The Formula That Lost?

Absolutely brilliant article in Wired on the Gaussian copula function. Put briefly this is the formula that was used in the finance markets to rate securities and created the credit default swaps (CDS)and collatoralised debt obligations (CDO).

Finance lends on risk, but needs to add a premium for uncertainty of risk. If I can add enough things together that look like they've got different uncertainties I can diversify that risk. The idea of the copula function was to measure the correlation of risk. While the maths was elegant and did what it did, the underlying assumptions were invalid. Put simply the one risk that wasn't allowed for was the non-diversifiable risk in mortgages that house prices would fall. But this itself is so unusual that is not surprising - the expectation that house prices don't fall is captured in the saying "safe as houses" or in the Basel convention that residential housing had a risk weighting of 100% in capital adequacy claculation (the bank required no underlying capital to make that kind of loan).

When I was chairman of Endeavour Credit Union we went through a lot of exercises on measuring market (interest rate) risk. The relevant manager Greg West and I discussed how banks did this - usually through an asset and liabilities committee (ALCO) of the Board. He was speculating then (mid 90s) that these committees no longer understood the structure of derivatives well enough to understand the exposures.

And that ultimately was the banks failings. he quants (as they are called) were accurately measuring what they were measuring, the managrs in charge of asset decisions were accurately making decisions on what they thought the measures were measuring. Despite the fact that the few people who knew what both sides of this decision meant were saying that this was unsustainable and bad banking, the joy of the moment and the immediate benefits of bing in it meant the behaviour continued.

In this sense this is little different to the telco execs who believed the WorldCom memo that the internet was doubling every hundred days while knowing they didn't see it in their own traffic. That ended in the dot.com bust of 2000.

What both exercises demonstrate is the core fallacy of the belief in the rational decision making of firms. Firms are just as "boundedly rational" as individuals, perhaps more so. It is a bad policy to rely on the rational decision making of firms.