The Li Formula
Wired has a good article about the “quants” on Wall Street that precipitated the financial crisis. David X. Li was the author of the formula that was used to manage the risk for bonds, mortgages, and other debt obligations. However, the problem and crisis are not Li’s fault. He routinely cautioned people, as did other math experts, that they were using the formula incorrectly.
The key points were that this formula tried to correlate the risk between different mortgages. There were two sets of problems. First, risk is not “normally” distributed. The usual bell curve - a gaussian distribution - is called a “normal distribution”. However not everything falls into this distribution.
Financial price series have been show to be fractally distributed, this is much wider so has more highs and lows than a normal gaussian distribution.. It’s not unreasonable to consider that risk also has a wider distribution too.
Secondly, correlation varies over time. The Wired article goes into this in much more detail that I will repeat here. But two separate loans that have a given correlation of risk over one time period may not always have that same correlation in a different period with different economic conditions.
In the end, the world is more complex that the Li formula allowed for. This isn’t unusual. Mathematical models don’t always model all aspects of a situation and they’re not necessarily intended to do so. But if you ignore the discrepancies between the model and the real world you’re asking for trouble. And trouble is where we ended up.