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.

Screenshot from Shiller CAPE Excel Sheet, as of October 3, 2022. Source: http://www.econ.yale.edu/~shiller/data.htm

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).

S&P 500 EPS estimates as of 10/3/2022. Source: SP Global. https://www.spglobal.com/spdji/en/documents/additional-material/sp-500-eps-est.xlsx

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:

Python output with updated EPS data. October 2022 index close refers to 10/3/2022.

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.

CAPE Ratio estimates: Shiller vs. ERN. October 2022 estimates are based on 10/3/2022 data.

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.

Klassen adjustment for changing corporate taxes.

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.

Stats for Corporations A and B. Due to the share buybacks in Corporation B, we spread the $10 in earnings over the larger share number resulting in lower EPS and a 53.3% higher CAPE!

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:

Corporation C pays no dividends and does not buy back shares. But investing the retained earnings creates the same quirk in the CAPE ratio!

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.

CAPE.ERN.2 is the new adjusted CAPE taking into account corporate tax rates and earnings retention ratios. I also throw in the 12-month trailing PE Ratios.

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.

CAPE: old and new since 1925.

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.

CAEY (=CAPE Yield) since 1970

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!

CAPE earnings yield (=1/CAPE) averages.

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!

Equity valuation (x-axis) vs. subsequent 10-year annualized return.

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.

Log of real, CPI-adjusted EPS (blue line, left axis) and 120-month rolling average dividend payout ratio (orange line, right axis).

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!

119 thoughts on “Building a Better CAPE Ratio

      1. Yup. I pretty much just used Shiller’s data page and didn’t really make an effort to extend CAPE / adjust CAPE since I would be looking at 10 – 30 year returns after the period with the CAPE. I couldn’t really evaluate that for anything after 1992.

        1. Are these conditional returns nominal or real? Total return or price return?

          I would probably use shorter windows. 30 years seems too long. Maybe try 10 years and then you can extend the study to include dot-com and global financial crisis.

    1. OK, I started listening to the podcast and it was painful but I made it to minute 27 where he “attacks” mean reversion and the CAPE ratio. He’s wrong. He uses one single example where a high CAPE ratio doesn’t produce a low 10-year return. That’s not refuting anything.
      And mean reversion does not rely on a Normal distribution either. Not sure where he gets that idea from…

      1. What I agree is the excessive pessimism around the SWR and the lower someone comes up with it the more “respected” that person is.
        The technicalities I don’t fully understand but if you say he’s wrong I think you know better for having worked at the FED.

        1. The reason you don’t understand his technicalities is that there were no technical arguments made on his podcast. Certainly none that would refute the usefulness of the CAPE ratio.

          By the way, I’ve taken on the excessive pessimism. Remember my post dismantling the stupid post by Financial Samurai (0.5% SWR)?

          And I’ve done a lot of work factoring in supplemental cash flows of early retirees and I have shown that some people can push their WR close to 5% or even above,
          But I’m no fan of the excessive optimism in the FIRE community either.

          1. Yeah I agree. To be fair I don’t understand much of your technical posts as well but I agree with your take. All in all, people will find SWR lower than 4% and above 4% but I still think 4% is the best number for the absolutely majority of people. There’s a lot of discussion but in the end the mean number is 4% and that’s not pessimistic and not optimistic, just right.
            Of course, the ability to make adjustments on the journey are more important than the absolute number you plan on using.

                1. Haha, sorry didn’t record this. But we had a very pleasant conversation. I just wanted to make sure Frank doesn’t put me in the bin of “intellectually lazy people”. He insists he doesn’t. And we had a great chat. He’s a funny guy.

  1. This is a great analysis – thank you! I am still left wondering whether there is also an element driving the price piece higher in the current environment, such as a greater amount of investable assets chasing the same asset class(es). I don’t know if there is a methodologic way to get a macro view on that. Just a thought.

