Investors are an emotional crowd, especially when US equities, measured by either the Dow Jones Industrial Average or the more accurate S&P 500 index, have just hit all-time highs. I am not sure who first remarked that market behaviour is motivated by two competing emotions, fear and greed. But I do know that Albert Einstein claimed that “Three great forces rule the world: stupidity, fear and greed”.
Some of the macroeconomists that I have learned not to ignore, like Lawrence Summers and Martin Wolf believe that the outlook for the US economy under President Trump is at best uncertain, and that the recent equity market highs are a “sugar rush”. I recognise that some of these critics have major political differences with the new Administration. But many others, like the perceptive and apolitical John Authers, are also very concerned about equity over-valuation.
So, are investors being “stupid”?
That does not make the models the only source of wisdom about future asset returns. Far from it. They are good at avoiding some of the behavioural mistakes that investors are known to commit, such as a tendency to dislike losses about twice as much as they like gains. But human beings may be better at recognising when the investment climate is about to change because of policy upheavals.
In this article, I will try to eliminate emotion by reporting some recent results from the suite of economic and financial models built by Juan Antolin Diaz and his team at Fulcrum. The results are somewhat encouraging: recession risks in the US are low and the over-valuation of equities is less clear cut (on some measures) than is sometimes supposed.
In the short term, however, there are signs that the most active short term traders in the market may be heavily exposed to equities at the present time. This could make the market vulnerable in the short term to policy shocks that cannot be incorporated into the models, such as a major outbreak of trade protectionism.
First, the state of the US economy. The latest nowcast models have identified a significant upswing in US economic activity since last autumn. Although this started before the Presidential election, it has intensified since then. Last week, the nowcast estimated that activity growth has reached 3.6 per cent, the highest growth rate reported since 2010.
The nowcast models suggest that the probability of recession within 12 months is extremely low, at less than 5 per cent. This compares with more elevated probabilities of 20-30 per cent at times last year. Furthermore, there is a 75 per cent probability that the US economy will experience sustained GDP growth at above trend rates in 2017, an outcome that has not been observed for years.
Since major bear markets in equities are almost always accompanied by recessions, these estimates are encouraging, though they are certainly not definitive. New shocks might hit the economy that cause recession probabilities suddenly to spike upwards, or a spontaneous collapse in equities could itself cause a recession. But for now the economy looks unusually healthy, regardless of any Trump effect. And analysts’ projections for corporate earnings are following economic activity upwards.
Next, the fundamental valuation of the stockmarket. Is the S&P 500 now so “overvalued” that a period of negative returns is inevitable in the years ahead? The forward P/E on the market stands at 17.4, which is about 1.5 standard deviations above its historical average, and the long run Shiller P/E (computed using 10-year averages of real earnings instead of today’s forward earnings) is also well above normal .
Many analysts (including Jeremy Grantham) warn that these valuations should be consistent with equity returns that are well below average over the medium term, and some argue that real returns may even be negative for many years ahead. These conclusions generally follow from assuming that today’s elevated corporate profit margins will return to normal, and the P/E will also return to its historical average, over (say) a 3-7 year period ahead.
These assumptions, however, are not supported decisively by the historical data. Juan Antolin Diaz and colleagues have estimated a 7 variable BVAR model on post war US data , and they do not find that there is much evidence of rapid “mean reversion” in the profit share and the price-to-dividends ratio over this period.
In the current version of the model – which is still only preliminary – the reversion to mean happens very slowly. This results in somewhat less depressed returns for American equities as over-valuation is eliminated only gradually in the years ahead.
The model’s “forecast” for real, inflation-adjusted returns over the next three years is shown below. Although real returns of 5 percent per annum would still be somewhat below the historical return of 6.7 per cent per annum, they are not as low as predicted by some other methods that impose a faster mean reversion in profit and valuation metrics. 
Finally, what do the models say about the positioning of short term traders in the market? This is not directly observable, but one approach is to design an algorithm that acts in a very similar way to the trend-following models that are used by CTAs and other short term risk takers.
In such a system, the positioning of active traders increases when market volatility is low, and when market prices are trending upwards. Both of these factors apply at present, so the model reckons that short term exposures are as high as they have been at any time since 2007:
The high equity exposure implies that the model’s best guess (or “unconditional prediction”) is that future returns will be relatively high, compared to volatility, provided that the market is not hit by adverse news. However, it also suggests that there could be a sharp near-term sell-off if the news flow deteriorates.
This is where President Trump becomes highly relevant. Most of the “Trump trades” that have been so important in driving macro and micro market behaviour peaked a few weeks ago, and have since seen partial retracements (see this report on the Trump trades). But the equity market trade has not retraced at all. It could be vulnerable, especially to news about protection against China.
Any sensible analyst should be cautious in expressing opinions about a market that is subject to near-perfect information flows, like the American stock market. As we all know, the wrath of the market gods can punish over confidence very severely. So I will restrict myself to a factual conclusion: the models reported here do not suggest that Dow 20,000 is the peak for equities in the current cycle.
 Pessimistic forecasts for equity returns are often underpinned by using the Shiller cyclically adjusted P/E, but, in an important recent contribution, Jeremy Siegel has suggested that the CAPE calculation has been distorted upwards by changes in the computation of GAAP earnings. When these distortions are removed, the implied forecast for medium term equity returns rises markedly. Siegel’s preferred definition predicts real equity returns of 4.41 per cent per annum from 2015-25, compared to a historical average of 6.70 per cent. These latter returns are not very different from those generated in the current version of the Fulcrum model.
 The model is a Bayesian Vector Autoregression using the following US variables: S&P 500 price index; log S&P 500 dividends (seasonally adjusted by Fulcrum); 3-month treasury bills; 10-year government bond yields; spread between government and Moodys corporate BAA bond yields; real GDP; and core PCE inflation. For the current quarter, the latter two variables use Fulcrum nowcasts. The final version of the model may be slightly different, but we do not expect the main conclusions to change.
 The current version of the Antolin Diaz et al empirical model is estimated to explain about 50 per cent of the variation in US real equity returns over 3-year periods ahead. That, of course, means that there is plenty of scope to be surprised, but the direction of the surprise is not known in advance.
This post originally appeared on Financial Times