Practical analysis for investment professionals
05 July 2016

The Vagaries of Using CAPE to Forecast Returns

The cyclically adjusted price/earnings (CAPE) ratio is one of the most reliable indicators of prospective long-term stock market returns. First proposed by Benjamin Graham and popularized by John Campbell and Robert Shiller, the formula is deceptively simple, dividing the current price of a stock market or single stock by the average earnings of the last 10 years — both adjusted for inflation.

Historically the CAPE ratio has worked well in predicting the future real returns of stock markets. But as is often the case with simple indicators, people love to poke holes in it, especially if the forecasts are not in line with recent market reality — or their own opinions.

Recently, the earnings side of the CAPE ratio has come under increased scrutiny. For example, Jeremy Siegel theorized that because of accounting changes since the 1990s, the earnings of current listed companies are not comparable to historical norms, and are systematically lower than in the past due to mark-to-market requirements that depress asset prices in times of crisis. These artificially low earnings lead to artificially high CAPE ratios, creating unwarranted pessimism about future stock market returns.

Siegel and others suggest that rather than comparing current CAPE levels to long-term averages going back to 1871, as is often done, compare them instead to the early 1990s, when these accounting changes were initially introduced. Still others contend that comparisons should go back to the World War II era, because after 1945 earnings growth seems to have gone through a lasting regime change. With these changes in time frame, they maintain, the CAPE becomes more predictive, and expected returns for the coming years are higher than those anticipated if long-term historic averages are used.

The theories in favor of changes in historical time frames are troublesome. In the following table, I calculated the CAPE for the US stock market and estimated a regression of beginning CAPE on subsequent five-year real returns (the reason for trying to predict five-year real returns instead of the more standard 10-year returns is to start the regressions at a later stage and do not necessarily require 20 years of data to make one forecast). Beginning in January 1910, the regression results in an annual real return forecast of 1.9% for the next five years — an abysmally low number. The fit of the regression as measured by the R2 is a mere 0.21.

If the regression begins in 1945, after World War II, things look different. While the fit between forecast and realized return is still low with an R2 of 0.23, the predicted return for the next five years is much higher at 3.6% per annum. If started in 1990, however, the return forecast increases to 6.3%, and the fit is much better with an impressive R2 of 0.58.

So far, so good, but what happens if the historic time period is shortened some more? Starting in 1995 results in a return forecast of 4.9% (R2 of 0.61), starting in 2000 yields 4.0% (R2 of 0.64), and starting in 2005 yields 3.6% with a fantastic R2 of 0.83. Thus as the period for the regression moves closer, the fit improves but return expectations drop from more than 6% to figures that are more in line with long-term historic averages. Similar effects can be seen in the United Kingdom, Switzerland, and Germany.


Expected Five-Year Return in Local Currency (R2 in Brackets)

Expected Five-Year Return in Local Currency


This exercise illustrates an important lesson that is too often forgotten in market predictions: Forecasts depend not only on the kind of variable, but also on the time frame used to calibrate the model. So far this discussion has focused mainly on how to calculate the CAPE, and all readers should review Laurence Siegel’s take on the benefits and drawbacks of different approaches.

The bigger uncertainty, however, stems from the time period used to calibrate the model and run the regressions. In order to provide a reasonable idea of expected returns for the coming five years, I have calculated the expected real returns in local currencies for 38 different countries for the longest historical time period possible, in addition to the starting points given in the table above. The two tables below show the predicted return for the full time series going back as far as possible, as well as the fit of the regression given by the R2. The last column shows the range of return predictions if the different starting points are used. This allows us to summarize the good, the bad, and the ugly truths about the current long-term market outlook.

The Good: Using CAPE as a forecasting tool for long-term stock market returns works in international markets as well as in the United States. The highest return forecasts currently come out of emerging markets, which seem to be the best value.

The Bad: The US market is poised to underperform European and Asian stock markets over the next five years in local currency terms.

The Ugly: It is impossible to say by how much the US market is likely to underperform or if it is going to underperform at all, since the estimation errors around these return forecasts are considerable.


KlementDevelopedMarkets


KlementEmergingMarkets

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.

Image credit: ©iStockphoto.com/CSA-Archive

About the Author(s)
Joachim Klement, CFA

Joachim Klement, CFA, is Head of Investment Research at Fidante Capital and a trustee of the CFA Institute Research Foundation. Previously, he was CIO at Wellershoff & Partners Ltd., and before that, head of the UBS Wealth Management Strategic Research team and head of equity strategy for UBS Wealth Management. Klement studied mathematics and physics at the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland and Madrid, Spain, and graduated with a master’s degree in mathematics. In addition, he holds a master’s degree in economics and finance.

9 thoughts on “The Vagaries of Using CAPE to Forecast Returns”

  1. JM says:

    There is always a risk in overemphasising the predictive nature of measures, such as the CAPE.

    For example, even without looking at the results of CAPE to date most analysts (or people with a grounded understanding of business valuation more generally) would probably agree that over the long term market values should, more or less, reflect the real value of the constituent’s earnings over a business cycle. Personally I think Shiller’s CAPE is a very logical measure, but I’m not sure it’s too helpful in making investment predictions.

