Mad math

J.P. Morgan saved the financial system twice. In 1895, following the Panic of 1893, the Federal Treasury had almost no gold left, following a run on the gold supply. Morgan came to the rescue, heading a syndicate that loaned enough gold to finance a bond issue that restored the Treasury’s surplus. He saved the day once again in the Panic of 1907, persuading New York bankers to follow his example by pledging money to consolidate the banking system.

So it’s ironic that the bank he founded was in some ways at the root of the current crisis. That may sound surprising, given the usual suspects (Lehman’s, AIG, Bear Sterns…). Yet, as Gillian Tett of the Financial Times explains in Fool’s Gold,  a team from J.P. Morgan invented a product called Bistro (Broad Index Secured Trust offering) that helped to fuel the massive expansion of the credit derivatives market.

Bistro was created to transfer a small part of the credit risk of $9.7 bn in corporate loans. It was worth $700 million and had two “tranches”. The “junior” tranche paid 375 basis points over the LIBOR (the rate at which banks lend to each other, where 1 point = 0.01 percentage point).

If any of the companies defaulted, investors in this tranche would be liable for the debt. If losses in this tranche exceeded the total sums invested in it, the “senior” tranche would have to start covering them.

Given the range and reliability of the borrowers (over 300 blue chip companies) the risk of losses to the senior tranche was so unlikely that it was given an AAA rating by the credit rating agency Moody’s. A triple A rating is very rare – even some OECD governments don’t get it for their bonds – so although this tranche only paid 60 points above LIBOR, it was an attractive proposition.

What if both tranches got wiped out by defaults? To Morgan, this seemed as near to impossible as you can get in a financial market. But the regulators still demanded that they cover this risk as a condition for meeting a request to relax the rules on the amount of reserves a bank had to carry.

The risk of an AAA tranche losing everything was so small that the bank saw no point in paying investors to cover the eventuality. So they chose a cheaper solution, paying AIG $1.8 million to insure them against this “residual”, practically non-existent, risk, dubbed the “super-senior tranche”.

This turned out to be the butterfly wing whose flutter would eventually lead to the storm. Other banks created offers inspired by Bistro, but they didn’t restrict them to corporate loans. They started packaging consumer debt, and in particular mortgages, too. The tranches were repackaged as well, creating a complex structure of nested, interdependent risks.

The way in which these risks were calculated is at the heart of the problem. Risk evaluators try to work out the correlations among potential defaults – the probability that if one borrower doesn’t repay, others won’t repay. If defaults are considered as one-off events, correlation is low. If clusters of defaults are more likely, correlation is higher.

The scale goes from 0 (no correlation) to 1 (total correlation) and for corporate debt, the usual correlation was 0.3, meaning the senior tranche was thought highly unlikely to be affected by defaults. This correlation was calculated using a huge database of information on firms, notably defaults.

No such database existed for mortgage backed securities, and the sophisticated mathematical tools developed for corporate debt risk evaluations had no real equivalent, especially for sub-prime mortgages. The financiers simply took the methods used for corporations and applied them to consumer debt.

They also took the 0.3 correlation, meaning they assumed that there was relatively little chance of large clusters of defaults. This looks crazy in retrospect, but in fact given the low level of defaults historically, it was reasonable. Moreover, mortgage-backed securities were never traded that much before the past few years. And since buyers tended to hold on to them as a safe investment until the contract matured, there was little data on their trading price on which to base correlations.

Mortgage-backed securities had been a highly specialised branch of finance, and those buying them had enough experience to assess the longer-term risks, and demand better guarantees if they thought the product too risky.

Risk evaluation changed when these securities started being packaged for quick reselling. At the start of the chain, it no longer mattered to the person negotiating the mortgage whether the borrowers could keep up payments, since the risk was sold on to another financial institution who would also repackage it, and so on.

Even so, it seems astonishing that Bistro-like deals, designed to spread risk, actually seemed to concentrate it, and to concentrate it dangerously in major financial institutions like RBS or Citigroup. To understand why, we have to go back to the super-senior tranche.

As we said earlier, the risk here is thought to be practically non-existent, so this tranche only pays a few points above LIBOR, unlike the lower, riskier tranches. Many banks simply kept the super-senior tranches, and insured them, as J.P. Morgan had done with Bistro. That’s how AIG ended up insuring $560 bn worth of super-senior tranches.

A big, well-respected bank can borrow at rates slightly less than LIBOR and use this money to buy super-senior tranches paying slightly more than LIBOR from other banks. The differences (the “spread”) are tiny, so to make the operation worthwhile, the deals have to be huge, which is why big banks ended up with such large concentrations of these products. (And of course for traders paid on commission, the bigger the deal, the bigger the bonus.)

This is where correlation comes in. If correlation among mortgage-backed securities really had been as low as the evaluations assumed, defaults would have hit some of the junior tranches and left the others untouched. For this to be the case, defaults would have had to be relatively rare, isolated occurrences, linked to the particular conditions of a given loan or group of loans and the people who contracted them.

In fact, correlation turned out to be nearer 1 than 0.3. Here it’s worth recalling a specific feature of the sub-prime crisis. On a traditional mortgage, the bank plans to make money from repayments on a loan. If the buyer defaults, it probably gets a sellable house for less than its market value, since the buyer has made at least some monthly payments, as well as a down payment in most cases. And in a booming property market, the house would be worth more and more. So after a few years, in case of default, the bank may get a house it can sell for $150,000 that it only “paid” $90,000 for as a loan, and it also got the monthly repayments.

Initially, this was the case for sub-primes too. True, these loans were riskier, but even so, the higher interest rates and rising house prices still made it worthwhile. But when the economy started to slow, the housing bubble burst, house prices fell, defaults started to increase and repossessed property became worth less and less.

The same economic causes produced the same economic effects all over the USA, and suddenly defaults weren’t a rare accident. Like the Titanic’s “watertight” compartments filling up and spilling over, the various tranches started to give way until even investments in super senior tranches became worthless. In fact, they became even worse than worthless – banks holding these tranches were suddenly responsible for billions of dollars in debt they couldn’t afford to reimburse, and the global financial system looked like it might collapse.

That’s when the governments stepped in to start bailing out the banks. And J.P. Morgan? They did get involved in some mortgage-backed securities, but avoided sub-primes and considered the whole business too risky to become a major player.

As a former anthropologist, Tett knows how to penetrate closed societies and gain the confidence of their people. Fool’s gold is a clear, fascinating account of a complicated world and the seemingly bizarre rituals, jargon and beliefs of the exotic tribes who inhabit it.

Useful links

OECD Financial markets website

The July 2009 issue of the OECD Jounal Financial Market Trends has articles on the turmoil in the financial industry

Patrick Love

Leave a Reply