This is the title of a 2009 article in Wired that discusses the huge problem that occurred in collateralized debt. At the heart of it all was a simple formula to calculate a correlation.
“The corporate CDO world relied almost exclusively on this copula-based correlation model,” says Darrell Duffie, a Stanford University finance professor who served on Moody’s Academic Advisory Research Committee. The Gaussian copula soon became such a universally accepted part of the world’s financial vocabulary that brokers started quoting prices for bond tranches based on their correlations. “Correlation trading has spread through the psyche of the financial markets like a highly infectious thought virus,” wrote derivatives guru Janet Tavakoli in 2006.
The damage was foreseeable and, in fact, foreseen. In 1998, before Li had even invented his copula function, Paul Wilmott wrote that “the correlations between financial quantities are notoriously unstable.” Wilmott, a quantitative-finance consultant and lecturer, argued that no theory should be built on such unpredictable parameters. And he wasn’t alone. During the boom years, everybody could reel off reasons why the Gaussian copula function wasn’t perfect. Li’s approach made no allowance for unpredictability: It assumed that correlation was a constant rather than something mercurial. Investment banks would regularly phone Stanford’s Duffie and ask him to come in and talk to them about exactly what Li’s copula was. Every time, he would warn them that it was not suitable for use in risk management or valuation.
I didn’t even have to add the bold-it was in the original article. It bears repeating that correlations between financial quantities are notoriously unstable. And it bears mentioning that mean variance optimization is based on returns, standard deviation, and correlation. Most formulas reduce each of these quantities to a single number, as if they were a constant. (Complex problems generally require complex solutions. Unfortunately, to paraphrase H.L. Mencken, most complex problems have a solution that is simple, plausible, and wrong.)
None of the inputs for a mean variance optimization model are constants. And, in fact, a return change of just a few percentage points will materially impact the weights in a strategic asset allocation. Adaptive, tactical asset allocation driven by relative strength makes sense when you realize how many assumptions are baked into the pie chart for a traditional strategic allocation.
