Black Box Models

A few years ago, Felix Salmon wrote this article in Wired called “The Formula That Killed Wall Street“. It was about a formula called “Gaussian Copula”, which was a formula for estimating the joint probability of a set of events happening, if you knew the individual probabilities. It was a mathematical breakthrough.

Unfortunately, it fell into the hands of quants and traders who didn’t fully understand it, and they used it to derive joint probabilities of a large number of instruments put together. What they did not realize was that there was an error in the model (as there is in all models), and when they used the formula to tie up a large number of instruments, this error cascaded, resulting in an extremely inaccurate model, and subsequent massive losses (the last paragraph is based on my reading of the situation. Your mileage might vary).

In a blog post earlier this week at Reuters, Salmon returned to this article. He said:

 And you can’t take technology further than its natural limits, either. It wasn’t really the Gaussian copula function which killed Wall Street, nor was it the quants who wielded it. Rather, it was the quants’ managers — the people whose limited understanding of copula functions and value-at-risk calculations allowed far too much risk to be pushed out into the tails. On Wall Street, just as in the rest of industry, a little bit of common sense can go a very long way.

I’m completely with him on this one. This blog post was in reference to Salmon’s latest article in Wired, which is about the four stages in which quants disrupt industries. You are encouraged to read both the Wired article and the blog post about it.

The essence is that it is easy to over-do analytics. Once you have a model that works in a few cases, you will end up putting too much faith into the model, and soon the model will become gospel, and you will build the rest of the organization around the model (this is Stage Three that Salmon talks about). For example, a friend who is a management consultant once mentioned about how bank lending practices are now increasingly formula driven. He mentioned reading a manager’s report that said “I know the applicant well, and am confident that he will repay the loan. However, our scoring system ranks him too low, hence I’m unable to offer the loan“.

The key issue, as Salmon mentions in his blog post, is that managers need to have at least a basic understanding of analytics (I had touched upon this issue in an earlier blog post). As I had written in that blog post, there can be two ways in which the analytics team can end up not contributing to the firm – firstly, people think they are geeks who nobody understands, and ignores them. Secondly, and perhaps more dangerously, people think of the analytics guys as gods, and fail to challenge them sufficiently, thus putting too much faith in models.

From this perspective, it is important for the analytics team to communicate well with the other managers – to explain the basic logic behind the models, so that the managers can understand the assumptions and limitations, and can use the models in the intended manner. What usually happens, though, is that after a few attempts when management doesn’t “get” the models, the analytics people resign themselves to using technical jargon and three letter acronyms to bulldoze their models past the managers.

The point of this post, however, is about black box models. Sometimes, you can have people (either analytics professionals or managers) using models without fully understanding them, and their assumptions. This inevitably leads to disaster. A good example of this are the traders and quants who used David Li’s Gaussian Copula, and ended up with horribly wrong models.

In order to prevent this, a good practice would be for the analytics people to be able to explain the model in an intuitive fashion (without using jargon) to the managers, so that they all understand the essence and nuances of the model in question. This, of course, means that you need to employ analytics people who are capable of effectively communicating their ideas, and employ managers who are able to at least understand some basic quant.