"Beyond the Normal Distribution"

Since we have recently been discussing the normal distribution in class, and its application in risk management, I thought it would be interesting to find an article and learn a bit more about it, beyond what I have learned in other classes thus far.

I found a great article titled "Beyond the Normal Distribution" by Ben Fehr about the normal distribution, and some new ways mathematicians are beginning to use this model and others, as well as possible problems it poses.

The article was really interesting because it explained that the normal distribution is a great tool for many situations, but for the true picture of the financial market as a whole, the normal distribution doesn't really do that great of a job. For example, using the normal distribution big shocks to the stock market would occur much less often than they do in reality. Like the crash in 1987, it should technically only happen every 10^87 years, but in reality it happens about every 38 years. So, by using the normal distribution one is really underestimating risk in this case.

I think this is quite interesting to think about, especially given the economy nowadays. Given the fact that we have never really seen an economy like the one of today, it would be very difficult to use such a mathematical model to predict what is going to happen, when everything is so volatile and unpredictable.

Another interesting thing the article discussed was the fact that they are replacing common risk measures such as "standard deviation," and "value at risk," with a new measure they call "expected tail loss." The traditional estimates we have learned about so far in class give an answer that for example, the daily loss of a particular company will not exceed $40 million with a probability of 99%. But this new approach answers the question about that remaining 1%, about what happens in that tail, which actually seems like a very interesting question to me. I think it would be interesting for example, so see how high this 1% likelihood of losses could get.

"Beyond the Normal Distribution"