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Bankers count the cost of the prisoner's dilemma

Investment banks have begun totting up the cost of playing their asset-backed version of the prisoner's dilemma, a puzzle philosophers framed in 1950.

The classic version of the problem begins with the arrest of person A and person B. The police run them into jail, claiming to have enough evidence to obtain a six-month prison sentence and a plan for getting enough extra evidence to secure a more serious conviction. They will keep A and B in separate cells overnight so they cannot speak to each other and in the morning ask them separately whether they will testify for the prosecution.

The police say if both keep silent, they will each serve six months. If one betrays the other and the other stays silent, the sneak will earn a pardon and go free while the other gets 10 years. If A and B both betray the other, they will each serve five years.

A starts thinking. If he betrays B, he can get off scot-free, provided B says nothing. But maybe B will sing too, condemning A to five years in prison. Maybe A should stay silent. That makes some sense, because if B is silent too, A serves only six months, which is better than five years. But it is a risky strategy: if B plays the traitor, A will have to serve 10 years.

The rational choice for A is to betray B, because this offers A the most attractive ratio of risk to reward: at worst, A will serve five years and at best he will walk away free. Reinforcing this, A might reasonably expect B to reach the same conclusion and betray him. So A rats on B and in the morning, the clever police get the serious conviction they want.

This is not the best outcome for A and B viewed as a pair because their combined jail time will be 10 years - five years plus five years, or zero plus 10 years - compared with a total of one year - six months plus six months - if they had both kept silent. But it sometimes makes sense for rational individuals to choose a course of action that none collectively wants.

Something similar has happened to investment bankers, who spent much of the past three years playing a version of the prisoner's dilemma, based on the proliferation of US sub-prime mortgages.

Some of the banks put themselves at risk by writing credit default swaps - financial instruments that might best be thought of as a kind of insurance contract. Banks that write CDSs sell them for a small annual premium and agree to pay the buyer the value of any fall in price of a specified credit security, should it default within a specified time frame.

A few US hedge fund managers, including Paulson & Co, realized in 2006 investment banks were writing CDSs on the BBB-rated tranches of securities backed by US sub-prime mortgages, for which the banks were charging a premium of 1% a year. The contracts were to last for two years.

Paulson raised a $500m fund and bought CDSs on bonds whose notional value was $6bn. The fund finished last year at more than $4bn having made a net return of about 590%.

The money was made at the expense of those banks that continued writing these CDSs. It is now clear they were taking a huge risk. Worse, the more they wrote, the more they helped nudge the sub-prime mortgage market towards the point of collapse.

Why did so many banks continue to do it? Because they were in a version of the prisoner's dilemma.

The analogy is not exact but it is close. Suppose bank A and bank B, alone among investment banks, have been writing two-year, sub-prime CDSs and making a lot of money from them. Their risk departments and public commentators warn of a possibly cataclysmic loss of value in sub-prime mortgage loans, maybe within the next two years.

Each of the banks' chief executives, who never speak to each other for fear of anti-trust lawsuits, could call a halt to the writing of the CDS contracts the next morning. If both stop writing, there is a slight chance their action will dampen demand for sub-prime mortgage loans, perhaps enough to delay any losses to beyond the next two years, thus saving the value of the contracts they have written.

Chief executive A starts thinking. If he stops writing sub-prime CDSs, his bank has a chance to avoid losses, provided B stops too. But maybe B will carry on, maybe pushing both towards future losses; certainly taking the lucrative business A would have written, which might have unpleasant consequences for the chief executive's career.

So maybe A should carry on. That makes some sense because it will protect A from falling behind B when the next quarter's profits are published. If B happens to stop, A will take its share of the money-spinning, sub-prime CDS market. And those supposed future losses may never materialize. It is rational to carry on.

This is more or less what happened. It might have helped if the banks' risk management teams had understood the risks being taken, but even if they had, many banks gave them too little authority to be effective.

Investment banks are paying the high cost: Citigroup last week effectively guaranteed the Government of Singapore Investment Corporation and other investors that it would pay a dividend of at least 7%, forever, on the $12.5bn convertible preferred securities it sold them.

But unlike in the classic prisoner's dilemma, the banks' ultimate potential loss is as yet unknown. Nobody knows how many CDSs they wrote.

Source: Financial News Online
Date: 23.01.2008 [162]

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