It will be virtually impossible for some of the US stock market’s largest companies to grow fast enough to justify their current valuations. That is the conclusion reached by a recent study conducted by Vincent Deluard, head of global macro strategy at investment firm StoneX.

His argument is not just that certain large-cap growth companies are trading on the assumption their revenues will grow at improbably fast rates. He adds that even if a given company does grow at a fast-enough pace, it soon would be larger than the market as a whole. In that case, “valuations are mathematically impossible”. There are limits to growth, in other words. As John Maynard Keynes put it a century ago: trees don’t grow to the sky.