Stock Return CAPEr: The Next Decade’s Returns

I have been in the investment industry long enough to know that it is difficult to forecast returns. I also know that markets can get into overvalued and undervalued zones, and then stay there or even go deeper in for much longer than I thought was possible. Having said all that, I still need to make judgements about the long term returns that asset classes will generate given their different risks. Although estimating long term returns is largely subjective, there are some objective tools that can be used. The Cyclically Adjusted Price Earnings (CAPE) ratio is one such tool. While I would not use it as the sole basis for estimating returns, it is intriguing to see what it says about the current level of the stock market.

Background Dossier

The price earnings ratio (P/E) is calculated by dividing the share price of a company or the level of a stock index by its earnings per share (EPS). EPS is net income divided by the number of shares outstanding. The P/E can be backward looking by using the last 12 months of earnings, or forward looking by using an estimate for the next 12 months. It is a shorthand method of comparing the value of different stocks or stock indices. Everything else being equal, for a value investor a low P/E is preferred as it means the investor is paying less for a dollar of earnings compared to a high P/E company. Of course, everything isn’t equal in the real world, so a P/E should never be the sole basis for buying a stock. For example, a company can have a low P/E for reasons related to a poor outlook or poor operating performance, without much prospect for improvement.

Broadly speaking, periods of falling interest rates can be associated with rising P/E ratios. Think of this in the context of the years since the Global Financial Crisis of 2008/2009. As bond yields have generally declined since then, P/Es have generally increased. The potential growth offered by stocks and their dividend yields becomes more appealing relative to bonds as interest rates fall. To the extent that this boosts the prices investors are willing to pay for stocks, the P/E ratios (based on the last 12 months of earnings) will increase.

CAPEd Crusaders

As outlined on Investopedia , Robert Shiller and John Campbell published an article “Valuation Ratios and the Long-Run Stock Market Outlook” in 1998. In the article they modified the standard P/E calculation by dividing the S&P 500 real (inflation-adjusted) price by the average of its real earnings over the last 10 years. This is the CAPE ratio. The CAPE ratio smooths out the fluctuations in earnings that happen over different business or economic cycles. But no one measure of stock value is perfect. The CAPE ratio is backward looking and is dependent on how earnings are calculated using generally accepted accounting principles.

With the CAPE ratio we can estimate returns over the next 10 years for the U.S. (S&P 500) and Canadian (S&P TSX) stock markets. The U.S. data and CAPE formula is from an excel file which you can download from Robert Shiller’s website. The calculations for the Canadian CAPE ratio used data from Siblis Research and returns using Investing.com. I did a linear regression analysis on 20 years of monthly data from July 1991 to July 2011[1].

Data Profile

Chart 1 plots the results of the regression using the U.S. data. It shows, for each monthly S&P 500 CAPE ratio, the resulting 10-year return for the S&P 500 (blue diamonds) and the estimated 10-year returns from the regression (black squares). For example, at a CAPE ratio of 30 the estimated 10-year return is 5.8%, and the actual returns were between 2.5% to 7.5%. Since we did a linear regression, the estimated 10-year returns have a linear relationship to the CAPE ratio, resulting in the downward sloping line. That make sense as a higher CAPE ratio means that the S&P 500 price is high relative to its earnings, which is likely to result in lower price gains and returns going forward.

Chart 1

The chart shows that the fit between the actual and estimated returns is strong. That is why the actual returns are reasonably close to the estimated ones. This is supported by the R-squared for the regression of 93%[2].

Chart 2 shows the regression results for Canadian stocks. At each monthly CAPE ratio it shows the actual 10-year return for the S&P TSX (red diamonds) and the estimated 10-year returns from the regression (black squares). For example, at a CAPE ratio of 30 the estimated 10-year return is 6.1%, and the actual returns were between 3.5% to 8.5%.

Chart 2

The chart also illustrates the moderately strong fit between the actual and estimated returns. The explanatory power of the regression is lower than the U.S. results, although it is still moderately high with the R-squared at 66%. It is interesting to note that, compared to the U.S. in Chart 1, Canada has had very few months where the CAPE ratio was over 30.

Prime Suspected Returns

Armed with the techniques of our CAPEd crusaders and our data profile, I can estimate 10-year returns for U.S. and Canadian stocks. Chart 3 below plots, month by month since July 1991, the actual return over the next 10 years for the S&P 500 (blue line, right scale) and CAPE ratio (black line, ratio inverted on the left scale). The last actual 10-year return I can calculate was as of July 2011, as it covers the period July 2011 to July 2021. The grey shaded band is the estimated return range (right scale) from the regression. It is two standard errors (estimated from the regression) on either side of the estimated return (mean return from the regression given the CAPE ratio). About 95% of the actual returns during the 20-year period from 1991 to 2011 were within the two standard error shaded band.

Chart 3

Now let’s use the regression model to predict the 10 year returns and the two standard error band going forward. The 10-year return from July 2021 to July 2031, based on the latest CAPE ratio of 37.4, is predicted to be within a range of -2% to +5%, with a mean of 2%.

The data for Canada is shown in Chart 4. The red line is the actual 10-year return on the S&P TSX (right scale). The CAPE ratio is the black line (ratio inverted on the left scale). While previously we saw that the U.S. CAPE ratio is in the higher end of its range, at 24 the latest Canadian CAPE ratio is around its average value. Given the lower Canadian CAPE ratio, the prediction from the regression model for the return over the next 10 years is higher than the U.S. The range is predicted to be 4% to 11%, with a mean of around 7%.

Chart 4

Closing the Case

Although the CAPE ratio is only one tool that can be used when trying to predict long term returns, it is an interesting one. The current level of the CAPE ratio in the U.S. is high while in Canada it is average. Based on these levels, the regression models predict single digit returns for both markets over the next 10 years. Given the relative levels of the CAPE ratios, the regression model also predicts that Canadian stocks will outperform U.S. stocks.

This information is helpful when formulating an asset allocation. The CAPE ratio estimates form part of the rationale for the predicted returns in the “conservative” version of my asset allocation scenarios. In that scenario I use an annualized expected return of only 4% for the S&P 500 and 6% for Canadian stocks. While those “conservative” scenario returns are low, they are still better than the expected return of 2.5% for bonds.

Invest Wisely,

Dave Schaffner, CFA

Principal, Wayfairer Capital Management Ltd.

[1] Since I was looking at 10-year returns, the July 2011 CAPE ratio is the last data point as it is compared to the return from July 2011 to July 2021. The regression technique uses an independent variable (CAPE ratio) to explain or predict the outcome for the dependent variable (return for the next 10 years). Return estimates can be constructed from the regression results.

[2] The R-squared, or goodness of fit measure, is the proportion of the variance for the dependent variable (10-year return) that is explained by the independent variable (CAPE ratio). The R-squared of 93% means that 93% of the variation is explained.