- Stuart Fowler

# Asset wars #1: Who’s telling the truth about equity risk?

I shall file regular dispatches from the frontline in the battle of ideas pitching bond investment against equity investment, ‘fair value’ accountants against traditional investment consultants. It’s a big issue for individuals because it’s really influencing what assets are held on their behalf. That, as we well know (the ‘90% Rule’ in No Monkey Business), will significantly affect their financial outcomes.

The first dispatch deals with the question of the relationship between equity risk and time. A popular claim made by professionals is that equities are less risky for a long term investor. As typically presented, this is a myth – a howler. The second myth is that people who make this mistake (professionals or their customers) are stupid – the modern equivalent of flat earthers. The real position is much more subtle. Uncertain equity outcomes do not narrow the longer the time horizon (we’ve known that since the 16th century) but (and it’s a whopping ‘but’) the time horizon makes a big difference to most individuals’ risk ‘utility’ function. The equity bet can perfectly rationally be rejected by an investor with one horizon and accepted by another investor who has the same risk preferences, approaches bets the same way, but has a longer time horizon. When related to investor utility, the statement that may be mocked as a howler could be perfectly valid.

An instance of this, a spat between Adair Turner and John Ralfe, prompted this dispatch.

**‘Ralfe challenges Turner report’**

This was the headline in FTfm magazine on 31st January 2005. As reported by Pauline Skypala (one of the most respected of personal finance journalists, who now edits the weekly FT fund management supplement), John Ralfe (in the bond corner) was mocking Adair Turner (in the equity corner) for making the howler in his Pensions Commission report. Ralfe says Turner says the risk of holding equities reduces the longer they are held, making them them safe (or safer) for longer term investors.

Ralfe knows this is a common misconception and that it is also an easy one to pin on smarter people who know their probability laws but also have something to say about risk utility functions. I don’t know which of these Turner is but I am very mistrustful of what anyone says about their opponents in this battle between ‘fair value’ accountants, for whom equity investing is a huge gamble by people who ‘should know better’, and traditionalists, investment professionals and many actuaries, who are much more trusting of the benefits of equity investing, for most individuals and for the nation state collectively.

John Ralfe occupies a special place in war lore because he was the person who led Boots to make a wholesale move in their pension scheme from equities to bonds. Several clever academics and consultants had already penned impeccably logical critiques of equity investors’ conventional thinking but Ralfe was the first finance executive to take them to their practical conclusions in a company pension scheme. The fact it turned out to be at the top of the equity market made this an even more dashing exploit in the popular imagination.

The howler Turner and the traditionalists are supposed to have made has a technical explanation. When talking about risk, the industry adopts the convention of ‘standard deviation’ as a measure of volatility or uncertainty, which is sensible enough if it captures the relevant dimension of risk in a particular context. A decade ago, a technical term like ‘standard deviation’ was a no-no in dialogue between professionals and their clients but this is rightly now seen as condescending. As a standard measure of dispersion of a set of numbers, its value in everyday life is in giving insights into degrees of uncertainty not picked up in an average or in a single point forecast, in expressing chances and helping people think about the certainty they attach to any target outcome, from not being late to an important meeting a long drive away to an acceptable minimum retirement income.

**Muddling rates and levels**

A feature of this measure of dispersion 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. In a purely random series, the rate falls as a function of the square root of time. This is a fundamental feature of the laws of probability, first understood in the 16th century. It is the same phenomenon we recognize as the decline in the chances of a coin landing repetitively heads up the more often we toss the coin. (Anyone interested in how our understanding of risk developed should read Peter Bernstein’s book, Against the Gods: the remarkable story of risk. It is rightly a world-wide best seller.)

For those less familiar with these concepts than our Renaissance forebears (see how easy it is to mock?), the decline in the annualized standard deviation the longer the holding period is often misunderstood and misrepresented as a decline in the level of risk when holding equities for longer periods. The proof of the error is that even with a declining standard deviation the random series still shows an increasing band of possible outcomes the longer the holding period, and indeed the range expands at a constant rate. The shape of these possible outcomes has been usefully termed ‘an expanding funnel of doubt’. Expanding outcomes are a symptom of increasing risk, not falling risk.

So any client report or marketing literature that makes the claim that risk declines with the length of the holding period, whether or not it is accompanied by a picture showing the narrowing band of annualized possible growth rates at, say, 1, 5, 10 and 20 years, probably falls into this trap. I have seen this countless times in stockbrokers’ and IFAs’ literature as well as in conversations and articles. I have some sympathy for people like John Ralfe who see this as a mark of the industry’s lack of technical competence.

