Here is a great example of the flaw in risk models that rely on historical correlations. Using data from Credit Suisse on leveraged loans and distressed leveraged loans, we compute the correlation of the loan markets to the S&P500 since 1997.
Correlation of this portion of the credit markets to the equity markets has generally been unstable, registering both positive and negative measures over the past decade. But in a real financial crisis we know that correlations rise, as evidenced by the loan markets. The spike in 2008 was significant, reaching correlation of 0.8 between markets that traditionally have been loosely correlated or even anti-correlated. This was in fact the case with other credit markets as well, including corporate bonds and ABS.
Now consider capital and risk models (such as the Basle Accord) that are based on the ability to "diversify" across exposures. Supported by academicians, regulators, rating agencies, and practicing risk managers alike, these models are intellectually elegant and have proved profitable by conveniently reducing "expected" losses. This spawned what amounts to a whole industry of these participants, all with a vested interest in maintaining support for correlation based capital models.
One notorious example of such approach has been the assumption that pools of residential mortgages spread geographically across the US are sufficiently "diversified". Property values under this model (and based on some historical data) would therefore not be expected to drop simultaneously across the country. The beauty of this approach is that it makes the pools significantly "safer", even as individual loans remain risky, lowering expected loss of such pools, and allowing a large senior component to be rated AAA. As we now know, these misguided correlation assumptions have created a clear path to under-capitalization, which is where the financial system found itself in the midst of 2008.