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There’s nothing like a 20 per cent-odd rally to bring knackered bulls to their feet. And good luck to them. The relentlessness of the fall in US equities has wearied even the hardiest investors. With the surge in optimism, however, come the same old fallacies about valuation. It does not matter whether the market has more or less halved from its peak – the risk to investors of being taken in by sloppy numbers remains real.

What to look out for? First, ignore valuation methodologies that compare current price to earnings ratios with history. Mostly the time periods used are too short, and the trouble with longer studies is that changed accounting standards tend to mix apples with pears. The least bad approach is to try to make the data consistent while using cyclically adjusted earnings based on a trend over a number of years. Smithers & Co, a research outfit, uses such a ratio and concludes that the S&P 500 index is, at best, fairly valued.

The second nonsense is to become excited when dividend yields exceed bond yields. Not only is it theoretically flaky to compare company payouts (which are risky and rise with inflation) with government bond coupons (which are fixed and risk-free), but much research has shown that this methodology – sometimes known as the “Fed model” – has weak predictive powers.

That is not to say that all analysis should be thrown out the window. Fundamentals do matter – although just as good a way to check whether equities are over- or undervalued is to take a very long-term chart, and with a pencil and ruler draw in the trend line. That is as fair a proxy as any for the steady-state growth rate of global profits. Again, that approach currently suggests fair value.

Still, markets can overshoot a long way. It is worth remembering that, since 1923, equities have, on average, bottomed four months before a recovery in the economy. Who would bet the US is at that point today?

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