Market timing with valuation ratios: A fresh look
Jeff Wurgler, consultant, Ryan Stever, director Quantitative Global Macro Research and Stephanie Mallinger-Dogan, associate portfolio manager at Acadian Asset Management argue that market timing is, to some degree, possible.
Is the market overvalued? Getting the answer right can be the difference between outperformance and underperformance.
Unfortunately, market timing is notoriously difficult. Many quant strategies have, over the long term, been successful at stock selection. However, identifying which of two retailers is relatively overvalued is easier than saying whether the whole sector—let alone, the whole market—is overvalued on a standalone basis. Further, whatever sentiment or extrapolative expectation caused misvaluation in the first place can get stronger before it reverts. The impossibility of forecasting mob psychology also helps to explain why few funds advocate market timing as a core strategy.
Nonetheless, a substantial body of evidence suggests that market timing is, to some degree, possible. If so, modest tilts toward or away from market exposure may be beneficial.
The standard approach is to compare the aggregate market price to some less capricious measure of aggregate size or performance. Such valuation ratios represent contrarian indicators that lean against prevailing sentiment and are long-term predictors that may require great patience to exploit. But they provide a natural, objective foundation for any market timing strategy.
Here we take a fresh look at the performance of a variety of such valuation measures. We start with a particularly well-known valuation ratio, the Cyclically Adjusted P/E ratio (CAPE), which has received much attention due to its bearishly high level.
After assessing the forecasting power of CAPE over its history, we move on to a broader set of indicators— including CAPE—and illustrate one way to combine them into a single forecast. This forecast performs substantially better than CAPE alone. In addition, its current outlook is not as bleak as CAPE implies.
What’s the takeaway? Market timing with valuation ratios should not be hastily dismissed. Straightforward measures do contain information about future returns. Used conservatively, and without relying solely on any one ratio, valuation ratios may enhance the long-run returns to tactical asset allocation.
CAPE: Popular – and rightly so
The construction of CAPE goes back to Benjamin Graham in the 1930s. It is simply the ratio of aggregate market cap to a 10-year trailing average of earnings. The choice of 10 years balances the need to smooth out transient gyrations in profits against the desire to minimize the influence of ongoing structural changes in the economy and earnings characteristics. CAPE was re-popularised by Campbell and Shiller (1998). It has, in fact, become known as “Shiller’s PE,” and was even described in his 2013 Nobel Prize citation.
Figure 1 shows the evolution of CAPE from January 1926 to December 2015. Its connection to market peaks and troughs is obvious, since variation in market cap swamps variation in earnings.
As of the end of December, 2015, CAPE stands at 26.0. This puts it in the highest historical decile.
Impeccable pedigree aside, does CAPE have investment value? Table 1 displays rolling deciles of monthly CAPE from 1950 – 2015. There are more months in the top deciles because CAPE has shown a rising trend over the full sample.
The figure and the table show why the factor has become so popular, and why its current level has some concerned about the outlook for U.S. stocks.
It is worth noting that achieving these average returns requires that investors keep faith in CAPE through some dark times—again, betting on valuation ratios is an intrinsically contrarian strategy that may be hard to stick with precisely when doing so has the greatest value. For example, given today’s high CAPE, Irving Fisher’s experience comes to mind.
Fisher destroyed his reputation by famously declaring that “stock prices have reached what looks like a permanently high plateau”—three days before the crash of 1929. Shiller’s own bearishness during the internet bubble run-up, on the other hand, was largely dismissed at the time, but his steadfastness was almost unique among market commentators when the bubble popped.
CAPE has demonstrated an ability to forecast long-term returns. While the buy and hold strategy performed well, a tactical strategy that incorporated CAPE in modest measure might have performed better.
No sophisticated bottom-up model would rely on a single measure of momentum, value, or quality, regardless of its past performance. The same is true in a market-timing model. In addition to CAPE, we consider seven valuation factors and describe one way to combine them. The factors fall into three groups: classic valuation ratios, Gordon growth model ratios, and partial least squares ratios.
Classica Valuation Ratios
These ratios, like CAPE, scale a measure of aggregate market value in the numerator by some book value or flow in the denominator. Dividends and earnings-based valuation ratios are the focus of other market timing studies such as Goyal and Welch (2008), for example.
To keep visual comparisons simple and meaningful, we computed and graphed all factors in this section such that they are (expected to be) positively correlated with future returns. This means we multiplied scaled-price ratios by negative one and explains why CAPE is flipped from Figure 1.
Figure 2a illustrates the high correlation among the standardized versions of these factors. They all capture the familiar booms and busts, bubbles and crashes, in roughly the same way. A close look reveals the smoothness of CAPE relative to the standard P/E ratio.
Gordon Growth Model Ratios
The second group of factors is inspired by Campbell and Thompson (2008).5 They are also based on aggregate cap, earnings, dividends, and book values, but forecast the market based on steady-state assumptions about how these factors move together over time. In particular, the Gordon growth model is combined with data on aggregate ROE and how this relates to long-term growth.
