For example, many people assume that because someone has just got a heads when tossing a coin the next result is more likely to be a tails. But those who have thought more carefully about the subject realise that each time the coin is tossed there is an equal chance of getting a heads as a tails.
For bookies it is just as well that statistics tend to be counter-intuitive. Their whole business model is based on the fact that those placing bets tend to substantially over-estimate their chance of
winning.
But for investors it is more problematic. They need to ensure that they are not misled by dishonest claims from fund management groups or become the victims of faulty reasoning.
Such fallacies are numerous. There follows an outline of some of the most common to be avoided.
* The fund awards fallacy
This is the notion that if a fund has performed incredibly well it must be a result of the skill of its manager. Clearly the marketing departments of groups with such funds have an interest in propagating such misconceptions. But even experienced commentators are often too ready to accept it.
Burton Malkiel, a professor of economics at Princeton, explains this point in a discussion of fund performance in his classic study, A Random Walk Down Wall Street (WW Norton 1999). To illustrate his point he gives an example of a coin-flipping contest involving 1,000 contestants with those who get heads being declared the winners.
As he argues there are likely to be about 500 winners in the first round, 250 in the second round, 125 in the third round and so on. Even by the seventh flip there are likely to be eight winners.
As Professor Malkiel argues: “By this time, crowds start to gather to witness the surprising ability of these expert coin-tossers. The winners are overwhelmed with adulation. They are celebrated as geniuses in the art of coin-tossing, their biographies are written, and people urgently seek their advice.”
What applies to coin flipping can also apply to funds. In a large universe of funds some are likely to perform spectacularly well simply through luck.
The point here is not that good performance is always the result of chance. It is rather that if a fund has performed well the onus is on the manager to prove it is the result of skill rather than luck.
* The fractional baby fallacy
The average couple in a particular country might have 1.82 children. But clearly that does not mean that anyone literally has 1.82 children.
A similar logic applies to funds. For instance, the average fund in a particular category might have risen by 1.82% in a year but that does not necessarily mean that any individual fund has risen by that amount. It could be that some funds have grown rapidly while others have slumped. Only a few of them or even none of them could conform to the average.
The same applies to the Morningstar Style Box. In an extreme case a mid-cap blend fund could contain no medium-sized companies and no blend shares in its portfolio. Instead it could be a mixture of large and small companies with growth stocks and value stocks.
Again the fact that averages can be misleading if not used carefully is not a reason for shunning statistics. It simply shows that interpreting them is not a straightforward business. Rather than just look at one number it is necessary to examine a range of data along with qualitative information.
* The blue eyes and blond hair fallacy
Just because most blue-eyed people have blonde hair it does not necessarily follow that one causes the other. Or in statistical language an association is not the same as a cause.
Given the number of statistical variables in the world it is likely that, over a given period, some might move together just by chance. For example, someone with a powerful computer and enough data might discover that, say, the price of bananas in Honduras moves in line with the Albanian stockmarket over a given period. But it is hard to see how one factor could cause the other.
Even when there is clearly some kind of relationship its nature is not necessarily clear. To explain why blond people generally have blue eyes it is necessary to develop a theory of genetics. The observation that the two variables often occur together is only the starting point rather than the end of the analysis.
One way this confusion arises in relation to funds is in country correlations. Fund strategists and global fund managers are often keen to observe how closely different national markets move in line with each other.
In this case too an association is not the same as a cause. If market A moves in line with market B it is not clear if one causes the other or perhaps there is a third factor causing both. If two countries have close trade and investment links that might be one reason why their markets are correlated. Or perhaps two small but unrelated markets might both be influenced by the American market.
If the relationship is not causal it could easily break down over time. Two markets might move in line for a while then start to move more independently.
Statistics for correlation, just like those for performance, are based on past experience. And in both cases the past is not necessarily a good guide to the future.
* The Indonesian fund fallacy
Even straightforward percentages have numerous pitfalls. Apparently simple calculations can be marred by basic errors.
Take a highly volatile fund such as one investing in, say, Indonesia. If the fund loses 50% in one year then gains 50% the next many people would assume they have regained their initial investment. That is certainly what many fund groups would like investors to believe.
But on closer inspection the investor has made a substantial loss. If his initial investment was £1,000 a loss of 50% would leave him with £500. And if the fund gained 50% the following year he would be up to £750. Overall he would still have made a 25% loss on his initial investment.
There are numerous variations on this fallacy. The basic problem is that people tend to underestimate the impact of compounding on their investments. For instance, bond investors often do not fully grasp the extent to which several years’ of inflation will erode the capital value of their investment. A more positive example is how investors in shares often underestimate the benefits of a slow but steady increase in the value of their assets when it is compounded over several years.
* The sex with aliens fallacy
If objective statistics are riddled with pitfalls those which measure inherently vague concepts such as confidence are more problematic. It is even harder to interpret individuals’ stated preferences than movements in prices.
Bedlam Asset Management provided a useful reminder of this point in a recent note which quoted a survey showing that about 0.5% of Americans said that they had sex with aliens. In other words according to the survey about 1.4 million Americans believe they have had some kind of sexual encounter with an extra-terrestrial.
Interpreting such statistics is not easy. One possibility is that 1.4 million Americans really have had sex with an alien – presumably along with a giant government cover-up - while another is that there are well over a million deranged people in the US.
A more likely explanation is the old maxim that if you ask a silly question you get a silly answer. When confronted by someone with a clipboard asking whether you have had sex with an alien it must be difficult to resist the temptation of answering in the affirmative.
The point is that without knowing more about the survey it is difficult to draw definite conclusions. How representative was the sample of people questioned? If it was conducted at a UFO convention it is hardly likely to be an accurate cross section of the American public. How were the questions phrased? When was the survey conducted?
Sexual encounters with aliens may seem a long way from fund management but there are some parallels. Like any subjective surveys those based on fund manager views, including those conducted by Morningstar, should be treated with caution.
This is particularly true when there is likely to be an element of wishful thinking in the responses. Few fund managers are likely to admit, often even to themselves, that it is possible that the markets in which they invest could fall over a significant period.
None of this is meant to imply that statistics are of no use. On the contrary, the development of statistics is one of the great achievements of civilisation. It has enabled individuals to go beyond common sense or educated guesswork to get a much better grasp of the social and natural worlds.
The point is that interpreting statistics properly is a great skill. Collecting them is simply the starting point of any analysis.
