My old professor Joel Moykr writes about economic history, and notes the importance of microinventions in productivity growth. Macroinventions include genuine “eureka” type of breakthroughs in which a single inventor revolutionizes a whole technical mode in one bold stroke. Microinventions are marginal improvements in a process. The relation between macro- and microinventions is one of complementarity. While microinventions are the principal source of measured productivity growth, without the original macroinvention there would be nothing to improve.

One current microinvention in finance is copulas, a way of measuring correlations, and their effects on portfolios. In today's WSJ, the inventor of copulas, David Li (pictured right), is rightly highlighted for his innovation (see here). Of course, they highlight this innovation in the context of the massive failure of this approach in May 2005, when Ford and GM were downgraded while most other BBB rated bonds stayed put. The result: risky tranches of CDOs lost a lot of value (say, the value of the Ford and GM portions of the portfolios they referred to), while the less risky tranches that would be breached only if other creditors also faltered remained steady. So a hedged portfolio long the risky tranche and short several units of the less-risky tranches lost a lot of money. Correlations, in this case between Ford, GM and everyone else, were too low.

It's a tough problem. Correlations are difficult because they are generally low during expansions, and much higher during crises and recessions, so estimating the correlation involves choosing the right sample period (eg, do you exclude 2001-2 data for current structures?). One symptom of this problem is the default rate on CDOs in the 1994-2003 period, which were orders of magnitude larger than for the basic corporate bonds. [CDOs are Collateralized Debt Obligations, whereby AAA, BB, etc. and equity securities are backed by pools of debt]

Source: Moody's Investors Services (see their excellent research site here)

That's a material miss. Ratings should have about the same default rates across products, and CDOs were much higher. In this period, this is because the CDO models underestimated both the severity of the credit cycle (and this cycle was really no worse than 1990), and the correlations of defaults within portfolios were much higher than expected. Clearly copulas are a helpful tool, but estimation of the parameters therein appears to be tricky. Correlations this spring were too low, but in the last cycle they were too high. A difficult problem indeed.