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A cracked rear-view mirror: Shiller price/earnings ratios and equity market valuations

Global views and trends


One of the metrics most often cited for measuring equity market valuations is the Shiller P/E, also known as the Cyclically-Adjusted Price/Earnings ratio (CAPE), defined as the price-earnings ratio based on average inflation-adjusted earnings from the previous 10 years.

The popularity of the measure has perhaps more to do with the prescient publication of Professor Robert J. Shiller’s book “Irrational Exuberance” in March 2000, which contained the assertion that stock markets were overvalued, than with the measure’s usefulness in identifying when stocks are expensive or cheap.

The main virtue of the Shiller P/E is that is has been calculated back to 1881, allowing one to calculate a truly long-run average. The value as at 11 April 2018 was 31.19, 85% or more than two standard deviations above that average, although still below the peak in December 1999 of 44.2 (see Figure 1). The weaknesses of the CAPE, however, are numerous. The first is actually the length of the series, in that that the current value is compared to an average calculated over the last 138 years. Given the radical changes not only in the economy but also in capital markets over that time, it is not obvious that comparing a P/E ratio from 2018 to one in 1888 really provides much insight. 

Figure 1: Cyclically-Adjusted Price-Earnings ratio


Data as at 11 April 2018. Source: Robert J. Shiller.


The second concern is that the measure is backward looking, comparing the current index price to the earnings over the last 10 years. One reason it is calculated in this way is that it can account for a typical business cycle. Deeply cyclical stocks, for example those in the energy sector, can incorrectly appear as expensive in the depths of a recession when prices will be very high compared to their recent, temporarily depressed earnings. The downside of this adjustment is that it does not account for the future. While it is interesting to know what the trailing earnings have been, an investor purchasing a stock today has no claim on a company’s past earnings, only those of the future. And as any investor knows, past performance is not the most accurate guide to the future.

The most common alternative to the Shiller P/E is the forward P/E ratio, calculated on next-12-month earnings estimates. Of course, any measure has its defects, and the defects for the forward P/E are several-fold. Analyst estimates for the S&P 500 are only available from 1985, and for even shorter periods of time for other international markets.

Secondly, the earnings estimate is the average of analyst forecasts, which are not necessarily any more accurate than history in predicting the future. The availability of estimates is also much thinner when one looks beyond major large capitalisation stock markets.

Thirdly, the forward P/E ratio compares the current price to earnings expected only one year ahead, when ideally it should take into account earnings for several years into the future, if not forever (which would address the business cycle issue). This variation would be analogous to the Net Present Value (NPV) methodology of calculating the correct stock price by forecasting an infinite earnings stream then determining its value today through a discount rate. The obvious problem is that if we justifiably doubt the ability of analysts to predict earnings one year into the future, infinity may be many steps too far.

The response to these concerns is that a one-year-forward estimate is the best option we have if we are trying to balance the desire for a forward-looking measure with an acceptable level of probable accuracy in the prediction. The importance of using a measure of expected earnings as opposed to an historical measure is clear from the reaction of stocks during earnings season. A company may report disappointing earnings but if it predicts better earnings growth ahead (‘positive guidance’), the stock is likely to rise, not fall. Another telling counter-example is the recent passage of corporate tax reduction in the US. Because companies would have significantly higher earnings in the future, earnings estimates and stock prices jumped following the passage of the measure. As a result, forward P/E ratios changed little, but the Shiller P/E jumped, suggesting stocks were less attractive than they were prior to the passage of the law, whereas in fact the opposite was true.

Of course, one should not rely on a single measure of valuation when evaluating an equity investment. Other popular measures are price-to-book (P/B), price-to-sales (P/S), price-to-cash-earnings (P/CE, to avoid accounting distortions in reported earnings), price-earnings-growth estimates (PEG), dividend yield (DY), and return on invested capital (ROIC). Each has its own advantages and disadvantages, but by using an amalgamated score, one hopefully arrives at a more robust and reliable measure of valuations.

