Smokes and Mirrors
It was about two years ago that I read a rather technical article on how triple A-rated derivatives were created, as it were, out of nothing. I had to read it twice. Eventually I understood it. But I could never work out how to explain it to other people in layman's language.
This was a bit annoying, because putting complex issues in simple terms is, in a sense, my job. Keefe Bruyette & Woods and Guy Carpenter can churn out stuff from technicians that are very good, but not very simple. I always try to write my work pieces so that the "non-expert" in the company can understand can understand them, even if the "expert" might occasionally mutter "well, why is he explaining that? It's fucking obvious".
The disintegration of nearly all forums and small-circle areas of work into initialisms, local slang and the like is probably well-documented. The 2+2 forums must be virtually incomprehensible to a person who spends more than 50% of his time in the non-poker world. Even when writing in these areas, I try not to fall into this trap. I remember well bad teachers who were incapable of seeing beyond their own area of comprehension -- so that anything which was "obvious" to them was glossed over, leaving poor pupil (me) to eventually conclude that the guy was a fucking idiot. He wasn't (or, rather, they weren't). They were just incapable of projection from the state of "knowing" to the state of "what would it be like not to know?"
So, back to the smoke and mirrors of creating safe derivatives from non-safe derivatives. Here's how it was done.
Take 10,000 US mortgages. Of these, we'll call 1,000 very safe ("AAA"), 4,000 fairly safe ("AA"), 4,000 not fairly safe, but not dodgy ("A") and 1,000 risky (triple B-rated and below).
Now, let's create our first level of derivatives.
1) 500 x AAA, 500 x AA (we'll call this Man Utd)
2) 3,000 AA (Arsenal)
3) 500 x AA, 500 X A (Liverpool)
4) 3,000 x A (Man City)
5) 500 x A, 1000 x B and below. (Everton)
That gives us five products. Now, derivatives are not like chains as steel. They are not as strong as the weakest link. They can actually be stronger than the weakest link. All that matters is the risk of failure.
Let's suppose that triple A's have a 1% chance of failure, double A's a 2% chance of failure, single A's a 3% chance of failure and B and below a 5% chance of failure. (In bold, because I shall return to these percentages later).
Now (and this is where it gets a bt complicated). Let's mix up our first level of derivatives.
I'll just create the two extremes of five new second-level derivatives.
Super League Derivative (1) consists of 50% Man Utd, 25% Arsenal, 10% Liverpool, 10% Man City and 5% Everton.
Premier League Derivative (5) consists of 5% Man Utd, 10% Arsenal, 10% Liverpool, 25% Man City and 50% Everton.
Now, just to add one further level of smoke and mirrors, as an investor, I can buy "tranches" of these second-level derivatives. Assuming that I'm a trusty bank, I would only want to buy the "safest" 10% of any of these derivatives. We'll call these tranches the "super safe" and the "less safe".
Now, let's crunch the numbers here for the "super-safe" part of our "least-safe" derivative.
It actually consists of (taking Man Utd, Arsenal, Liverpool, Man City and Everton in turn):
25 AAA loans
25 AA loans
__
300 AA loans
___
50 AA loans
50 A loans
___
750 A loans
___
250 A loans
500 B and below loans
_____
That gives us 25 AAA loans, 375 AA loans, 1,050 A loans, 500 B and below loans.
Loaded up, that gives us something like a 3.1% chance of failure overall in the Premier League Derivative.
However, we are taking the "super safe" tranche of the Premier League Derivative. The best 10%. Let's suppose that there's a gradual decrease in the level of default. Within the 3.1% chance of default, default is 5 times more likely on the unsafe side than on the super safe side (remember, the super safe side is the last 10% of the tranche to which default would be applied).
That in turn means that the supersafe part of this tranche only takes a fifth of the 3.1% risk, or 0.6%. Well, a 0.6% risk of failure is less than the 1% threshold for triple A, so this "supersafe" investment is a triple A product, even though it has only 25 AAA loans in the entire product of 1,950 loans.
And, this, remember, is the least-safe second-level derivative. It's far easier to create triple-A-rated products from the "middle-three" second-level derivatives.
So, where's the logical hole? What went wrong?