    This leads us to the question as to why the CAPE is such a poor predictor of future performance as surely most astute investors should (if even half rational) pursue investment horizons much longer than even two or three business cycles.

    In this case the CAPE model fitting too well over the medium term (30 yrs+) may be more a reflection of a paradigm shift than a flaw in the model. For example, as countries develop it’s normal to expect to see advances in production methods, technology and infrastructure, as well as changes in consumption patterns; this is followed by increased foreign capital and reduced costs of lending and lower (at least perceived lower) market/geopolitical risk. These accelerated periods of growth aren’t (as far as I know) incorporated in the CAPE, which means that comparing historical CAPE to current isn’t really a like-for-like comparison. Of course in the case of mature, developed economies we see the opposite happen as lower inflation and interest rate expectations lead to higher prices being paid for future earnings.

  2. John says:

    Joachim,
    all good work, but don’t you think the biggest problem with the CAPE is the first assumption that everyone forgets

    assumption 1. use 10 years of historic earnings so as to approximate a business cycle

    … the reason you are trying to capture a full business cycle is then you capture the peaks and troughs of the cycle .. hence the name, cyclically adjusted PE.
    problem is the real world didn’t get the memo about the 10 year assumption. Business cycles are of varying length. To offset peak period earnings you need a trough. So some 10 year periods capture just one peak and one trough, other 10 year periods may have two peaks and one trough or two troughs one peak etc … all of this then makes for a very blunt indicator

    So in concept, CAPE is good … but in practice the period it is calculated over needs to be aligned to business cycles and this means any rolling 10 year period creates a nonsense. that is why it has very little predictive value other than the bluntness of high markets (and hence almost any accounting indicator) due to mean reversion of capitalism, means lower forward returns.

    using a 5 year period would likely miss a full business cycle – so refutes the cyclically adjusted part of the name.

    So a long slow expansion will result in a high CAPE, simply because earnings weren’t ‘re-based’ from recessions. Equally double dip downturns end up producing artificially low CAPEs
    the fact is, leading into a bear market (which is when you want the predictor to predict) the CAPE has been anywhere from 7 to 44 !! Just before the dotcom crash, the CAPE was 44. Just before the 1981/82 deep recession it was only 9.

    Please tell me what is the correct level of CAPE to sell my investments on – in advance of the downturn please, I’m struggling to see it clearly.

    predictive indicators are only as good as their ability to enable you to predict.

    all the best
    john

    1. Jay Weinstein says:

      Really, I cannot for the life of me understand why people think CAPE is useful for anything. As John, Jeremy Siegel, Laurence Siegel, and literally dozens of others point out, the calculation of this historical series is fraught with potential problems. Then, the concept of mushing these numbers together, averaging them over 140 years or so, and coming up with something valuable/predictive strikes me as total lunacy. You cannot even compare the S&P multiple of today with ten years ago, not to mention a time when the US economy was all railroads and utilities. The underlying world changes too much.

      As John says, please let me know in advance the “correct level of CAPE”–and good luck with that.

      Ultimately, it is just another canard from those who think that if they just crunch enough numbers or think hard enough, they can add impose order on the total chaos that is the “stock market.” It simply doesn’t work that way, not in 1916, 1966, or 2016.

      CAPE has probably been the costliest creation ever, having kept so many people out of equities with its long term bearish silliness. I understand the appeal of the original exercise, but please just give it up once and for all. There is no “market” indicator of value, now or ever.

  3. Raymond Guevara says:

    Nice article. What is data source for your CAPE calculations?

  4. Garrett M says:

    The “Quantitative Methods for Valuation” section of the level 2 material spends a great deal of time going over the methodology for using linear regression in time series. In particular it goes over checking for unit roots and cointegration, as well as reviewing the errors in time series models. Did you do any of those checks when building your model, or did you only look at the R^2?

    1. Yes, Garrett, I did. There are older papers of mine on SSRN where I go into somewhat more econometric detail, but the essence is that as long as you have reasonably long data series there are no issues with unit roots and cointegration. The situation may change, however, if you take just five years of historic data.

  5. Jaswant Aditya Singh says:

    Can any one please tell how to calculate inflation adjusted 10 year average EPS of Nifty.

    I have derived the EPS of Nifty by simply dividing Nifty index value by PE (as indicated in the website http://www.nseindia.com)
    Example Today 7th July 2016 Nifty is at 8337.90 and PE is 22.89 , therefore EPS is 8337.90/22.89 = 364.25

    Similarly i have calculated EPS of last 10 years on every 31st March 2007……2016

    and similarly CPI inflation % of all the 10 years.
    current CPI inflation is 5.7%

  6. It is an analytical frame….a reference point to which you add/amend inputs/structural assumptions to assess risks to valuations/return expectations. Many factors are impacting market forces and hence the ability of rules of thumb such as the CAPE to work: i.e. unconventional monetary policy, increasing share of national income going to profits. Other risks are building up: lower capex re future returns; higher leverage to underlying GDP flows; aging/declining pops etc. Just because a market appears to be defying gravity in a valuation dimension does not mean valuation is irrelevant or that valuation measures that strongly suggest over valuation are incorrect. we have an excess of asset focused money supply growth that has strongly influenced asset valuations for some time. The risks are building up, the divergence between asset prices and their flows and the growth rate of flows are widening…..

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