    1. And I think that may be the missing piece explaining drop in the average CAPE yield.
      It’s obviously a bit of a circular argument: There is a lot of net worth flushing around BECAUSE the stock market is so highly valued.
      But decade-long easy monetary policy and vast money growth might be the culprit for the whole thing.

      1. Happened to start reading the collab fund blog by Morgan Housel yesterday. One of the links in his article pointed me here:

        http://www.philosophicaleconomics.com/2018/01/future-u-s-equity-returns-a-best-case-upper-limit/

        Granted it’s 4 years old, but wanted to get a flavor for what this person was discussing.

        In it, he calls out the impact that pension funds have significantly increased their equity allocations over the last 50 years. Not sure how much capital that represents as a % of total market cap, but thought it was an interesting data point to consider as we think about increasing CAPE ratios.

        Haven’t gotten my head around all the implications or whether they’re truly meaningful, but thought it fit in well with this discussion.

        1. Great read. Similar to my old post here:
          https://earlyretirementnow.com/2017/08/09/us-equity-returns-history-and-10-year-forecast/

          There’s a limit to how much PE ratios can expand. It’s impossible to pinpoint the exact expected return and the pinpoint the turning points. Likely you’ll end up with a post that doesn’t age well for a number of years when stocks keep rallying. But who knows, maybe the dire return expectations from Bogle back in 2017 will still come to pass. 2027 a a long time away!

  2. Karsten, perfect timing! I’ve been digging into this lately. Thanks so much for this detailed post.

    On tying withdrawal rates to CAPE: Can we assume a simple rule-of-thumb that withdrawal rate = 1/CAPE, or is that too simple?

    1. I wouldn’t. Too much risk of depleting assets!

      I would use a lower slope, only about 0.5. And then add an intercept.

      For example:
      WR = 1.75% +0.5/CAPE

      One could even raise that a little bit to maybe 2%+0.5/CAPE.

      See Part 18 of the SWR series.

      1. Do I use today’s CAPE or “Previous Month”?
        Today is Oct. 6, 2022. Do I use a CAPE value from 2022-08-31, 2022-09-30 or 2022-10-06?

        Huge fan of your work. I quit work in 2018 and my wife and I use your CAPE method to calculate our SWR. I may be a bit conservative, I use 1.5% + 0.5/CAPE. (And then we spend even less.)

        In today’s post there is a big difference in CAPE.ERN.1 and CAPE.ERN.2 this month. I am not sure I am ready to use CAPE.ERN.2.

        1. Thanks!
          I would use the CAPE as of today not last month. The difference will likely be due to the change in the S&P 500. The two different EPS measures have an overlap of 119 out of 120 months, so that would be the same.
          Well, if you can make the 1.5+0.5/CAPE SWR work even under the old CAPE of 27, then good for you. But I thought I might be able to give an alternative to people who have not saved as well as you.
          Congrats on your retirement!

      2. Would you recommend using your adjusted CAPE or the standard CAPE when doing this rough WR calculation?

        1. I would recommend using the new adjusted CAPE from now on. That’s why I built it.
          But caution: those CAPE-based SWRs don’t factor in (partial) asset depletion and/or supplemental flows. Stay tuned for SWR Series Part 54, coming soon!

      3. At today’s adj. CAPE of 21.379 and an intercept of 1.75% and a slope of 0.5, the WR is greater than 4%.
        I wasn’t expecting that!

        WR is almost 4.4% when the intercept is 2%. Wow.

        Thanks so much for posting your CAPE numbers on google drive.

  3. While I’m not great at math, it is very interesting to see someone tackling CAPE to try to figure out a better way to measure valuations over time. Looking forward to part 54!

  4. Yes I stayed awake, and this was a fun read, because it addressed each of my “what about…” concerns as I thought them. My final thought – “what does a ~4.x% adjusted CAPE yield mean for SWRs” – is something I’ll have to watch and wait for. However, the last chart showing adjusted CAEY looks roughly like what I would expect the SWR for a 100% equities portfolio to look like over that same time period. We already know that unadjusted CAPE correlates with past SWRs, so improvements on CAPE can only get us closer to predicting future SWRs.

