Why equity returns do not take investors on a ‘random walk’

Andrew Smithers
Financial Times [In Letters], 14th November 2016

Zvi Bodie and John Ralfe’s letter (“A thought experiment worth repeating”, November 9) is in error and, furthermore, the error it makes is a well known one.

Paul Samuelson’s thought experiment was proposed at a time when it was assumed that real equity returns to shareholders followed a “random walk with drift”. It is now agreed and, as far as I am aware, almost universally agreed by financial economists that equity returns are not random, but exhibit marked negative serial correlation. If returns followed a random walk, the past would have no influence on future returns. In fact, due to their negative serial correlation, below average returns in the past increase the prospect of above-average future returns and of course vice versa, which is a rational cause for concern among investors today.

Long-term equity investing is less risky than short-term investing, and the reduction in risk is significantly greater than would occur if returns were random. In this sense there is a “loyalty bonus” for long-term investors. The negative serial correlation can be demonstrated by comparing the observed long- term volatility of real returns with the volatility that they would have had if returns followed a random walk. If returns were random, the volatility of US real returns, measured by their variance over 20 years, would have been 2.5 times greater than it has been.

Professor Bodie and Mr Ralfe claim that for 20-year outcomes there will be many periods of loss and some major ones. The data, however, show that since 1801 there has been no period of 20 years in which US equities did not give a positive real return. This is not some miracle of good fortune, it is because equity returns do not, as they assume, follow a random walk.

Models which are refuted by the data should be discarded. The random walk model is one of these and investors should not take advice from those who refuse to accept it.

Andrew Smithers
London W8