $1,000 of capital that generates $100 in CPI-adjusted profits every year for each corporation. They are also both valued at $1000. Imagine they each have 100 shares in circulation, valued at $10 a share.

Corporation A pays out all of its earnings as dividends, i.e., $1.00 per share. Corporation B retains all its earnings and simply buys back shares in the equity market. Thus, the investors in corporation B, in lieu of receiving a dividend, will see their share price increase by 10% every year. And if they want to get the same cash flow as the Corporation A shareholders they simply sell 10% of their shares every year. On average, people would have to do so anyway because of the buyback demand.

In a perfect world then, investors should be completely indifferent between the two corporations. You make 10% p.a. and people shouldn’t care if they get their 10% return through dividends or capital gains. Of course, in a slightly imperfect world, retail investors with taxable accounts might prefer corporation B because you can defer your capital gains taxes. But let’s abstract from that issue. A lot of retail money is in tax-deferred accounts and a lot of institutional investors (pension funds, endowments, sovereign wealth funds, etc.) don’t pay income taxes directly either; only the retirees that will eventually get the benefits will pay income taxes. In any case, we should agree that the equity return from investing in the two corporations will be identical in a perfect world and close to identical in the real world.

What would be the CAPE ratio of the two corporations? Corporation A had $1.00 earnings per share in each of the last 10 years. With a share price of $10.00, we get a CAPE of exactly 10. People might be tempted to argue that Corporation B has the same CAPE. But that’s incorrect! Recall that Corporation B has 100 shares now, but the share number has been declining by 10% every year. So, one year ago, we had 100/0.9=111.11 shares. Two years ago there are 100/0.9^2 shares=123.46 shares, and so on. Thus, earnings were only $0.39 a share at the beginning of the 10-year window and then grew by 10% each year to reach $1.00 in the current year, see the table below. Thus, the rolling 10-year average EPS in Corporation B was only about $0.65 vs. the $1.00 in the dividend-paying company.

This implies a CAPE of 15.35, more than 50% above the CAPE of the dividend payer. Thus, share buybacks would consistently hurt CAPE valuations relative to dividend payers. To adjust for this disadvantage, Klassen proposes to make an adjustment to the EPS to account for the changing number of shares. Specifically, he scales up the past EPS numbers to exactly undo the effect of the shrinking share base due to the buybacks. Basically, scale up corporation B’s EPS sequence [0.39,0.43,…,0.90,1.00] back to [1.00,…,1.00] to make it comparable to Corporation A.

Accounting for all retained earnings

I agree with Klassen’s general idea, but there are two problems with his approach: First, I don’t trust the share buyback data, certainly not the historical data. And second, not only buybacks, but any kind of reinvestment of retained earnings should trigger an adjustment in the CAPE. To illustrate this point, let me introduce Corporation C. It pays no dividend and it does not buy back shares either. Instead, it uses its corporate earnings to grow its productive capital. We could imagine that this corporation purchases more machines that will yield that same 10% return on equity. Or alternatively, this corporation might even purchase shares of the other two companies. In either case, if I assume again that Corporation C also has 100 shares outstanding and $10 in earnings in 2022, then the stats for Corporation C look as follows, see the table below. We get the same messed-up CAPE ratio, even though this company generates the exact same annual returns per share as the other two corporations:

Summary so far: an adjustment has to be made not just for buybacks but for all retained earnings, provided they are directed at investments that are at least as profitable as the return on equity (ROE) of the overall corporation. That certainly doesn’t have to be the case for all corporations. Some companies have a terrible record of investing – looking at you General Electric under Jeffrey Immelt. But for the economy as a whole, that should be a good assumption.

And you know what’s the advantage of taking into account all retained earnings? Data availability! Screw the whacky buyback data because we do have reliable earnings and dividends data. We can just calculate the reinvestment percentage equal to the earnings yield minus the dividend yield, create an EPS scaling factor equal to 1.0 in the current year and then compound the growth in that scaling factor from reinvested earnings going backward. If you’re interested, Klassen posts his Excel Sheet and he shows how he calculates this with the buyback percentages. I use the same methodology but I simply use the earnings minus dividend yield numbers instead of the buyback percentages.

So, with all those adjustments, what CAPE ratio do we get today, as of 10/3/2022, when I’m writing this? That’s in the table below. We go from a 26.59 CAPE without adjustments to 21.40. That’s a 20% drop in the CAPE Ratio. Quite meaningful. But keep in mind that even at that CAPE we’re significantly above historical average CAPE ratios (about 15). So, we’d still expect below-average returns going forward.

