Formulas for Disaster, Part 3

I mentioned in my first post on this subject, a few days ago, that I had originally not intended to write about it at all, but had changed my mind.  Here’s why.  It occurred to me that, after reading a number of the articles about the factors that contributed to the Wall Street meltdown, it would be easy to come to the conclusion that all of the people involved were either totally venal or desperately stupid.  I think I could even weave quite a convincing “Just So” story to that effect.

Unfortunately, however, I think that story would be a little too economical with the truth.  I have seen, first hand, situations where otherwise well-qualified, intelligent, sensible people have temporarily, in essence, lost their minds.  The combination of rushed time scales and knowledge of how one would like the results of an analysis to come out can definitely impair one’s judgement.   I think the following remark of Richard Feynman’s is relevant:

Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.

I want to relate a couple of actual situations at which I was present to illustrate what I mean.  As is usual, I have tried to change the details to avoid any personal embarrassment.

The first example I want to talk about came about as part of the evaluation and pricing process for a proposed over-the-counter option deal.  This deal was for what is sometimes called a “barrier option”.  Let’s think about an ordinary option on Microsoft’s stock [MSFT], which Yahoo! tells me closed at $21.73 today.  An ordinary  American put option might give me the right to sell 100 shares of MSFT for $21.00 (the exercise price) during the next three months.  A barrier option might add the feature that, if the price goes above $24 any time during the three-month life of the option, the new exercise price would be $24.  In other words, it would give me the right to “lock in” a certain gain if it occurred.

At the time this took place, barrier options were something of a novelty.  So, before the terms of the deal could be finalized, a good deal of background work had to be done on how the option should be specified and priced.  One key question was whether (using my MSFT case above as an example) the barrier feature was “activated” if the price reached $24 at any time, or only if the closing price reached $24.  I can no longer remember the details of the discussion, which went on for some time, but the traders and the mathematicians came to the conclusion that, in terms of pricing, it didn’t matter which way it was done.

By the time the conclusion was reached, it was probably about 8:00 PM, so we were glad to call it a day.  A colleague and I decided to stop in the pub across the road to have a quick beer.  We got to talking about the prospective deal a bit, and something — neither of us, then or now, could put a finger on just what — bothered us.  So we decided to go back to the office, and set up a simple stochastic (Monte Carlo) simulation of the proposed option’s behavior.  (A Monte Carlo simulation essentially generates a large number of possible future scenarios by figuratively “rolling the dice”, and then computes the resulting gain or loss.  Although this approach is inefficient in terms of computer time, its great virtue is that it is simple, and thus relatively easy to check for correctness.)   We did it more from being stubborn than anything else; perhaps we also thought we’d score some points by demonstrating that our consensus view was correct.

We did the simulation; and to make an already long story a bit shorter, found out that our earlier conclusion, that the details didn’t matter, was severely flawed.  I lost the ensuing coin toss, and had the pleasure of telephoning the Managing Director at home, at about midnight, to convey the happy news.  I am glad to report that I suffered no permanent damage to my hearing.  The next day, though, he was suitably grateful that we had saved him a good deal of money, not to mention embarrassment.  The deal was eventually done, with only a minor delay, and with corrected terms.  As far as I know, all the parties were reasonably well satisfied with the outcome.

My purpose in telling this story is emphatically not to say. “Look how clever we were.”  Rather, it is to say someting like, “Even with a group of experienced and well-qualified people, look how easy it was to come very close to a disastrous mistake.”   I am as sure as I think I could ever be that no one involved had any bad intentions.  But all of us were intrigued by the possibility of doing a new type of deal, and we really wanted to make it work.  Despite what the motivational books might say, the moral of the story is that that can be a dangerous combination.