I think you can understand why the innocents in the fund management business went so horribly awry here, because it all looks so transparent, and the hole is hard to spot because it assumes something that isn't even mentioned in the description of the products.
This is where the flaw lies: Let's suppose that there's a gradual decrease in the level of default. Within the 3.1% chance of default, default is 5 times more likely on the unsafe side than on the super safe side (remember, the super safe side is the last 10% of the tranche to which default would be applied).
In fact, that apparently conservative assumption proved to be wildly optimistic. Although at the ground level (the actual mortgages) you could assume a gradual increase in the likelihood of default, depending on the credit-worthiness of the borrower, as you move up through the levels of derivatives, that line stops being a straight line and starts to become a curve. and that curve becomes curvier and curvier each time you create a new derivative from a collection of other derivatives.
What does that mean? Effectively, it means that, once you get to third- and fourth-level derivatives, if one brick (tranche of risk) falls, all of the bricks fall. The "super safe" and "less safe" tranches at the higher-level derivatives were actually about as safe as each other.
Why does the likelihood line become curvier? Because of correlation. Suppose you have a recession. 10% of people are put out of work, and 10% of people default on their mortgage. That's fine if you a boring old mortgage bank, because 90% of people are still paying.
But what the derivatives did was slice and dice the borrowers so that you had all of the 10% groupings (from lots of different towns) in a single derivative. No longer did you have a straight line. If a small recession hit and 5% of people were put out of work, then the super-safe part of the least safe derivative was safe, but if 10% of people lost their jobs and defaulted, then the derivative, all of it, went tits up.
Much of the analysis of the past disaster has focused on the moral hazard of being able to lend and then being able to securitize those loans straight out of the back door. And certainly too many loans were made to people who should not have been allowed to borrow. But this point about the "curvy" correlation line in derivatives is perhaps the more important point, because it doesn't require bad lending to make it a bad product. The flaw is in the derivatives themselves. Far from spreading risk, the derivatives actually concentrate the risk.
There's a simple answer, of course -- the rating agencies just have to change their modelling techniques. And, to their credit, they are (although they are being a bit quiet about it). Once you get to third-level derivative and above, I'd claim that all of the tranches should have the same rating, because it's almost inevitable that if one tranche goes, the lot go.
__________________
This was a bit annoying, because putting complex issues in simple terms is, in a sense, my job. Keefe Bruyette & Woods and Guy Carpenter can churn out stuff from technicians that are very good, but not very simple. I always try to write my work pieces so that the "non-expert" in the company can understand can understand them, even if the "expert" might occasionally mutter "well, why is he explaining that? It's fucking obvious".
The disintegration of nearly all forums and small-circle areas of work into initialisms, local slang and the like is probably well-documented. The 2+2 forums must be virtually incomprehensible to a person who spends more than 50% of his time in the non-poker world. Even when writing in these areas, I try not to fall into this trap. I remember well bad teachers who were incapable of seeing beyond their own area of comprehension -- so that anything which was "obvious" to them was glossed over, leaving poor pupil (me) to eventually conclude that the guy was a fucking idiot. He wasn't (or, rather, they weren't). They were just incapable of projection from the state of "knowing" to the state of "what would it be like not to know?"
So, back to the smoke and mirrors of creating safe derivatives from non-safe derivatives. Here's how it was done.
Take 10,000 US mortgages. Of these, we'll call 1,000 very safe ("AAA"), 4,000 fairly safe ("AA"), 4,000 not fairly safe, but not dodgy ("A") and 1,000 risky (triple B-rated and below).
Now, let's create our first level of derivatives.
1) 500 x AAA, 500 x AA (we'll call this Man Utd)
2) 3,000 AA (Arsenal)
3) 500 x AA, 500 X A (Liverpool)
4) 3,000 x A (Man City)
5) 500 x A, 1000 x B and below. (Everton)
That gives us five products. Now, derivatives are not like chains as steel. They are not as strong as the weakest link. They can actually be stronger than the weakest link. All that matters is the risk of failure.
Let's suppose that triple A's have a 1% chance of failure, double A's a 2% chance of failure, single A's a 3% chance of failure and B and below a 5% chance of failure. (In bold, because I shall return to these percentages later).
