# Ignore correlations, lose \$9 billion

I am reading, and enjoying, “The Big Short:  Inside the Doomsday Machine“, Michael Lewis’ book on the 2008 financial crash. Judging from the book, the main reasons for the crash were human factors, basically people were placing multi-billion dollar bets they didn’t understand. They assumed the bets were virtually risk free. This was a mistake. One reason they underestimated the risk was that they neglected correlations. Correlations are important in the both bond markets and in physics. In physics for example, we know that nearby electrons are correlated, as they repel each other.

Correlations can be subtle, which is presumably why intelligent, well-educated and extremely well-paid people missed them. They also tend to cause so-called extreme events to become much more common. A simple example of this is as follows. Consider an ice cream shop which sells chocolate and vanilla ice cream. In the traditional theoretical physics way, let us make a silly assumption to make things simple for ourselves. Let us assume that on average exactly 50% of people buy a chocolate ice cream and 50% buy a vanilla ice cream.

Now if every customer makes a completely independent decision on what flavour to buy, then the probability of 10 customers, one after another, all buying chocolate ice cream is only 0.1%. The probability of this extreme event, 10 successive people all buying the chocolate flavour is very low, the odds are 1 in 100. However, if everyone likes the look of the ice cream of the customer  in front so much that 80% of the time they buy the same flavour as the guy in front, then the probability of 10 customers all buying chocolate is 13%, i.e., much higher at more than 1 in 8.

Correlations between one customer and the next have made a rare extreme occurrence much more common. With ice cream this is not so important. For a multi-trillion dollar market in subprime mortgages it is more of a problem. Quite-but-not-very-clever traders realised that by aggregating many mortgages together they could reduce the risk as it was unlikely all the borrowers would default. This is right. However, roughly speaking, they assumed that one guy defaulting was independent of another defaulting.

This is not right and led them to hugely underestimate the probability of what they thought was a rare occurrence: many borrowers defaulting at the same time. Borrowers are correlated, if one has financial problems due to a economic down turn, so will many others. Forgetting that contributed to a crash that we are all paying for.