The Bell Curve

Most of us in uni have to live the Bell curve. And we often hear that 'your results are bell-ed' so all you have to do is to perform better than the majority. So even if you fail, just make sure your failing mark is higher than average.

The bell curve, or the normal distribution, explains an amazing numbers of phenomenon. Height, or instance forms a rather nice bell curve, so does mortality rate and some say intelligence. However, it fails remarkably when it is used as a measurment for systems that respond to feedback and extreme sensitivity to initial condition.

Population of cities rarely follows a normal distribution. Imagine a small area where pple gather to trade. Once that area reaches a critical mass of population, infrastructures will be built around this area. City dwellers will try to stay as near to these area as possible. Thus having a high concentration of population/square foot. A related example would be the number of offices in Raffles Place vs Choa Chu Kang. Assume you plot a graph of offices per square foot for all the districts in Singapore, you wouldn't get a bell curve, but a very 'lumpy' curve.

In finance, there's also a huge obession over the 'average'. Be it average return, average risk, etc. Average return are sometimes called "Expected Return". However be wary of such terms, the "expected" is rarely to be expected. How many times have you heard where people sell you financial products that promises this 'expected return' but fail to highlight the fact that results over the years would be bumpy? It is like saying its safe to put one hand in a tub of boiling water and the other in ice water as the 'average temperature' is room temperature.

My amazing CAT (computer as an analysis tool) prof, Michelle Cheong, told us that most Uni teaches only normal distribution because its the easiest to teach, and the math behind is also one of the most elegant one. An important quality of the normal distribution is, The odds of a deviation decline exponentially as you move away from the average.
E.g. from The Black Swan, assume that average height is 1.67m and we consider the odds of someone being x cm taller than average.

10 cm taller than average, odds: 1 in 6.3
20 cm taller than average, odds: 1 in 44
30 cm taller than average, odds: 1 in 740
40 cm taller than average, odds: 1 in 32,000
50 cm taller than average, odds: 1 in 3,500,000
60 cm taller than average, odds: 1 in 1,000,000,000
70 cm taller than average, odds: 1 in 780,000,000,000
80 cm taller than average, odds: 1 in 1,600,000,000,000,000
90 cm taller than average, odds: 1 in 8,900,000,000,000,000,000
100 cm taller than average, odds: 1 in 1.3 x 10^23 (i gave up typing the zeros)

It may be true through emprical testing that the odds of meeting someone who is alive and have a height of 2.67m is that rare ( 1 in 1.3x10^23). However, economist (or later finance professors) applied the bell curve to financial market. This is one of the contributing factor to the famous LTCM debacle which caused the financial market to seize up in the late nineties. The super successful hedge fund was destroyed as they over bet on a series events that should only happen in 1 in a few billion years as predicted by their model. But it all happend within the short span of a few weeks starting with the default of Russian bond.

I think as human beings we love certainty, and cannot see risk that has not happened before. However, it would be just wrong to simply use fancy models or theories to predict the future when the underlying assumptions are flawed. As Lord Keynes said, "It is better to be roughly right than precisely wrong. "

DO YOU KNOW? John Maynard Keynes was also a great investor. His Chest Fund returned a 9.1% from the period of 1927 to 1945, surviving both the great depression and World War II, and far surpassing the -0.9% return of the general British stock market. Read more about him here. Hiaz, why my JC econs textbook never did mention this?