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The Great Moderation of GDP that took place in the mid-1990s came along with a striking rise in the volatility of businesses' real earning. As can be seen below, the volatility of real earnings rose dramatically during that period while that of GDP fell to a new regime and has stayed low in comparison with the post-war period - even if the Great Recession is taken into account.

This sharp increase in earnings' volatility suggests that it more important than ever to smooth past earnings from the economic cycle when using valuation metrics based on past earnings. This is the very purpose of the so-called CAPE or Cyclically Adjusted Price Earnings ratio. The CAPE is defined as the ratio of the real price (assessed in today's price) of the S&P 500 divided by the 10-year average of real earnings. Today's reading can be seen below:

We can clearly see the volatility of earnings and in particular the huge plunge of 2009. We can also see that the current reading for the CAPE is slightly below the average level of the 2003/07 period and well below that of the late 1990s when real earnings were much lower and the PE much higher. From a very long run point of view (that is one century) though, the CAPE is well above its average value, which would, according to many, call for an overvalued US stock market

If the crash of the early 2000s was clearly justified by the over-stretched level of valuations, that of the late 2000s was much more macro-driven (recession, collapse in global trade, dollar and capital shortages, systemic risk) than justified by the level of valuations. The chart below based on 12-month trailing earnings would foster this view. 2008's PE may have been close to the x15 level - where they could be deemed "rich" - they did not show any disconnect similar to that of the late 1990s. This is clearly where we stand. A simple rule of thumb calculation would prove that the S&P 500 can easily grow by 8/10% without having its PE ratio breaching today's valuation level: nominal GDP is expected at 4.5% and listed companies' earnings generally grow by twice this number.

The current CAPE reading calls for caution especially since it may be skewed on the upside by the unusual and exceptional fall in earnings that took place in the wake of the Great Recession. I reassessed the CAPE with the assumption that real earnings did not fall below the trend defined by the latest two troughs (see dotted line below left). The new CAPE is, not surprisingly, slightly lower. This should tame the fear of overvaluation.

For the proponents of the CAPE it might not change the conclusion. The use of CAPE based on the statistical concept of mean reversion, the tendency of the ratio to revert to its mean. When there is mean reversion, shocks that affect prices fade away with time. In statistical terms, a time series mean reverts if it is stationary, that is shocks die out and the series evolves around a constant mean.

If the PE is stationary then its level can be used to infer future price action: when the PE gets too high (or too low) the likelihood of a forthcoming fall (increase) increases (PE correct mostly through prices rather than earnings, big exceptions being 2001 and 2008). Yet, history shows that there are no genuine threshold from which a fall or rebound in the CAPE is triggered (see chart below, since 1880).

There are several reasons why the CAPE/Mean reversion model should be used carefully:

i. PE ratios might have shifted upward permanently from 1990 onward: lower inflation regime, lower transaction costs, accounting rules, changes in risk preferences. This would not reduce the robustness of the CAPE analysis but recommends not using the very long run average for mean reversion targets. More generally, the average level of the PE ratio might encounter some structural breaks from time to time which would suggest different mean reversion targets.

ii. There is a conflict between the PE ratio mean reversion hypothesis (CAPE) and the Fed Model (in which stocks and bonds compete for yields). If the Earnings yield (E/P) follows US Treasury yields and if those yields are not stationary (don't mean revert, which is statistically proven), then the PE ratio cannot be stationary and mean revert in the medium run. This would just mean that using CAPE could be useless.

In a nutshell, PE ratios might be stationary (valid) or not (then the Fed model is a better tool) or, something that has to be tested, valid but only in different regimes/levels of PE (first point above). Mean reversion would be observed but in a shorter span of time (in between structural breaks that have to be identified).

I did a quick estimate of the "stationarity" of the CAPE since 1990. In other words, I checked if the mean was dependent on time or not. Using different "unit root tests" I found that since 1990 the CAPE is not stationary, which would call for a very cautious use of the CAPE as an indicator of under/over valuation.

Bottom line: many investors consider that because the current reading of the CAPE is above its (very) long run average, stocks are overvalued. Even the father of the CAPE (Shiller) was quoted as saying that he was "worried about the boom in the US stock market."

Based on the above analysis, I would not resort to the CAPE to gauge the vulnerability of US stocks. It will all depend on the pace of increase of US Treasury yields. For 2014, higher US Treasury yields should have a negative impact on stock returns only while uncertainty of monetary policy prevails. When the Fed finally tapers (today ISM is consistent with my call for an early 2014 tapering), stocks will continue to ramp up. Stay long US stocks.

Source: CAPE CODE: Why Shiller's Model Could Prove Wrong