    If you can correlate adjusted CAEY with SWRs, then you will be 90% of the way to having a model that prescribes an optimized, SWR-specifying asset allocation based on current bond yields and current adjusted CAEY. If said model backtests well, you could have solved or beaten the 4% rule dilemma by specifying a dynamic AA that changes according to a relatively simple model.

    1. Yes, that’s the plan, stay tuned for SWR Series Part 54.

      One caveat with CAPE-based rules: If the market falls and you recalibrate the SWR (rate will be higher) but apply that to the diminished portfolio, then your withdrawal amounts will be lower during a recession. Unlike the static withdrawal calculations in my Google sheet.

      So, CAPE-based usually allows higher rates but with some volatility around those withdrawals. It’s a risk/return tradeoff!

  5. Doesn’t CAPE use GAAP earnings (after non recurring) versus estimates that use operating earnings (before NR)?

  6. I can’t wait to read about the historical simulations and impact on SWRs! And then for Toolbox 3.0 (2.1?) that uses ERN-adjusted CAPE :-).

  7. Hi Big ERN, This is my first comment but huge fan and long time reader of your blog. But I hope you don’t mind but my questions are not about this post but I was wondering if the dramatic rise in interest rates in the past year has altered your opinion on bonds or you think it has any impact on SWR’s? And I was also wondering if you have continued to use PFF as part of your option strategy as preferred’s and other bond like securities have got hammered in 2022 along with bonds or are you now using something else? Thank you.

    1. Both good questions.

      I said elsewehere that the 10y bond is certainly a buy at close to 4%.
      TIPS at 1.5-1.9% real yield (depending on maturity) also look really good.

      I have no more PFF in my portfolio but I’d rather use the underlying preferred shares, most of them floating-rate to hedge against rising rates. See section 8 in this post: https://earlyretirementnow.com/2022/07/05/hedging-against-inflation-and-monetary-policy-risk/

      1. If you want variable rate preferreds, there’s PFFV. However when recession hits it will be a better deal to lock in long-term yields with non-floaters from the clearance shelf.

  8. One thing I struggle with in using CAPE-based methodology to inform future returns is the sensitivity to cost of cash / discount rate / fed funds rate.

    With all this talk of “regime change” with perhaps rising interest rates to stay, that could degrade PEs for quite a while. And of course it could all be noise.

    But stick with a conservative set of assumptions, and assuming rising interest rates are a medium to long term trend, my intuition is that you’d see CAPE move like it did in the 70s – ever lower. With ensuing risk to the retirees portfolio and a nasty sequence of returns for early retires.

    Your thoughts appreciated!

    1. That’s one of my concerns too. Once interest rates and monetary policy normalize again, we might drift to a lower “normal” CAPE again. Not the best news for the stock market if we go back to a CAPE=15 again. Another 30% down, compared to today’s adjusted level of 22.

      1. Exactly. There is a plausible scenario that the stock market goes down or stays flat due to interest rate policy. So CAPE on its own really can’t predict what happens in the short to medium term (which I think is the primary goal of the crowd here – trying the answer the question “can I retire in the next 5 years?”)

        Some further musings – it feels to me that the fed funds rate needs to be accounted for in any use of CAPE as a predictor of future returns. Just looking at the fed funds rate since 1970 vs. CAPE earnings yield appears as near mirror image of each other. E.g. CAPE is very sensitive to interest rates.

        For CAPE to be useful as a near/medium term predictor it seems to me that you need to make an assumption on the cost of capital somehow include it.

        Question – in what time frame does CAPE seem to have statistically significant predictive power? 20 years?

        Looking forward to seeing your analysis as you grapple with this in the SWR series

        Thanks Karsten, appreciate all you do!

