- Stuart Fowler

# Equity risk and time

Talking Head, FTfm, 2nd May. The relationship between equity risk and time is a key battle ground in the conflict between ‘fair value’ accountants, for whom equity investing is a huge gamble by people who ‘should know better’, and investment professionals and many actuaries, who are more trustful of the benefits of equity investing, for most individuals and the nation state collectively. FTfm has been reporting one particular confrontation, between John Ralfe, a champion of fair value accountants, and Adair Turner who, though not a professional, relied in his Pensions Commission report on a popular claim made by professionals that equities are less risky for a long-term investor. As typically presented, this claim is indeed the howler Ralfe suggested. Yet it does not need much rephrasing to turn Turner’s intuition into wise counsel.

The howler has a simple explanation. The industry adopts the convention of ‘standard deviation’ as a measure of risk. A feature of this is that when expressed as an annualised (or other standard period) rate, as it usually is, it has the characteristic that the rate falls as the period lengthens. This is a simple feature of the laws of probability, first understood in the 16th century. In a purely random series, the rate falls as a function of the square root of time. In a mean-reverting series, the rate falls faster than for a random series, depending on the strength of the mean as a ‘magnet’.

The decline in the annualized standard deviation is often misunderstood and then misrepresented as a decline in the amount of risk. The proof of the error is that the same series will show both a declining standard deviation and an increasing band of possible outcomes the longer the holding period. The shape of these possible outcomes has been usefully termed ‘an expanding funnel of doubt’. It is a symptom of increasing risk, not falling risk.

It is perfectly valid to make (or have in mind) a different point about the time dependence of risk, based on the interaction of uncertain outcomes and some risk ‘utility’or preference function. An equity risk premium earned over time, even allowing for uncertainty of outcomes, alters the relationship as time passes between, for example, the worst expected outcome and the minimum acceptable outcome, or between the mean expected outcome and some desired target. So any investor with a fixed utility function may reject the equity bet at one expected holding period but accept it at a longer one. Indeed, it is theoretically feasible that, if equity real return deviations from a sustainable trend have in the past been bounded, where the bounds lie is explained by a common average investor utility, common at different points in history and even between different markets.

When providing for individual retirement income, the time horizon during both the accumulation and decumulation phases can be 60 years or more. If the plan is funded very conservatively, to provide the required real outcome assuming investment in a matched index linked gilt, all of the upside in equity returns is given up, even though at some far horizon (say 20 years – depending on the model assumptions) all of the equity uncertain outcomes are above the risk free rate. Giving these up is only rational for an investor who places much more weight on how smooth is the path of the fund than on differences in the fund outcome. Altering the accounting rules makes it rational for defined benefit schemes to optimise paths rather than outcomes. The effect is to make pension provision a radically different bet for defined benefit schemes than for individuals.

The new nature of the defined benefit bet does not have more integrity than the individual bet and in some respects has less. It was an accounting magic wand that arbitrarily made the market yield on non-inflation-proofed AAA corporate debt the discount rate for future defined benefits and hence the ‘matching asset’. For any investor with targets expressed in purchasing power terms, non-indexed corporate bonds have uncertain outcomes and, on any realistic assumptions about the nature of the inflation process, this risk is time-dependent. Indeed, at some long horizon the range of real outcomes is likely to be nearly as wide for these bonds as for equities.

The idea that the wedge driven by accounting practice between institutional and individual utility functions may be inefficient and costly for the nation as a whole surely has merit. Hopefully Adair Turner will not be put off pursuing it by the flak from John Ralfe.