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Theory vs Practice

Numerical methods are useful only in analyzing the past, not in quantifying the amount of risk in investments…

Sachin Tendulkar has a test match batting average of 56.3. For those unfamiliar with the exact mechanics of the way cricket’s statistics work, that’s the average number of runs scored per completed innings. By completed, we mean innings in which the batsman was out. In Tendulkar’s case, he has scored 14,965 runs and lost his wicket 266 times. Does that mean every time Tendulkar walks out to bat, we can expect him to score 56 runs? Of course not, the idea that average means the number of runs he is going to score in an innings is absurd and every cricket fan knows that. As it happens, he doesn’t get out in his fifties much and has gotten out on 56 only thrice in 298 innings. If you were betting on how much Sachin would score in a particular innings, then the average would be worse than useless.

Why is this so? After all, a simple statistical measures like the average are good at predicting real numbers in other fields. For example, in medicine, take the blood glucose level of the general population. The average here is about 90 and if you take any individual and test him or her, the chances are pretty good that you’ll get a value that is quite close to 90. The further you go from 90, the fewer readings you will get. If you were to bet on a random person’s blood glucose level, the average would be a good guide.

The difference in the two cases is in the nature of the underlying data, in the way it varies from the average. In both cases, the average is a useful source of information, but in the first case, it is useless as a way of trying to predict anything and bet on it. In a very fundamental way, these examples illustrate what is wrong with most statistical approaches to understanding and predicting the markets. Currently, as the stock markets drift around at depressed levels, there seems to be additional attention paid to such approaches. Not only does this not work, it can’t work.

Here’s a great explanation of why it can’t work from Nassim Nicholas Taleb, the ex-trader and writer of the book ‘The Black Swan’. Taleb is answering an interview question on what people should learn if they want to understand investing, “I would tell people to learn more accounting, more computer science, more business history, more financial history. And I would ban portfolio theory immediately. It’s what caused the problems. Frankly, anything in finance that has equations is suspicious. I would also ban the use of statistics because unless you know statistics very, very well, it’s a dangerous, double-edged sword... The field of statistics is based on something called the law of large numbers: as you increase your sample size, no single observation is going to hurt you. Sometimes that works. But the rules are based on classes of distribution that don’t always hold in our world... It uses metrics like variance to describe risk, while most real risk comes from a single observation, so variance is a volatility that doesn’t really describe the risk.”

The key phrase in Taleb’s comment is, ‘most risk comes from a single observation’, which is his famous black swan (the low probability, high impact event). The distribution of risk in investments is highly skewed and numerical methods of quantifying it are adequate only in providing an analysis of the past. Most of the time, it can also provide an indication to the future. Unfortunately, once in a while, ‘most of the time’ is not enough.