Today, we will talk about the Bell curve again. As we quoted Nassim Nicholas Taleb in How the folks in the finance/economics industry became turkeys—Part 2: The Bell curve, that great intellectual fraud,
So the Gaussian [Bell curve] pervaded our business and scientific cultures, and terms such as sigma, variance, standard deviation, correlation, R square, and the eponymous Sharpe ratio, all directly linked to it, pervaded the lingo. If you read a mutual fund prospectus, or a description of a hedge fund’s exposure, odds are that it will supply you, among other information, with some quantitative summary claiming to measure ‘risk.’ That measure will be based on one of the above buzzwords derived from the bell curve and its kin. Today, for instance, pension funds’ investment policy and choice of funds are vetted by ‘consultants’ who rely on portfolio theory. If there is a problem, they can claim that they relied on standard scientific method.
For the mainstream money-shuffling professionals in the finance industry, their training are rooted on the Bell curve. The Bell curve was formulated back in early 19th century by a mathematician named Carl Friedrich Gauss. It gave a ‘structure’ for systematically evaluating risk and estimating probability. It is the root of mainstream finance and economics and is used everywhere, from options valuation, risk management and measurement, forecasting, portfolio allocation and so on.
There is an underlying assumption with the Bell curve. As Peter Bernstein wrote in his book, Against the Gods- The Remarkable Story of Risk,
… two conditions are necessary for observations to be distributed normally, or symmetrically, around their average. First, there must be as large a number of observations as possible. Second, the observation must be independent, like rows of the dice…
People can make serious mistakes by sampling data that are not independent.
In today’s volatile financial market, price movements are not independent. As we mentioned in Fading glory of the financial services and ‘wealth’ management industry, October 2008 saw the most fear and panic in the financial markets. We see instances whereby highly leveraged funds have to sell because prices are falling, which in turn depresses prices further. Traders and investors, being confused about what is going on, reacted as prices moved, which in turn leads to more price movements. Funds have to liquidate their positions because investors are demanding redemptions due to falling prices, which in turn lead to more falling prices. Central bankers, governments and regulators observed the behaviour of the financial markets and reacted accordingly, while the markets observed and reacted according to authorities’ reaction. New information about the economy are confusing, contradictory and yields no insight, therefore forcing market participants to base their decision on other participant’s reaction. If price movements are not independent, this basic assumption of the Bell curve breaks down. If so, then all these financial theories that the finance and economics industry rely on breaks down as well.
Assuming that governments are going to fight vigorously the natural deflationary forces with inflation, we can expect more confusion and volatility ahead. Meanwhile, there will be more soul-searching, witch hunts and re-evaluations in the finance and economics industry.
Tags: bell curve, Carl Fredrich Gauss, Gaussian, Nassim Nicholas Taleb, Peter Bernstein, risk management