        1. The time frame should be around 1-10 years. And within that, it’s concentrated in the front end and then dies out toward 10. I don’t think there’s any statistical info of today’s CAPE when predicting year 11 returns. Even years 7-10 would be a stretch.

  9. Can you share your source code for the computations? I am really interested in playing with it and tweaking parts to see how things change. As always, thanks for such great analysis!

      1. I am asking because I am not able to recreate the numbers you are getting when I use those spreadsheets and I am not sure why. I end up with a CAPE (using what I believe is the information you posted above of 22.923 where you get 21.058 for 2022-09-30. I must have something off…

        Also, when I correlate your data with the real 10Y yield I get an R-squared of 0.157, but with my calculations I only get 0.149.

        Without your raw data or how you are performing the calculations I am at a loss for verifying this myself. Do you have any guidance?

        1. Yeah, as I said, I don’t provide the code. And I don’t even attempt to debug other people’s calculations on this. Too many moving parts.
          But a few pointers:
          1: Klassen shifts the corporate tax by 6 months to take into account that tax changes are anticipated and priced in 6 months in advance.
          2: There’s missing dividend data after June. I use the Python “.ffill” method to fill in missing data.
          3: CAPE calculations always use a 1 month lag, i.e., for September 2022 you use the September 2022 index close, but the September 2012 to August 2022 real earnings.

      2. Is there a reason you won’t post the source code? It’d be nice to verify the results and/or be able to reproduce them going forward in case you lose interest or something else happens. Thanks for the great content!

  10. Given CAPE is looking historically, I have always used it as a marker for a trend and I’ve not given considerations to the details you covered. So I am actually pleased to see your analysis does not throw my planning off course. Great read and never too long at all.

  11. Karsten,

    Welcome back – you were missed. This was a interesting and thought provoking read (no shut eye here). I always look forward to your insightful, penetrating work. Looking forward to Part 54.

    I am struggling with the CAPE concept though. The current price is all about my expectations of future earnings (it is what I care about). However, CAPE uses trailing 10 years of earnings (appropriately adjusted). Conceptually, it seems just wrong and out of whack to be a useful predictor – using the past 10 years to predict the future 5-10 years. There may be some correlation (history repeating, momentum and trends), but I do not see the causation.

    Someone once said in the short term, the market voting machine (supply & demand for a share), and a in the long term, the market is a weighting machine (weight being future earnings).

    1. It does sound counter-intuitive. Correct! Why use even more backward-looking data?

      Because macro variables (GDP, earnings, stock prices, etc.) are all fundamentally linked. They clearly deviate and pull away from each other, but mean reversion pulls them back again. Longer-term average EPS trends are often a better estimate for futures earnings than the last 1 year or even a market “expert” forecast.

    2. My explanation is that we are actually investing in the continuation of a centuries-long trend in which more and more people specialize in more and more activities that are more and more productive at generating value. I.e. the descendents of subsistence farmers around the world are working in manufacturing plants today, and instead of generating no surplus they supply thousands of people with something they want. In other places the descendents of manufacturing workers are designing software or curing cancer, which are things that could revolutionize productivity and how we accomplish things.

      All this aggregate behavior cannot be summarized as “earnings” – it is better described as the production of economic surpluses. The reason you live a more luxurious lifestyle than the kings of just a few generations ago (AC, air travel, vaccines, running water…) is because so many people are behaving in a way that generates economic surpluses – producing more satisfying things than their labor costs. As Steven Pinker points out, wars over resources are getting less and less common, and I think this is because the easier and less risky way for an ambitious leader to make a fortune is to start a business. “Earnings” are a twitchy and abstract measure that does not directly measure the trend we are investing in.

      GDP, stock index earnings, standards of living, cash flows, etc. are just different ways of measuring this overall behavioral shift toward production, which is only ever interrupted for a few years of recession at a time. CAPE is useful for spanning a wide range of time to identify the value of assets relative to a long-term trendline. You want to rise above the noise of any given metric and be able to state, amid a recession or panic, that investing in the trend is or is not a bargain right now because prices are or are not below a long-term trendline.

