Risk Management and the Statistical Distribution of Asset Prices

The NY Times Magazine has an article today that discusses the "Value At Risk" (VaR) model of risk used in the financial industry. It's primary benefit for me was to add to my suspicion that if you skim the ego and bombast from Nassim Nicholas Taleb's cup of wisdom, you're left with a pretty weak tea. It purports to question the validity of VaR, but according to Yves Smith's takedown at Naked Capitalism, it completely misses the fact that the fundamental problem with VaR is not the amount of data that it takes into account, but that it assumes that asset prices are normally distributed when everyone knows they are not.

The New York Times Sunday Magazine has a long piece by Joe Nocera on value at risk models, which tries to assess how much they can be held accountable for risk management failures on Wall Street.

The piece so badly misses the basics about VaR that it is hard to take it seriously, although many no doubt will.

The article mentions that VaR models (along with a lot of other risk measurement tools, such as the Black-Scholes options pricing model) assumes that asset prices follow a "normal" distribution, or the classical bell curve. That sort of distribution is also known as Gaussian.

But it is well known that financial assets do not exhibit normal distributions. And NO WHERE, not once, does the article mention this fundamentally important fact.

Yves goes on to quote from this post written by Paul De Grauwe, Leonardo Iania, and Pablo Rovira Kaltwasser.

We selected the six largest daily percentage changes in the Dow Jones Industrial Average during October, and asked the question of how frequent these changes occur assuming that, as is commonly done in finance models, these events are normally distributed. The results are truly astonishing. There were two daily changes of more than 10% during the month. With a standard deviation of daily changes of 1.032% (computed over the period 1971-2008) movements of such a magnitude can occur only once every 73 to 603 trillion billion years. Since our universe, according to most physicists, exists a mere 20 billion years we, finance theorists, would have had to wait for another trillion universes before one such change could be observed. Yet it happened twice during the same month. A truly miraculous event. The other four changes during the same month of October have a somewhat higher frequency, but surely we did not expect these to happen in our lifetimes.

The rather obvious conclusion of these gentlemen?

Our conclusion, therefore, should be not that these events are miraculous but that our finance models are wrong. By assuming that changes in stock prices are normally distributed, these models underestimate risk in a spectacular way. As a result, investors have been misled in a very big way, believing that the risks they were taking were small. The risks were very big. We now know why.

It is time to throw away the models and to go back to the drawing board. In the meantime banks should be forbidden to hold complex assets on their balance sheets that have been priced using one of these models.