The American stockmarket has hit repeated highs over the past 12 months—most recently on Friday—amid signs of faster economic growth. Japanese shares have likewise reached 15-year highs, European markets are at seven-year peaks and London’s FTSE is nearing its record, set at the end of 1999. But Robert Shiller, a Nobel prize-winning economist, has sounded a warning. His valuation measure, the cyclically adjusted price-earnings ratio (CAPE), is at 27.8, higher than in 2007, just before the financial crisis. The CAPE averages profits over ten years to adjust for the cycle. Bulls are pooh-poohing Mr Shiller’s analysis, but then they were sceptical when he pointed to an even higher CAPE of 44 in the dotcom bubble and to an overvaluation of housing in the mid-2000s. And S&P 500 companies’ profits are expected to fall in the first quarter of 2015, thanks to the decline in oil firms’ earnings.

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