      1. Chris & Karsten,
        Thanks for your thoughts. I would concur that “CAPE is useful for spanning a wide range of time to identify the value of assets relative to a long-term trendline” at least when aggregating a large piece of the economy and only as one benchmark. The correlation is not great. But it will mislead you when there are fundamental changes – taxation changes (the new “book income” tax, shifting HQ to low tax countries), privatization (spin off of divisions removing the earnings from the S&P500), and new tech enhancing productivity (internet).
        Cheers and keep up the great prose and insights.

  12. Thank you for the article. One question on compensation for share buybacks — I am wondering if instead of arithmetic mean of EPS over the present SharePrice, ideally, geometric mean of EPS/SharePrice over the years should be used instead. Geometric mean could be justified since we usually imply year-over-year reinvestments. With geometric mean, there seems to be no need to correct for share buyback.

    1. No, you don’t want to use a geometric mean of EPS(t)/SPX(t). That’s not the spirit of the Shiller CAPE. You take the arithmetic mean of EPS(t) and relate that to one single SPX(T) at the end of the window.

  13. Karsten,
    If you make an adjustment for stock buybacks, then shouldn’t you also adjust for new shares sold – dividend reinvestment, stock option exercises and secondary offerings. Or at least, adjusting for the net buybacks. As you know, many companies buyback shares to reduce (or eliminate) the dilution for all of the issues (and eventually exercised options).

    1. So, if a company issues $100 million in stock options and buys back $100 million worth of shares, it’s a wash; existing shareholders have not benefitted. If the company buys back $150 million in shares, only $50 million of the buyback really benefits shareholders.

  14. Thanks Karsten, I’ve bookmarked your link as one of my key metrics to check in on. I would be interested in your take on how the current interest rate and QT compares to how far the Fed will need to go. I’ve heard you mention it several months ago on a podcast.

    1. Thanks!
      My worry is that the Fed has to go much further than people realize right now. The current estimates (FFR top at 4.5%) are all using the most optimistic assumption that CPI is moderating soon. I don’t see that. We could go to 6%, even 8%. But I certainly hope we don’t have to go that high.

  15. Maybe instead of building a better CAPE ratio, we should look at doing something with an aggregated Economic Value Added (EVA) metric [EVA is is NOPAT – (InvestedCapital – WACC)] and creating a CAPE-like trendline of entire indices off of that. Easier said than done, I know.

  16. You really are a treasure to many of us so thanks! I was curious if you still planned on wrapping your SWR series up into an eBook at some point along with maybe an updated Google sheet. I guarantee that I’ll be first in line to buy! I have some of your posts printed out hardcopy to flip through, cut and pasted some others into a quick summary guide, and have rebuilt your Google sheet more than a few times. Enjoy your retirement, but I think that a market exists for something like this. Cheers.

    1. Ahhh, yes, the book. It’s 2/3 done but I get distracted and have a hard time finishing it. Once it’s 90% done, can I count on you as a test reader? As a thank you, you will get the final book for free.
      Well, there you go, I gave a away the book for free to one of the few paying customers. 😉

      1. I appreciate the CAPE post. I’m not a math person but I’ve been interested in this for some time.

        Nice – a SWR book would be great. I find myself going back to different posts to get additional detail or answer a question. AND an updated Google sheet would be awesome.

        The entire website has been helpful as a resource for managing our retirement finances.