Now (and this is where it gets a bt complicated). Let's mix up our first level of derivatives.
I'll just create the two extremes of five new second-level derivatives.
Super League Derivative (1) consists of 50% Man Utd, 25% Arsenal, 10% Liverpool, 10% Man City and 5% Everton.
Premier League Derivative (5) consists of 5% Man Utd, 10% Arsenal, 10% Liverpool, 25% Man City and 50% Everton.
Now, just to add one further level of smoke and mirrors, as an investor, I can buy "tranches" of these second-level derivatives. Assuming that I'm a trusty bank, I would only want to buy the "safest" 10% of any of these derivatives. We'll call these tranches the "super safe" and the "less safe".
Now, let's crunch the numbers here for the "super-safe" part of our "least-safe" derivative.
It actually consists of (taking Man Utd, Arsenal, Liverpool, Man City and Everton in turn):
25 AAA loans
25 AA loans
__
300 AA loans
___
50 AA loans
50 A loans
___
750 A loans
___
250 A loans
500 B and below loans
_____
That gives us 25 AAA loans, 375 AA loans, 1,050 A loans, 500 B and below loans.
Loaded up, that gives us something like a 3.1% chance of failure overall in the Premier League Derivative.
However, we are taking the "super safe" tranche of the Premier League Derivative. The best 10%. Let's suppose that there's a gradual decrease in the level of default. Within the 3.1% chance of default, default is 5 times more likely on the unsafe side than on the super safe side (remember, the super safe side is the last 10% of the tranche to which default would be applied).
That in turn means that the supersafe part of this tranche only takes a fifth of the 3.1% risk, or 0.6%. Well, a 0.6% risk of failure is less than the 1% threshold for triple A, so this "supersafe" investment is a triple A product, even though it has only 25 AAA loans in the entire product of 1,950 loans.
And, this, remember, is the least-safe second-level derivative. It's far easier to create triple-A-rated products from the "middle-three" second-level derivatives.
So, where's the logical hole? What went wrong?
I think you can understand why the innocents in the fund management business went so horribly awry here, because it all looks so transparent, and the hole is hard to spot because it assumes something that isn't even mentioned in the description of the products.
This is where the flaw lies: Let's suppose that there's a gradual decrease in the level of default. Within the 3.1% chance of default, default is 5 times more likely on the unsafe side than on the super safe side (remember, the super safe side is the last 10% of the tranche to which default would be applied).
In fact, that apparently conservative assumption proved to be wildly optimistic. Although at the ground level (the actual mortgages) you could assume a gradual increase in the likelihood of default, depending on the credit-worthiness of the borrower, as you move up through the levels of derivatives, that line stops being a straight line and starts to become a curve. and that curve becomes curvier and curvier each time you create a new derivative from a collection of other derivatives.
What does that mean? Effectively, it means that, once you get to third- and fourth-level derivatives, if one brick (tranche of risk) falls, all of the bricks fall. The "super safe" and "less safe" tranches at the higher-level derivatives were actually about as safe as each other.
Why does the likelihood line become curvier? Because of correlation. Suppose you have a recession. 10% of people are put out of work, and 10% of people default on their mortgage. That's fine if you a boring old mortgage bank, because 90% of people are still paying.
But what the derivatives did was slice and dice the borrowers so that you had all of the 10% groupings (from lots of different towns) in a single derivative. No longer did you have a straight line. If a small recession hit and 5% of people were put out of work, then the super-safe part of the least safe derivative was safe, but if 10% of people lost their jobs and defaulted, then the derivative, all of it, went tits up.
Much of the analysis of the past disaster has focused on the moral hazard of being able to lend and then being able to securitize those loans straight out of the back door. And certainly too many loans were made to people who should not have been allowed to borrow. But this point about the "curvy" correlation line in derivatives is perhaps the more important point, because it doesn't require bad lending to make it a bad product. The flaw is in the derivatives themselves. Far from spreading risk, the derivatives actually concentrate the risk.
There's a simple answer, of course -- the rating agencies just have to change their modelling techniques. And, to their credit, they are (although they are being a bit quiet about it). Once you get to third-level derivative and above, I'd claim that all of the tranches should have the same rating, because it's almost inevitable that if one tranche goes, the lot go.
__________________