Thursday, May 13, 2010

the trick of it

Suppose we have 100 mortgages that pay \$1 or \$0. The probability of default is 0.05. We pool the mortgages and then prioritize them into tranches such that tranche 1 pays out \$1 if no mortgage defaults and \$0 otherwise, tranche 2 pays out \$1 if 1 or fewer mortgages defaults, \$0 otherwise. Tranche 10 then pays out \$1 if 9 or fewer mortgages default and \$0 otherwise. Tranche 10 has a probability of defaulting of 2.82 percent. A fortiori tranches 11 and higher all have lower probabilities of defaulting. Thus, we have transformed 100 securities each with a default of 5% into 9 with probabilities of default greater than 5% and 91 with probabilities of default less than 5%.

Now let's try this trick again. Suppose we take 100 of these type-10 tranches and suppose we now pool and prioritize these into tranches creating 100 new securities. Now tranche 10 of what is in effect a CDO will have a probability of default of just 0.05 percent, i.e. p=.000543895 to be exact. We have now created some "super safe," securities which can be very profitable if there are a lot of investors demanding triple AAA.

Alex Tabarrok on MR reviews Robert Pozen's Too Big to Save?