      2. Yes, I will be a test reader. Yes, I’m the same one that bugged you on this before. No, I expect to pay full boat for it when it is done. With what you have given me I wouldn’t have it any other way. With Alan H. below, that is at least two book sales! Flying off the virtual shelves for sure!! At $15 x 2 locked in, and another 200 hours…$0.15/hour. Consider it a labor of love, or a legacy. Alan H. hit on something below about not being a “math guy” which is interesting. I’m very much a math guy as an early phase development engineer for the last +20 years. There are two levels to your posts which I’m sure you are aware of, although you blur them together. One that can be digested by everyone and fun to read, and one that goes deeper into the math. Since it is 2/3 done I’m not sure how you approached this, but I find it an interesting way of organizing things. My wife is a former Random House publicist and thinks your specific perspective and voice has unique value and is worthy of publishing in a fully legit way. I think many would agree.

  17. “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.”

    Not really. If you want the long term equity outlook it can be predicted almost perfectly, don’t bother with this valuation crap with a R2 under .5

    https://www.philosophicaleconomics.com/2013/12/the-single-greatest-predictor-of-future-stock-market-returns/
    https://financial-charts.effingapp.com/

    1. It’s always better to have more signals, not fewer signals. The fact that you can’t grasp that and you call a valid and useful signal “valuation crap” (ironic when your signal is also a valuation metric) just shows that you’re really not very serious.

  18. Hi! Always great reading on this site!
    Can you explain how to figure historical CPI with your adjusted spreadsheet? Shiller indicates 2.26% (1871-2021) and I was wondering if there is a difference with your data. Regards,

  19. So glad to see you taking on this desperately needed “version control/apple-v-orange” problem with CAPE.

    Do you know how often Shiller’s site gets updated? Is he following a schedule or is it just whenever he gets around to it…?

    e.g. Is it “normal” for his data to get this far behind (e.g. Oct 8 vs July 5 data)

    Anxious to see your next chapter in this thread….

    1. He doesn’t update his sheet very frequently. Maybe his research assistant is on summer break. But a 2-3 month gap is normal.

      I wrote a Python code that generates this automatically, so I can run this daily. Saves me a ton of time. But there was significant time spent setting up the code. 🙂

  20. A question regarding your adjustment to include the effect of all retained earnings. It sounds like you’re assuming that all retained earnings are (on average) invested productively. But, historically, periods of lower dividend payout ratios are NOT followed by higher earnings growth – which is what I think (?) your assumption would predict. Isn’t that a problem?

    1. “But, historically, periods of lower dividend payout ratios are NOT followed by higher earnings growth ”

      Disagree. Ever since the dividend payout ratio dropped real EPS growth has accelerated. In contrast, early on, when almost all earnings were paid out as dividends we saw very little real EPS growth.

        1. I don’t disagree with their findings.
          But consider this: In anticipation of an economic downturn, dividends are cut. Then the downturn happens and earnings decline. Does that mean that the dividend cut caused the economic downturn? Post hoc ergo propter hoc fallacy!

          I’m operating off the longer time series chart looking at real EPS. Put it on a log scale and you see a clear trend break to higher trend growth, exactly at the time when the average S&P dividend payout ratio dopped.

          In other words: Arnott and Asness are regressing the *fluctuations around* the trend. I’m operating with the trend growth rate itself. I hope you see the subtle (or not so subtle) difference.
          For my research project, my approach is more useful.
          But I admit: If you ever want to forecast 10y ahead earnings and returns or SWRs, it might be useful to throw in not just the CAPE but also the D/EPS ratio as an additional variable.
          Thanks for the link and I will put that on my to-do list! 🙂

          1. Interesting, thanks; you wrote: “I’m operating off the longer time series chart looking at real EPS. Put it on a log scale and you see a clear trend break to higher trend growth, exactly at the time when the average S&P dividend payout ratio dopped.” – would it be possible to post this chart for us to see?

              1. Awesome, thanks.

                One might worry that if you consider buybacks alongside dividends, the orange line in the graph would actually trend upwards quite strongly over the past 3-4 decades. Since you’re suspicious of buyback data, maybe that doesn’t worry you?

