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The Actuary The magazine of the Institute & Faculty of Actuaries
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Mowing the lawn with a Hoover

Past performance is not an indication of future
results’, states the risk warning on investment management advertisements. Carefully chosen words, but ones which any stockbroker or fund salesman will tell you are widely ignored by investors.

Learning from the past?
At the heart of the problem lies a shared cognitive bias, which, in the guise of ‘common sense’, reassures people that the past must provide an insight into the future. The intuitive extrapolation from past experience is second nature to people. This mindset, however, is singularly unsuited to activities such as investment, involving tackling datasets with a high degree of randomness and calling for complex statistical evaluations. While the human brain is extraordinarily skilled at solving all sorts of intricate problems involving mathematical algorithms beyond the reach of the most powerful computers (have you ever seen a computer snowboarding?), for the majority of people, applying intellect to investment is like trying to mow the lawn with a Hoover!
Even if potential investors were to be persuaded to resist the common instinct for simplistic extrapolation, a number of complicating factors concerning the assessment of past information, and its significance, would persist, compounded by widespread business practices and reporting methods.

The limits of market predictability
The dominant orthodoxy of efficient market theory states that investment markets operate by always instantaneously and correctly reflecting all the information that could have a bearing on their value: that the prices are always right. If this is so, then the markets’ next move is always a random one, and it is impossible for any individual investor to consistently perform better than any other. Despite considerable empirical evidence that the theory could not really be completely true, in the form of the extraordinary success of investors and speculators such as Warren Buffet and George Soros, and in the face of mounting academic criticism, the theory has maintained very wide currency.
It is perhaps worth suggesting that the persistence of efficient market theory is due to the fact that it is not unfair to assume that price movements in markets are nearly random. Markets often do quite a good job at calculating the fair value of assets; after all, if they didn’t it would be easy to make money out of them and the opportunities would be arbitraged away rapidly. Because price movements are nearly random, markets are difficult to predict with any useful degree of reliability. Market price movements thus constitute a stochastic process, and the job of trying to forecast anything about them becomes one of investigating the statistical characteristics of this process a task infinitely more laborious than projecting a straight line into the future.
If we imagine that 99% of the movements of the markets are random and 1% of the movements is in some way predictable, then it follows that past performance neither is nor isn’t predictive of future performance. There is information to be gleaned from past performance, but it is not of the form ‘the stock/fund/asset class is up 100% over the last three years therefore it will be over the next’!
This is not only true of stocks. Studies of hedge fund and CTA returns reveal little or no evidence of performance persistence. Indeed, one study concluded that the performance persistence of CTAs relative to the surrounding ‘noise’ is such that ‘picking CTAs based on returns in the most recent year may even be worse than a strategy of randomly picking a CTA’. In the case of actively managed investments, and particularly those classed as hedge funds, the question of persistence may be further complicated by changes in strategy, but also by the phenomenon of survivor bias (more of which below).

Randomness v skill
The observation of near-randomness applies not only to markets, but to any portfolios or funds or other elements composed of markets. It is occasionally violated when an agent (individual or corporate) discovers some previously unknown information and exploits it for a period of time to produce some non-random returns. However, under normal circumstances this can be achieved only on a relatively small volume of assets, as large size restricts the range of investment opportunities into which portfolios can be diversified.
Because the search for ways of making easy money is competitive and unrelenting, there are always millions of people looking for the next superstar fund or stock or manager, whose focus is almost inevitably on historical performance. The task at hand is to distinguish results that are the result of manager skill rather than stochastic (random) elements. The question therefore is: over how long does the fund or stock or manager have to have produce how much superior performance to convince us that they have discovered something? And what else should we do to check up on a candidate ‘performer’ if we think we’ve found one?
These are complicated questions and it is not our intention to answer them here. It is worth pointing out, however, that in general random performance will dominate over short time horizons (eg 12 years), whereas predictability and skill tend to become manifest over longer ones (1020 years).

Selection bias and misrepresentation
All this would be complicated enough were it not muddied by the effects of what we might term ‘selection bias’. Disclaimers aside, the marketing of investment products is prone to capitalise on the past performance factor. It is difficult enough to assess the validity of varying performance claims between stocks or funds or managers when each claims only a single performance. When several funds are available from a manager or there are several styles to an asset class, it is easy to foster the illusion of historical success by simple sleight of hand.
The multiplicity of track records is enough in itself to create a very tempting (from a marketing standpoint) illusion of outperformance. Discounting the skill factor altogether, it is possible to demonstrate that the more track records one creates, the greater chance there is of one of them performing in a manner that appears exceptional. The graph opposite (figure 1) shows the potential outperformance of the best over the average in a portfolio of N uncorrelated assets with volatility s.
In figure 1, if one were to select only the best performer as representative of a group of, for example, five assets with a standard deviation of 20%, the realistically achievable return could be overstated by 23% simply by having five funds to choose from. In practice, of course, no investor could reap these returns.
It may be argued in response to the above calculations that the assumption of N uncorrelated assets is an unrealistic one, since it is almost impossible to achieve practically. In figure 2 we present the case of two correlated assets, across a range of degrees of correlation. We can see from the results of the calculations that although the outperformance is somewhat dampened by the correlation, it is far from negligible.
In the course of the 1990s the average cross-market correlation between stock indices was in the range of 50%; according to our calculations, the better performing of any choice of just two index-linked funds would outperform the average of the two after one year by around 8%!
Creating an illusion
Without accounting for any skill, it is therefore possible to produce the illusion of superior results simply by setting in motion a large enough number of track records. Use of these egregiously misleading techniques is widespread in the traditional fund management industry and more recently in the hedge fund industry. The hedge fund industry has deliberately structured itself as a portfolio of uncorrelated asset classes by dividing up performance reporting into different strategies (event-driven, convertible arbitrage, etc) and promoting the analysis of these strategies based on their assumed shared characteristics. Badly performing assets or funds have in the past simply been allowed to disappear from the record, leaving a track record artificially inflated by survivor bias; poorly performing strategies also tend to disappear from view pretty quickly (for example, we do not hear any more of mortgage-backed strategies).
Selection and survivor bias create a compounding effect, and the line between them is often blurred. Funds of hedge funds introduce survivor bias in their manager selection, frequently creating meaningless track records by combining biased selections with the benefit of hindsight. At a more basic level, it is common for multiple stocks or funds or managers to be set up and for the seller to claim success at any time based upon the performance of only the most successful. Hedge funds can set up multiple programmes, thus increasing the probability of lucky good returns, and promote biased results to the funds of funds. Unethical salesmen with no binding allegiance can choose to represent one or more funds, or managers, or stock from among the tens or hundreds of thousands out there and take credit for the performance. Hypothetical vehicles can be created, with represented investment profiles bearing no relation to what can be realistically expected. In short, there is substantial scope for misrepresentation.
Selection bias is not an ‘at-the-margin’, ‘correct-for-later’ kind of phenomenon. It is central to the problem of honest estimation of forecast risk and return, which in turn is central to successful investment management.

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