The principal determinant, however, of which metric is best is to consider which one is the best predictor of future stock market returns. The Shiller P/E, for example, often flags stocks as expensive when they subsequently provided attractive returns over the following years (2016-2017 is a prime example). We have taken the above metrics for major markets as far back as the data allows, and then calculated the correlation with future 1-year, 3-year, 5-year and 10-year stock market returns (see Table 1). 

Table 1: Correlation between valuation metrics and forward real returns


Data as at 26 April 2018. Start dates: CAPE January 1881, P/E January 1985, P/B December 1974, P/S March 1998, PCE January 1970, PEG December 1987, ROIC March 1998, DY January 1969. Data as at 31 March 2018. Sources: MSCI, IBES, BNP Paribas Asset Management.


What we see is that the best single metric is price-to-sales (a high negative correlation meaning that a high value of the metric corresponds with negative future returns), followed by price-to-forward-earnings; the CAPE measure generally does poorly. The correlations over one year are low across the board, and with the exception of price-sales low over three years, meaning valuations are less useful in predicting near-term stock market movements. A caveat as regards the price-to-sales metric, however, is that it only begins in March 1998, and so the high correlation is less robust than the one for price-to-forward earnings, which begins in 1985. The last column shows the adjusted R-squared for each metric, which on a relative basis shows a similar level of explanatory power. The adjusted R-squared for the price-to-forward earnings over the same period as the price-to-sales ratio is higher at 39.2, suggesting that the price-to-sales metric would likely be lower if it were calculated over the same period as price-to-forward earnings.

How do equity market valuations appear today? It is worth noting how much valuations based on expected earnings have improved so far this year relative to the performance of the markets. If there is, say, a 10% correction in the market, one would expect NTM P/Es to improve by 10%. But compared to the end of 2017, multiples have fallen by more than the change in price. This is because earnings estimates have continued to rise, despite the higher volatility. So, markets that appeared quite expensive in December (when the forward P/E for the S&P 500 was 18.6x compared to a long-run average of 14.7x, or 13% above the average), now seems only modestly high at 16.6x, a decline of 12% in the multiple when the market is largely flat. As they say, it has ‘grown into the multiple’. Given low inflation, solid growth, and a recession unlikely over at least the next 18 months, the current premium today appears fair.

The z-scores (or normalised value) of the metrics for major markets are at most around ‘fair value’ (i.e. a z-score between -0.5 and +0.5), 13% are cheap (z-score less than -0.5) to very cheap (z-score less than -1.0), and 39% moderately expensive (z-score greater than +0.5) to very expensive (z-score greater than 1.0). See Table 2.

Table 2: Normalised valuation metrics (z-scores)


Data as at 26 April 2018. Note: For price-to-book, multiple based on IMI indices from 1974. **Japan value calculated only since 2001, otherwise from 1987. Tech+ z-score based on median, not mean. Price-to-book ratio is relative to median since 1974 except EM which is from 1995. Tech+ = IT sector plus Internet & Direct Marketing Retail. Sources: IBES, MSCI, FactSet, BNP Paribas Asset Management.


It is worth noting that breaking the S&P 500 into the tech+ sectors (information technology plus internet & direct marketing retail, which is normally categorised as consumer discretionary) and the rest of the market, does not significantly alter the view on how expensive US equities are. One might have assumed, given the very strong performance of the tech+ sector last year (up by 40% versus 16% for the rest of the market), that multiples would be very high (as they were before the tech bubble crash in 2000). The reason that’s not the case today is again that the price appreciation has been matched by earnings growth, and despite trade tensions and the prospect of higher taxes and regulation, earnings estimates have yet to flag (see Figure 2). In fact, the relative forward P/E for the sector is less than it is than for energy and utilities and similar to that for financials. It appears that one is in fact getting above-market earnings growth for a not particularly above-market price.

Figure 2: Tech+ sector earnings revisions
Next 12-months earnings per share


Data as at 27 April 2018. Sources: IBES, BNP Paribas Asset Management.