                1. No. I’m interested in the D/EPS. Buybacks are contained in the 1-D/EPS portion, and if I don’t trust them then any error in the buybacks would show up in the retained earnings, which is also a part of 1-D/EPS. It’s a rob Peter to pay Paul deal. D and EPS are very transparently observable and don’t rely on the whacky buyback data.

      1. I have now tried it again with my computer. All the data is there. Obviously not everything is displayed correctly on the iPad.

  21. How do feel about plotting your earnings yield (one divided by the CAPE) side by side with constant maturity treasury yields?

    10-year treasuries and 30-year treasuries for example.

    To show how they move together, or don’t move together.

    Finally, add me as one of the buyers of your book. I am definitely willing to pay full price for something that documents an objective way to determine SWR.

    1. Yes, and it’s useful in the following context: In an asset allocation context, it’s not enough to determine whether stocks are cheap or expensive. Cheap relative to what? When you move the money out of stocks you have to put it somewhere: 30y bonds, 10y bonds, money market, etc.
      So. in the context of using this measure, yes, compare it to other expected returns! Good point.

      Thanks for the kind words! I got 3 buyers already! Yay! 🙂

  22. Thank you for the interesting analysis, BigErn. Very thought-provoking and I really appreciate you sharing the spreadsheet with ongoing updates!

    Have you thought about incorporating prevailing risk-free rate (e.g., rate on Treasuries or Fed ‘s fund rate) to adjust the CAPE even further? I am thinking that earnings are worth more or less depending on the prevailing interest rates.

        1. No. What if both equities and bonds have are really low? I’m interested in the absolute return, not the relative return.
          Though, for asset allocation decisions, i.e., tactically shifting between equities and bonds and/or cash, I’d certainly look at the relative yields.

  23. There are a few things here that I don’t understand
    – Why does it make sense to apply the current effective tax rate to past earnings that were subject to a different tax rate? Isn’t stock value subject to the cumulative effect of reinvested earnings that, at the time, were subject to the tax rate at the time they were reinvested?
    – Before TCJA, corporate taxes had brackets, just like individuals – only the max marginal tax rate was 35%, meaning the effective tax rate was always less than 35%. Both before and after TCJA, there are going to be companies who in any given year paid no taxes at all for various reasons – why assume they all did?
    – You plot CAEY vs. subsequent real return for the new CAPE methodology – can you plot the same thing using Shiller’s? Would like to see both the R^2 value of each and the mean squared error between CAEY and 10 year real returns to understand what, if any, improvement there is on predictability of future returns.
    Thanks!

    1. The taxes are adjusted to determine how past gross profits would have looked under today’s tax regime. As pointed out in the post, the positive effect of a tax reduction will priced in immediately, as it should bee, rather than overt time.

      I’m not a tax attorney. C corporations (a very small share of all corporations) used to have a tiered rate before. How many of the corporations in the S&P 500 are C corporations? None to my knowledge, but maybe you know more about this and I.

      i may plot that in a future post. If you want it now, you know where to get the data.

      1. Thanks – yeah I could always look at the data myself and that’s in my plans. Just figured that if the purpose is to improve CAPE then there needs to ultimately be a final result that shows the changes resulted in an improvement, didn’t result in an improvement, or was in the statistical noise in terms of being able to use it for something. Something that in my opinion is kinda fundamental to concluding this exercise.

        1. Agree. but keep in mind that the purpose of the exercise was an accounting exercise to make the CAPE better comparable over the decades.

          But, here’s the result over the entire history.
          Not sure this is even readable, because this is the output from Python, which looks nice in my Python window. In any case, there’s a very slight improvement in the R^2 and the (Newey-West adjusted) t-stat.
          In this simple univariate regression you can deduce the correlation as sqrt of the R^2.

