*Michele Gambera uses UK equities to reveal how excluding or including companies with negative earnings skews the P/E ratio of the market*

Are stock markets overvalued? Everybody would love to know the true answer to thisquestion. Regrettably, the truth is quite elusive, and all we have are estimates of noisy proxies.

The price-to-earnings ratio (P/E) is a well-known measure of market valuation. It tells you how many pounds sterling you need to pay to become a stockholder and receive a pound of annual earnings. Consequently, a high number suggests that the market is expensive because you pay much to get the earnings, while a low number suggests that the market is cheap.

This sounds intuitive. But there is a catch: which earnings should we use? The earnings for the past 12 months, perhaps, or maybe those of the next 12 months as predicted by that optimistic lot, the stock analysts? And in any case, should we weight these earnings according to the weight of the stock in the portfolio (or market index), or should we just compute a straight average (or maybe a median, which is less affected by outliers)?

In any case, a further complication comes from companies with negative or zero earnings. If you compute your P/E ratio bottom-up - that is, if you take the P/E of each company and feed it into your statistic of choice, you might need to exclude companies with zero earnings, because the denominator of the P/E ratio would be zero and, therefore, you would have an undefined value. Moreover, if you use statistics such as the geometric mean to limit the weight of outliers, you might not be able to handle negative P/E values.

Finally, from an accounting point of view, large negative earnings could happen just because of a one-off loss and, therefore, might not be representative of the market situation. For these reasons, many data providers prefer to report P/E ratios excluding companies with negative earnings. For example, Morningstar reports P/E excluding negatives and MSCI generally does the same, while Standard & Poor’s reports P/E including negative earnings. All approaches have pros and cons, and none is perfect.

An alternative way to limit the power of one-off losses was suggested by professors John Campbell and Robert Shiller, who choose to compute the ratio of current price to average real earnings. In practice, they calculate the trailing average earnings for the last 10 years, adjust them for inflation, and then compute the ratio. In this way, they are computing the ratio of today’s price to the ‘normal’ earnings for that basket of stocks. This is reasonable, since they are filtering out one-time charges as well as short-term earnings fluctuations. Campbell and Shiller find this P/E variation to have higher predictive power on the total returns to the stock market over the following 10 years than traditional P/E ratios.

It is important to remember that 10-year horizon: academic studies consistently find that valuation measures are better suited to long-term predictions of which asset class will outperform, while momentum-based measures are more effective for short-term forecasts.

Let us now take a look at the current state of the UK equity market. Using FactSet data, we have P/E ratios computed both including and excluding negatives back to 1986.

Moreover, we compute the Campbell-Shiller P/E in the following way. We start by dividing the price index by the P/E including negatives, which gives earnings because P / (P/E) = E. We then calculate a trailing average of E (since inflation was relatively benign in the period for which we have data, we take a shortcut and do not adjust earnings for inflation).

Finally, we divide the price index by the moving average of earnings to obtain the price to average earnings ratio. The results are summarised in the chart.

The first thing that one notices on this chart is how high the P/E, including negatives (blue line), was during the 2001-04 recessionary period, when so many companies had negative earnings and therefore the aggregate market earnings (denominator of the ratio) were a small number. Note that the data provider censors the number at 150 when total market earnings are tiny and the ratio might become a very large number.

As can be seen, the ratio has been quite high recently, and is currently sitting just above 65. The median for 1986-2009 is 18.7 and the current value is between the 90th and the 91st percentiles of the distribution during the period. According to this measure, the UK stock market valuation is outrageously expensive.

The grey line represents the P/E excluding negatives. Right now, the value of the ratio is 16.3, while the median is 15.3. The current value is close to the 52nd percentile and, therefore, we conclude that this measure suggests that the market is fairly priced.

The rust coloured line with the Campbell-Shiller P/E starts later in the chart because we need to average 10 years of returns to compute the first observation. The statistic currently reads 24.2, which is near the 33rd percentile of the distribution. We note that the UK stock market appears undervalued according to this measure. But since we only have 14 years of data for this statistic, we would not bet the house on this conclusion.

Altogether, the valuation measures presented here confirm that the current state of affairs makes it difficult to judge whether the market is cheap or expensive. The more industrious readers will look for longer data series and, following the methodology we summarised, may obtain a clearer picture.

One way to look at the data would be to consider whether you expect most companies to book a healthy profit in the next few years, in which case the P/E excluding negatives would be more representative; or if you expect companies to post lacklustre results, in which case the P/E including negatives would be a better guide.

In general, however, given that the two traditional P/E measures state that the market is either expensive or fairly valued, we would maintain a prudent stance.

**Michele Gambera is chief economist at Ibbotson Associates, a Morningstar company**

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