The valuations for Japanese equities also warrant a mention. Given the extreme levels that prices reached during the market’s boom in the 1990s, when the forward P/E ratio topped out at 74x, it is inevitable the any P/E ratio today is going to seem cheap. To account for that, we have excluded the years where valuations were at their highest, but even then, both on an absolute and relative basis, Japanese equities appear undervalued.


Expected returns 

We have shown already how accurate each metric has been historically in predicting future returns. Given multiples today, how much appreciation can investors expect in the future for US equities? The following table shows what each metric suggests returns will be over the same time horizons, with the average for the whole period in the top row.

Table 3: Forecast returns given current metric level, long-run average index return over entire sample, and difference of forecast from long-run average

Forecast-expected returns

Forecast-expected returns 2

Note: Annualised real returns. Forecast based on linear regression of metric and real index returns. Data as at 26 April 2018. Sources: MSCI, IBES, BNP Paribas Asset Management.

Over the next three years, one would expect below-average real returns judging by the historical returns when price-to-sales ratios and price-to-forward earnings ratios were around these levels. In absolute terms, a price-to-sales ratio of around 2x as is the case today would correspond to an expected annual real return over the next three years of -6.2%, below the average since 1998 of 1.5%. The expected return based on current P/E levels is positive at 3.4%, but still below the long-run average return since 1985 of 5.5%.


Earnings trends

However important valuations are in evaluating equity markets, in the end it is all about earnings, earnings, earnings. A high multiple is acceptable if earnings growth warrants it, and a ‘cheap’ stock is worth little if earnings never recover. Recent earnings trends globally, measured by the change in the next 12-month estimate, shows ongoing momentum in most markets. The lines jump sharply for the US at the beginning of 2018 as analysts factored in the benefits of the tax cuts, but since then growth has reverted to the positive, pre-reform trend (see Figure 3).

Figure 3: Earnings revisions


Data as at 27 April 2018. Sources: FactSet, BNP Paribas Management.

Since 31 January 2018 (after the tax cuts had been factored in), the growth rate in the estimates is highest for the US, particularly the US Tech+ sector, followed by Japan.


Earnings growth expectations

A simple way to establish a baseline for potential market appreciation over the next year is to calculate the anticipated earnings growth. If multiples do not change, prices should go up by roughly this amount. Current forecasts are for growth ranging from 8% to 20% (local currency terms) for the major markets. Deviations from long-run valuation averages, however, could add to or subtract from the market return. The following table shows how the major markets look currently.

Table 4: Market-implied next 12-months earnings growth and valuation z-score*


Data as at 27 April 2018. *Average of price-to-sales and price-to-next 12-months EPS estimate. Source: IBES, BNP FactSet, MSCI, BNP Paribas Asset Management.

Not surprisingly, the market with the highest earnings growth estimate, the US and particularly US Tech+, also has the highest valuation and therefore lower expected price appreciation over the medium term. The growth rates for the US, however, should be lowered to take into account the one-off boost earnings will receive this year because of the tax cut. By our calculations, tax reform will add approximately six percentage points to the growth rate, so instead of 16% year-on-year growth, it would likely have been around 10%.

Moreover, evaluating a market based on implied earnings growth assumes the forward estimates are accurate. One factor that could upset them is a significant move in the US dollar or the imposition of tariffs. Large capitalisation companies in Japanese and European indices, in particular, derive a meaningful share of their earnings from exports. Futures markets currently forecast the euro at USD 1.23/EUR at the end of 2018 and JPY 107/USD for the yen (compared to USD 1.21/EUR and JPY 109/USD as at 29 April 2018); however a bigger move, either because of a change in growth expectations or the imposition of tariffs, would certainly affect profits.



The Shiller P/E has a poor track record of predicting future market returns relative to other metrics. Most measures today suggest markets are modestly expensive, meaning that investors should anticipate slightly below-average returns over the next several years. In the short-term, however, earnings momentum is strong thanks to the ongoing global recovery, supportive central banks and modest inflation. While volatility is higher than it was in 2017, this will simply provide the opportunity to reallocate opportunistically to more appealing markets.

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