          Shiller CAPE:
          OLS Regression Results
          ==============================================================================
          Dep. Variable: Ret_real R-squared: 0.285
          Model: OLS Adj. R-squared: 0.285
          Method: Least Squares F-statistic: 36.01
          Date: Fri, 14 Oct 2022 Prob (F-statistic): 2.40e-09
          Time: 10:24:07 Log-Likelihood: 2918.0
          No. Observations: 1700 AIC: -5832.
          Df Residuals: 1698 BIC: -5821.
          Df Model: 1
          Covariance Type: HAC
          ==============================================================================
          coef std err z P>|z| [0.025 0.975]
          ——————————————————————————
          Intercept 0.0011 0.015 0.071 0.944 -0.028 0.030
          CAEY1 0.9232 0.154 6.001 0.000 0.622 1.225
          ==============================================================================
          Omnibus: 20.699 Durbin-Watson: 0.018
          Prob(Omnibus): 0.000 Jarque-Bera (JB): 16.141
          Skew: -0.150 Prob(JB): 0.000313
          Kurtosis: 2.629 Cond. No. 33.8
          ==============================================================================

          Notes:
          [1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 120 lags and without small sample correction

          And the new CAPE:

          OLS Regression Results
          ==============================================================================
          Dep. Variable: Ret_real R-squared: 0.289
          Model: OLS Adj. R-squared: 0.289
          Method: Least Squares F-statistic: 57.56
          Date: Fri, 14 Oct 2022 Prob (F-statistic): 5.38e-14
          Time: 10:24:07 Log-Likelihood: 2922.9
          No. Observations: 1700 AIC: -5842.
          Df Residuals: 1698 BIC: -5831.
          Df Model: 1
          Covariance Type: HAC
          ==============================================================================
          coef std err z P>|z| [0.025 0.975]
          ——————————————————————————
          Intercept -0.0040 0.014 -0.291 0.771 -0.031 0.023
          CAEY2 1.0013 0.132 7.587 0.000 0.743 1.260
          ==============================================================================
          Omnibus: 31.081 Durbin-Watson: 0.018
          Prob(Omnibus): 0.000 Jarque-Bera (JB): 22.854
          Skew: -0.182 Prob(JB): 1.09e-05
          Kurtosis: 2.565 Cond. No. 36.4
          ==============================================================================

          Notes:
          [1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 120 lags and without small sample correction

          1. Hi Karsten – Not a huge difference. If the purpose is to make it better comparable over the decades then wouldn’t some sort of rolling analysis give us a better view of that that instead of full period? Meaning would we see the predictability of future returns to be more stable with the new method vs. Shiller method? Or will the reduced amount of data per calculation add more uncertainty to the results of each?

            Anyway – thanks a bunch for doing the analysis!

            1. Agree. But keep in mind that most of the change in the CAPE came over the last 10 years, which is the part that’s not even considered in that correlation. Because the 10y ahead real return only goes to 2012.

              But a CAPE of 21 vs. 27 makes a huge difference going forward.

  24. Thanks for the very insightful work.
    I followed you well with all the adjustments to CAPE until the share repurchase. Essentially, A and B are earning the same amount of money across 10 years, so they should have the same CAPE ratio.

    I found the adjustment related to earning reinvestment a bit harder to follow. 10 years back corporation C had much smaller total earnings. So why should C get the same CAPE ratio as A and B?
    The whole idea of CAPE is to average earnings across 10 years to eliminate cyclical nature of earnings. I thought that the idea was to value a company that can sustain steady earnings across 10 years more.

    The new definition of CAPE is saying that we don’t care about the cyclical part of the earnings as long as the profitability is not affected. In that sense this is a fundamentally different valuation metric.

    Is my thinking in the right direction?

    1. The new definition of CAPE is saying that we don’t care about the cyclical part of the earnings as long as the profitability is not affected. In that sense this is a fundamentally different valuation metric.

      Never said that. The lower earnings from 10 years ago are not due to anything cyclical. This is the antithesis of cyclical. What matters is that 1 share held by an investor over the last 10 years and over the next 10 years has generated and will generate the same returns. And yet, corporations A, B, and C don’t have the same traditional CAPE ratio. My adjustment aims to fix that issue.

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