Letter: Equity Risk is not in step with 'random walk' theory

Andrew Smithers
Financial Times - Letters, 19th July 2021


The letter from Zvi Bodie and John Ralfe (“Apply the hat trick and equities are not a free lunch”, FT.com July 14) has short-term returns being randomly selected as evidence that actual returns are not mean-reverting.

But their argument is incorrect. Stock market returns are not in fact distributed in a random manner, as the American economist Paul Samuelson — whose “hat trick” is cited by the Bodie and Ralfe letter — seems to have implicitly assumed in his “Proof that Properly Anticipated Prices Fluctuate Randomly” (Industrial Management Review 1965).

His argument was based on a priori assumptions and is inconsistent with the evidence. In fact, equity returns rotate around a stable long-term average. So markets that have subsequently given high returns were cheap and those which gave poor returns were expensive.

These now well-known characteristics have only been accepted with reluctance by many economists and, as the letter shows, are still disputed by some people.

In their A Non-Random Walk Down Wall Street (Princeton University Press, 1999) Andrew W Lo and Craig MacKinlay give an amusing account of the strength of this resistance: “ . . . when we first presented our rejection of the ‘random walk hypothesis’ at an academic conference in 1986, our discussant — a distinguished economist and senior member of the profession — asserted with great confidence that we had made a programming error.”

The risks of holding equities do not fall year by year, since the annual risk is unchanged. But they do fall the longer the expected period for which they are held.

Above all, being mean-reverting, they fall faster than they would if returns were random.

For example, to have a less than 5 per cent chance of getting a negative real return the intended holding period would have been 30 years if returns were random but has been only 14 years, given the mean-reversion. We must not let a priori assumptions override the evidence, which is perfectly clear.

Andrew Smithers
London W8, UK


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