**What mean reversion means for risk**

Amongst people who understand this point, there is still a secondary level of dispute, which is whether the data series in question is really random or has the feature of reversion to the mean. If the latter, the rate at which the annualized standard deviation declines with time is faster than for a random series. If we could be totally sure of the slope of any upward trend, such as for real equity return, certain of where we were in relation to the trend, and sure of our assumption about the strength of the reversion coefficient (the strength of the ‘magnet’) then we might assume the band of outcomes at some point ceases to expand. But since we cannot be that certain, some expanding funnel is always a sensible assumption.

Randomness versus mean reversion is another battle ground in the asset wars. Using option pricing, as market-based valuation does, tends to build in an assumption of randomness whereas traditional actuarial projections of equity returns, most investment advice practice and many (but not all) asset models assume mean reversion. Options have developed mainly for short term purposes where randomness is almost certainly the right assumption. But mean reversion of very long term fundamental investment inputs as a result of some underlying economic equilbrium theory is also very persuasive, though hard to ‘prove’ statistically. I shall return to the randomness versus mean reversion battle in another dispatch.

Time and individual utility functions

Coming back to the main argument, it is perfectly valid to make a different point about the time dependence of risk, based on the interaction of uncertain outcomes and some risk utility 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, or fixed risk tolerance, 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 are bounded, where the bounds bite is actually explained by a common average investor utility (common at different points in history and even between different markets). Chris Drew, at Lambda Investment Technology, is writing a paper advancing this theory and when published I will post it here – though probably coded black.

For the individual saving for retirement income, and planning on a drawdown with no pre-determined annuity purchase, the time horizon during an accumulation phase could be as long as 75 years and even at the start of the drawdown phase some capital may have up to 45 years maturity. If an annuity purchase is assumed at age 75, the time horizon when accumulating assets could still be between 25 and 45 years. If the scheme is funded very conservatively, to provide the required outcome at the risk free rate (ie a matched Index linked gilt), and then invested in an ILG, all of the upside in equity returns is given up, even though at some far horizon (say 20 years or more – 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 accumulating wealth than on differences in the wealth outcome.

Even then, it is perfectly feasible to invest in equities but fund on the basis of the risk free rate. Then, if the assumption about the equity risk premium is right, it will generate a surplus. Still pretty robust, but less certain, would be to fund on the basis of the lowest expected equity risk premium and invest in equities.

This distinction between funding risk and investment risk is important, but the protagonists in the debate often muddle the two. What annoys Ralfe et al, quite rightly, is that companies funded their schemes as if the mean expected equity return had a 99% certainty instead of 50% certainty.

Another example of this fallacy should be familiar to No Monkey Business graduates: because endowments typically generated surpluses at maturity, somebody decided you could safely fund a low-cost mortgage endowment at a rate of premium (or contribution) that only required 50% certainty! Funding risk and investment risk are not the same and it is individual risk utility functions that link them.

**Accounting treatment can transform the utility function**

It’s an accounting magic wand that arbitrarily made the market yield on non-inflation-proofed AAA corporate debt the discount rate for future liabilities and hence, in accounting terms, the ‘matching asset’. For any investor with target outcomes expressed in purchasing power terms, corporate bonds not inflation indexed are risky: they have uncertain real outcomes but lower expected real returns than other risky assets like equities. 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 as wide for these bonds as for equities. Pension plans and most individual savings goals have a purchasing power objective so non-indexed bonds cannot be risk-free. (To spoil a good story, Boots initially switched from equities to non-inflation indexed bonds and it was only about 18 months later that it quietly corrected this in favour of index linked gilts!)

Fair value accounting, by changing the rules and altering consequences, in practice shifts all affected investors’ risk sensitivity from outcome uncertainty to the volatility of the path. I say ‘in practice’ because, whilst it is possible to tighten up funding risk without altering the asset bets, the most tempting route is to follow the herd into bonds; and whilst it is possible to hold only index linked bonds, there are not enough to go round.

A consequence of this is that individuals investing through a regulated principal, particularly one offering gurantees (eg pension trustees, with-profits life funds), will now have decisions made for them based on a different risk utility function, driven by accounting risks, from the ones they would probably exhibit if well informed and making their own choices. This carries a cost for individuals. Maybe Adair Turner was sensitive to this as inefficient for the nation collectively. I will return to the way the asset wars threaten this collateral damage in another dispatch.

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