Prof Rajan, Fault Lines, has written an interesting addition to the volumes on how we got where we are now. In Chapter 7 of the book he offers an interesting discussion on how judgment can be flawed.
Let me go thru the example:
Assume we have a pool of 10 mortgages. They may be good or bad but there they are. Now assume that we can assign a probability of 10% to failure on any one of them and each one has a possible $1 return. Then we can use simple Benrnoulli statistics to determine what the average return would be. The statistics are shown below and the return is $9.
Now this assumes that the probabilities of failure are independent and uncorrelated. Dumb assumption. They are not. When stuff happens things get sticky and the whole house of cards falls. Confidence, also the basis of high frequency trading, albeit a different time scale.
Now what really happens. Well most likely a Markov chain is created and then we have the following:
Say at the beginning we have with no failures a failure probability of 0.1.
Now we see the first failure, then the probability of failure for the remaining 9 is say 10% higher, or 0.11.
Now number two goes under, then what. We see the probability of failure for the remaining 8 as say 0,13. And so forth....as the failures occur the probability of the remaining failing goes up.
Now let us assume the same as before but we add a 10% increase in failure each time we have one. This is what it will look like:
Some difference would you not say. This frankly is what happened. Namely when things go bad they frequently get worse before they get better. People have learned about the bad and they impute it upon themselves. Ask any physician, when there is a news story about some deadly but rare disease with the patients come in with it. It is amazing how many Medical school students come down with Dengue Fever when they never left Boston!
So what is the result. We see that in the following two charts:
and the following:
The returns are no where what was expected. Why did the brilliant quants see this? Good question. Why did the traders not see it, well they were traders. What about the great management? Well on p 142 Rajan writes of the Trillin observation that the problem was that top management was just plain dumb. Perhaps. But it is clear that some one missed the ball.
Let me go thru the example:
Assume we have a pool of 10 mortgages. They may be good or bad but there they are. Now assume that we can assign a probability of 10% to failure on any one of them and each one has a possible $1 return. Then we can use simple Benrnoulli statistics to determine what the average return would be. The statistics are shown below and the return is $9.
Now this assumes that the probabilities of failure are independent and uncorrelated. Dumb assumption. They are not. When stuff happens things get sticky and the whole house of cards falls. Confidence, also the basis of high frequency trading, albeit a different time scale.
Now what really happens. Well most likely a Markov chain is created and then we have the following:
Say at the beginning we have with no failures a failure probability of 0.1.
Now we see the first failure, then the probability of failure for the remaining 9 is say 10% higher, or 0.11.
Now number two goes under, then what. We see the probability of failure for the remaining 8 as say 0,13. And so forth....as the failures occur the probability of the remaining failing goes up.
Now let us assume the same as before but we add a 10% increase in failure each time we have one. This is what it will look like:
Some difference would you not say. This frankly is what happened. Namely when things go bad they frequently get worse before they get better. People have learned about the bad and they impute it upon themselves. Ask any physician, when there is a news story about some deadly but rare disease with the patients come in with it. It is amazing how many Medical school students come down with Dengue Fever when they never left Boston!
So what is the result. We see that in the following two charts:
and the following:
The returns are no where what was expected. Why did the brilliant quants see this? Good question. Why did the traders not see it, well they were traders. What about the great management? Well on p 142 Rajan writes of the Trillin observation that the problem was that top management was just plain dumb. Perhaps. But it is clear that some one missed the ball.
Posts
