Stuart **wrote last year** on some of the challenges associated with relying solely upon the Shiller P/E as a measure of equity valuation. This debate has been widely covered and is somewhat moot at any rate, given that the US market is looking expensive relative to history on a whole range of metrics (as** ‘this one chart’** helpfully **shows**).

However, a** recent piece** from the Federal Reserve Bank of San Francisco highlighted an interesting element of the debate. As well as echoing our own observations on the nature of **regimes,** the authors also note the important features of the denominator of the metric. The Shiller P/E takes the current price of an index and divides it by the average (mean) of the last ten years’ real earnings.

Ten years ago, the US economy was about to enter one of the** largest recessions** of the modern era, but in two years’ time, the effects of that recession will have largely dropped out of the average earnings figure used in the Shiller P/E. Even if real earnings and prices in the US were to stay the same for the next year, the Shiller P/E would show the market ‘getting cheaper’ due to the effect of the rolling ten-year average (as illustrated by the red dotted line in figure 1).

Is this fair? If the purpose of cyclically-adjusting the earnings is to give a better picture of sustainable corporate earnings power, is massaging out the impacts of the last serious recession disingenuous? It is after all, not unreasonable to assume that there is a crisis of some sort** every ten years or so.**

Regardless, this observation highlights the fact that in analyzing a metric that is supposed to tell us something about price, there can be a temptation to ignore the other side of the equation. This can lead to problems when it may be the denominator that is doing a lot to drive current levels.

And it’s worth reminding ourselves of quite how severe the impact of the crisis on corporate profits was.

Shiller’s metric uses** reported earnings** figures in the left hand chart, which include ‘temporary’ factors like impairments and write-downs. This looks especially bad but even operating earnings suffered the biggest peak-trough collapse in over 30 years.

This could happen again of course, and whether (and when) it does is arguably a more pressing question for whether equities are expensive or not.

We need to consider whether comparing a valuation metric which embeds such a significant earnings collapse in its denominator to periods which do not is a fair comparison, and if ten years is anything but an arbitrary time frame (particularly if ‘boom and bust’ has been replaced by** ‘crawl and crash’** or the nature of companies within an index have different sensitivities to cyclical dynamics).

**Denominator neglect**

More broadly I think this example reflects a general tendency to give insufficient thought (or at the least insufficient focus in the press) to the denominators of certain ratios in finance/economics because of how and why these metrics are constructed. This is related to a concept in behavioural finance known as** ‘denominator neglect’** whereby people misjudge probabilities because they pay more attention to the most salient aspect of a ratio (e.g. number of times you win, discounting number of times you don’t).

In many metrics, the variable of interest is generally the numerator, with the denominator helping to contextualise/compare across different instances. Since the Shiller P/E is designed to tell us about what will happen to the price, it is natural that people will cite the P/E ratio with a focus on the “P” and ignore the fact that even a simple price-earnings ratio is conditional on an underlying assumption around profits growth. If your P/E is unchanged and earnings were to continue to grow at a long term rate of 6%, then you’ll still double your money in less than 12 years – regardless of whether that ratio appeared “expensive”.

**China’s leverage issue**

A related case is seen in measures of indebtedness of the form Debt/GDP. China, for example, is regarded as having a debt problem. Leverage is commonly cited as a likely source of economic issues, with a recurring discussion over whether and when this may result in a so-called “hard landing” for the Chinese economy.

Such discussions generally neglect the alternative to widespread default in resolving a debt sustainability problem though. If nominal growth outpaces debt growth, then leverage ratios will come down through time. This can be seen occurring in the latest numbers where the recent pick-up in Chinese nominal growth has caused combined household and corporate leverage to stabilise and decline slightly. Were this trend to persist then measured leverage would begin heading back down.

I’m not forecasting that this *will* happen. Merely that it’s rarely mentioned that the above chart could simply normalise through growth over time. This receives significantly less airtime when it’s the debt part that people are worried about, but it should at least feature somewhere in your probability distribution.

Similarly, we cannot consider the stock of debt without considering the rate payable on it. An individual household’s debt to income ratio would tell very different stories if it has to meet mortgage payments of 25% per year than if they were at 2%.

**There are two sides to every ratio**

Part of the reason that we create valuation metrics is as tools to help provide discipline and avoid the human temptation to become caught up in the excitement of the moment. However, an equally powerful temptation is often to use these metrics to oversimplify.

Behaviourally, we are drawn to focus on the most salient aspect of a ratio, such as the ‘p’ in ‘p/e’ or the debt rather than the GDP. These are what the ratios were designed to analyse after all.

But this is incomplete analysis. It’s important to remember that there are two sides to every ratio (as well as the variety of forces that drive each of them) and a simple focus on one of them can be misleading and potentially dangerous.