Here’s the same chart as in the blog post header again, the CAPE time series since 1925. The adjustments didn’t make a large difference in the 1920s and 1930s. From the early 40s to the mid-50s, the adjusted CAPE was even higher than the unadjusted one (due to a rise in corporate tax rates). Only in the mid-1980s did we really see the adjusted CAPE come down, as a result of both corporate tax rates as well as dividend payout ratios moving down.

And here’s a time series chart since 1970, when the adjustments are really the most noticeable. Instead of plotting the CAPE, though, I transform this into an earnings yield (one divided by the CAPE), so this would be a series with a positive correlation with future earnings.

There are meaningful differences. In the late-1980s the adjusted CAPE yield was about 2 percentage points higher. It didn’t make too much of a difference during the dot-com bubble and more recently we see an impact of about one percentage point. But of course, the CAPE adjustment can’t so easily explain away the crazy CAPE valuations we’ve had over the last two decades. Even with the adjustment, earnings yields are still low compared to historical ones. Indeed, looking at longer-term averages in the table below, we see that the average CAPE yield has been about 6.78% (roughly a CAPE of 15, the widely-cited historical average) over the last 100 or so years. The standard CAPE yield since 2000 has been only 3.87 (a CAPE average of about 26). Even with the adjustment, we can lift that most recent CAPE yield to only 4.55%. Still much lower than long-term averages. But keep in mind that a 0.67 percentage point (absolute) increase, is still a relative increase by more than one-sixth. For example, if someone wanted to tie his or her withdrawal rate to the CAPE, then the withdrawal rate may only go up by 0.67 percentage points, but the annual withdrawal amounts will rise by 17.37%. That can be tens of thousands of dollars annually!

Oh, and before I forget, I post my CAPE numbers, specifically, the entire time series since 1871, here on my Google Drive:

https://drive.google.com/file/d/1ugtRN3TaAVwQi-20mjt4DctF-glppSMD/view?usp=sharing

Please let me know if you have trouble accessing the file. As usual, you can view the file, but before you do edits, you’ll have to download it to your own computer and/or Google Drive. I will run this (almost) every weekday, so you should be able to get regular updates on the most recent CAPE estimates, both the standard CAPE.ERN.1 and the adjusted CAPE.ERN.2. And for fun, you can also monitor how hopelessly outdated the Shiller numbers are. 🙂

Update 1 (9am 10/5/2022)

Someone in the comments section pointed out that Frank Vasquez from the “Risk Parity Radio Podcast” recently had an episode criticizing valuation in general and the CAPE ratio in particular. If you don’t want to listen to the whole thing, the relevant part starts at the 25:00 mark. The “definitive proof” he puts forward: The CAPE was high in 2011 and subsequent returns were high as well. One single counter-example!? Well, that’s not really proving anything. Even if he had found one single counter-example it would only weaken, not eliminate the case for the CAPE. But Frank’s argument is even worse! In fact, his precise example works in favor of the CAPE ratio. The 2011 CAPE earnings yield (using my new adjusted series) hovered around 4.6% and subsequent returns were almost 14% (Dec 2011 to Dec 2021). But guess what? Compared to the valuations prevailing during that time, say starting in 2000, we get a beautiful positive correlation between valuation and subsequent returns. 2011 had much more attractive valuations than 2000 or 2007, right before the respective bear markets starts. And 2011 had much better subsequent 10-year returns than 2000 or 2007. Thanks, Frank, for providing more proof that valuations matter!

Update 2 (10/11/2022)

Someone in the comments section asked if there’s any evidence that a lower dividend payout ratio coincides with higher real EPS growth. Let’s plot the two series, see the chart below. The blue line is the log of the real EPS (normalized to 0 in 1871). Because of all the business cycle fluctuations, it’s not that easy to see, but you will notice that between 1871 and 1945 you had a pretty slow average growth rate (0.0->0.75) and a lot of the growth in real EPS came after that (0.75->3.0). In fact, it’s quite clear that a linear trend line will not fit this blue line very well. The fitted curve (dotted blue line) is a quadratic line, which beautifully creates an accelerating growth rate (=slope of the dotted blue trend line). So, in other words, the earnings trend growth rate accelerated when firms retained more earnings.

Conclusion

Time to wrap up since we’re already pushing past 3,000 words. To sum up, we can easily fix Shiller’s data reporting lags and we can certainly apply some adjustments to the Shiller CAPE. But the measure remains solidly above its long-term average, even after the major drop this year. What does this all mean for retirees? Initially, I had planned to make this part 54 of my Safe Withdrawal Rate Series with additional calculations on how the different CAPE Ratio scenarios impact your retirement safe withdrawal rates, but I will defer that to another post, hopefully in the next one or two weeks. Stay tuned!

I’m glad you stopped by today! Looking forward to your comments and suggestions below!