Handle numbers with care

This is my column for the July issue of Fund Strategy.

Those who work in investment are more guilty than most of being too ready to accept the authority of numbers. Words can be doubted but numbers are often seen as virtually sacrosanct.

Indeed, financial news often revolves around numbers. An index is down by X over the day’s trading and another index is up by Y. One currency has moved by a certain amount against another. Why those who invest with a time horizon of several years should be expected to be preoccupied with day-to-day price movements is seldom explained. This is the classic error of short-termism. The problem is not that the numbers are incorrect but that they are the wrong tools for the job.

Of course, numbers can be useful but they should be handled with care. It is only when their pitfalls and limitations are understood that they can come into their own.

 The recent row over Thomas Piketty’s best-selling book on inequality, Capital in the Twenty-first Century, illustrates one pervasive problem: confirmation bias. When it emerged that the French economist had made some data errors, many of his critics claimed triumphantly that his arguments had been discredited. When Piketty, acknowledging some small mistakes, defended his overall thesis, his supporters condemned his opponents as inequality deniers. The to and fro more resembled chanting between rival football fans than reasoned debate. It is likely that few had examined the data closely.

One common error is to confuse correlation with causation. Although anyone who has done a statistics course can probably recite the difference between the two they are often confused in practice. Once again, the inequality debate provides a clear example. Arguments along the following lines all too frequent:

A: Inequality widened in the run-up to the economic crisis of 2007-08.

B: The world then plunged into an economic crisis.

Therefore A must be the cause of B.

There are so many problems with such reasoning it is hard to know where to start. Just because two phenomena track each other it does not necessarily follow that one causes the other. It could be a coincidence or there could be another factor driving both trends. For example, blue eyes and blond hair frequently coincide but that does not prove one causes the other.

The pitfalls of confusing correlation and causation are wittily illustrated in the Spurious Correlations website (www.tylervigen.com/). Tyler Viglen, a doctoral student at Harvard Law School, has mined numerous data sets to find unlikely correlations. Who would have thought that the number of people who drowned by falling into a swimming pool correlates with the number of films Nicholas Cage appeared in?

However, confusing causation and correlation is not the only error embodied in the example of widening inequality and the economic crisis. Another is known as cherrypicking: selecting the data that supports your case but ignoring other data. Inequality, in fact, has widened by some measures but not by others.

 According to one popular gauge, the Gini coefficient, household income inequality in 2010-11 was at about the same level as in the early 1990s. Yet according to some other measures, particularly those that focus on the top of the income distribution, inequality had widened. Both sets of data are correct as they both measure different things.

But perhaps the most tempting error is what could be called mathematical correctness. The challenge is to find the best available numbers to make a case. But sometimes there is no correct mathematical answer. For example, whether or not inequality is regarded as a problem is ultimately a political question. Some will view it as an inevitable part of the human condition while others might see it as a damning indictment of society.

In such cases the right answer cannot be worked out simply by getting the maths right.