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The first quarter of 2009, the bottom for US stocks during the financial crisis, is now remembered as what it was: a once in a lifetime chance to acquire shares. With perfect hindsight anyone who held their nose, bought near the bottom and held on would have more than doubled their capital in the seven or so years that have passed.

One excuse for those who did not was that back then one of the most widely used benchmarks for US equities, the S&P 500, appeared expensive, trading on a seemingly rich trailing price to earnings ratio of more than 20 times. Why the index appeared expensive at its bottom is salient for those not wanting to repeat the same mistake.

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A vast amount of human energy is spent debating whether the “stock market”, typically depicted as an index such as the S&P 500, is heading for a fall or not.

Considering the popularity of p/e multiples it is important to understand how the earnings of popular indices such as the S&P 500 and Russell 2000 are calculated, and how this method can make shares as a whole appear more or less expensive than they may actually be.

The S&P 500 is a market capitalisation-weighted index, meaning the most valuable of its constituents comprise a proportionately greater part of its price than smaller ones. As such the performance of the shares of Apple, the largest company by value in the index with a weighting of 3.4 per cent, has a far larger impact on its performance than smaller members. If you spend $100 purchasing a fund that tracks the S&P index today then $3.40 of your initial investment goes into Apple stock.

This all changes when it comes to calculating the earnings of the S&P 500, which are then used to calculate its p/e ratio. S&P simply adds together all of the reported earnings and losses of the members of the index. A dollar of Apple’s earnings is worth the same in this calculation as a dollar earned by Murphy Oil.

The trailing 12-month earnings of Apple were $47bn, according to Bloomberg data. The combined losses of the four least profitable members of the index over the same period — Apache, Devon Energy, Freeport-McMoRan and Chesapeake Energy — were roughly the same at $48.3bn. Apple as we know makes up 3.4 per cent of the index, while the combined weight of those four biggest lossmaking companies is just 0.023 per cent. All of Apple’s profits, when calculating the price to earnings ratio of the S&P 500, are wiped out by these four tiny members of the index.

The top eight most valuable members of the S&P 500 made a combined $135bn in net profits on a trailing 12-month basis. These earnings are all but cancelled out by the 30 largest lossmaking companies in the index, which over the past 12 months reported combined losses of $125bn. The eight largest companies — Apple, Microsoft, Exxon, Johnson & Johnson, Amazon, Facebook, General Electric and Berkshire Hathaway — together have a 15.5 per cent weighting in the S&P 500. The 30 biggest lossmakers have a combined weighting of just 4.5 per cent, which is reduced to about 3.5 per cent if you remove Chevron, which reported a loss of less than $1bn over the period.

A different problem occurs if you try to draw conclusions from the p/e of the Russell 2000 index, which is frequently used to represent the performance of US small-cap companies. Russell, which since 2014 has been owned by the London Stock Exchange, publishes two versions of the Russell 2000 p/e multiple. The most commonly used version excludes any losses at all, including only the profits made by index constituents. Using this method the Russell 2000 stands at a multiple of about 40 times trailing earnings. Using the other method, which includes the losses, the Russell trades at a considerably higher 84 times last year’s profits.

Traders work on the floor of the New York Stock Exchange (NYSE) in New York, U.S., on Monday, June 20, 2016. U.S. stocks surged, with the S&P 500 Index jumping the most in four weeks, after the latest polls showed the U.K. campaign to remain in the European Union is gaining ground before Thursday's referendum. Photographer: Michael Nagle/Bloomberg©Bloomberg

The next time a big stock market sell-off occurs investors should ensure they take a closer look

David Blitzer, chairman of S&P’s Index Committee, has faced these questions before, most notably from Jeremy Siegel, a Wharton School professor of finance who has dissected S&P’s methodology. Mr Blitzer argues that a dollar earned or lost by S&P 500 member should be counted the same. The index, in his view, should be treated like a company with 500 divisions. If one part loses money, the losses are suffered by the company as a whole regardless of the value of that division compared with another.

This does not change the fact that back in 2009 stocks as a whole would have appeared to many casual observers as misleadingly expensive rather than cheap if they relied on the p/e of the S&P 500. About 80 companies, mostly banks, at the time reported $240bn of losses — yet they made up only a 6 per cent weight in the index. The next time a big stock market sell-off occurs investors should ensure they take a closer look.

miles.johnson@ft.com

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