The ratios all derive from substitutions of the steady-state relationship between growth and profitability into the Gordon growth model, D/P = R – G. We further describe the series of calculations in the Appendix. The ultimate forecasts are:
RD/P = D/P + (1 – D/E)*ROE
RE/P = (D/E)(E/P) + (1 – D/E)*ROE
RB/P = ROE*[1 + (D/E)(B/P – 1)]
These factors have at least two appealing features. First, they have an explicitly economic motivation. Second, these are actual market return forecasts. They do not require parameter estimation to make return predictions and thus avoid overfitting problems. These features come at the cost of the assumption that these steady-state relationships hold. (This is obviously in contrast to the motivation behind the classic valuation ratios—the market is mispriced, i.e., out of steady state.)
Figure 2b looks at these ratio-based forecasts. Their correlation with the classic ratios is loose at best, with the possible exception of the internet boom and bust, despite the fact that some of them have classic valuation ratios built into their definition.
Partial Least Squares Rations
The last and most novel factor is based on the work of Kelley and Pruitt (2013). The idea is that some firms’ own valuation ratios predict market returns better than others. Using the technique of partial least squares (PLS), one can identify the firms whose price-to-book ratios are most informative about the market and overweight them when constructing a single aggregate valuation ratio. Details of the calculations are in the Appendix.
We standardise the PLS factor and plot it in Figure 2c. It is not highly correlated with the other ratios and forecasts at high frequencies, but from the early 1970s onward it does display some low-frequency commonality with the classic ratios.
Combining Indicators: An Approach
There are many ways one might construct a timing forecast based on these indicators. It seems like a bad idea to be too elaborate, however, both to avoid data mining and to maintain visibility into the forecast. Our approach is simply to use the eight indicators to produce eight individual forecasts of the equity premium, average the forecasts within each category, and then equally weight each category’s forecast to produce a combined model forecast.
We obtain the forecasts for the four classic value factors and the PLS factor by adding the historical average equity premium, i.e., the naïve equity premium prediction going forward, to the component of the past equity premium that was predictable using that particular factor. That is, the forecast for each factor is: Forecast = (Historical Average) + (Factor Scale)*(Factor Score) where the factor-specific scale is based on the slope coefficient from a regression of market returns on that factor’s score (standardised value). If the estimated slope coefficient is negative, then we reset it to zero—a simple way to impose prior beliefs. We produce all of this on a rolling basis to avoid look-ahead bias.
This gives us five of the eight forecasts we need. The other three, based on Gordon growth model ratios, are already in terms of market excess returns. Now we simply average the forecasts within each category and equally weight those averages to produce a combined forecast.
Figure 3 shows how the combined model forecast evolves. It is still settling down for the first decade or two, because only a short time series of classic ratios were available to fit scale parameters; the direct and more stable forecasts from the Gordon growth model are not available yet.
Visually, the combined forecast has more in common with the classic ratios than the other series, even in recent years. But by construction it reflects information from each of the eight. The diverse information has the side effect of smoothing out the forecast, implying fairly modest, low frequency reallocations between equities and cash. This is both a sanity check from a research perspective and, from a practical perspective, attractive for risk management and transaction cost purposes.
In any case, the most interesting aspect of the combined forecast is its performance. Table 2 shows the annualized 10-year returns and gives a sense of the risks associated with the combined model.
There is again a very strong relationship between the forecast and average 10-year returns. Moreover, the combined forecast’s ability to identify market extremes is better than that of the implementable CAPE-only forecast, as indicated in Figure 4. Some of the forecast-irrelevant variation in CAPE is eliminated by forecast-relevant variation in the other seven indicators.
In a head-to-head comparison, the combined forecast seems superior to the CAPE-only forecast. Its general ability to forecast is better; a regression line fit through the bar tops is about 42% steeper (a 1-10 spread of 10.6% annualized returns versus 8.9%) and the difference is statistically significant (one-tailed p=.08 when comparing the slopes of the fitted lines). In addition, the average returns are somewhat more linear or monotonic across forecast deciles; a line through decile averages fits with an R-squared of 85% for the combined model versus 78% for the CAPE model. Finally, the combined model seems to do a better job identifying market bottoms.
Let’s summarize the historical evidence. Both the CAPE-only and a combined valuation indicator forecasts have some predictive power for market returns. Thus, any pundit’s indictment of CAPE need not cast a shadow on valuation indicators more generally. The more constructive conclusion is that valuation-based forecasts might be able to add modest value through tactical asset allocation, although we have not attempted to construct or test a specific strategy here.
What does the combined forecast say about the current outlook? Table 3 breaks down the 10-year annualized forecast S&P return of 5.8% over cash. This is slightly more bullish than the historical average of 5.5%.
A drilldown into the current forecast shows that CAPE, in fact, is the most pessimistic of the lot. It and the other three classic ratios are bearish relative to the historical average, while the Gordon-based ratios and the PLS indicator are more bullish. The Gordon-based ratios are more bullish on equities largely because they produce a total return forecast of equities. In the formula, ten-year rolling ROE estimates have increased. In addition, the real interest rate that is subsequently subtracted from the forecast has been trending down. Since the real rate that is subtracted is small and ROE has not fallen, the forecasted equity risk premium has not moved down in conjunction with the statistical model forecasts. It is debatable whether ROE should be based on interest rates. Here it is only noted that Campbell’s paper that introduced these formulas as a tool for equity market forecasting did not suggest such an adjustment. On balance, despite the emphasis some have given to CAPE’s currently high level, a forecast based on a fuller set of valuation indicators would be consistent with a neutral or perhaps modest overweight in equities.