Risk Professional - December 2009

MODELING

Case-Shiller are non-stationary, which means that we cannot rule out that housing prices will continue to grow at ever higher rates. Though explosive growth rates mirror the “bubble mentality” that was common in the US, economic reasoning should lead to concerns about the robustness of results. One should not trust a model that attaches a large probability to scenarios in which housing prices explode and forever decouple from the rest of the economy.

Another widely used housing price index is the HPI, compiled by the Office of Federal Housing Enterprise Oversight (OFHEO). Like the Case-Shiller Index, the HPI (spawned in 1975) is based on the repeat-sales method. With this index, stress scenarios are much bleaker. Predictions made in 2005 or earlier would have not only included housing price levels that were lower than the actual ones at the end of 2008 but also scenarios in which housing prices continued to increase until 2006 and then fell sharply (much as they did in reality). The probability of these scenarios was in the range of 0.1% and 1%.

The Unlikeliness Dilemma

The crucial question then is whether financial institutions should have cared about scenarios that happen with a probability of 1% or less. Here, it is useful to note that before the crisis, many financial institutions had a AA or A rating. Moreover, they were proud of such ratings, and communicated in their annual reports and elsewhere that they aimed at maintaining or improving their credit quality in the future.

On a three-year horizon, the long-run average default probability of AA-rated companies is roughly 0.1%. In order to test whether one’s default probability is indeed in that range, looking at three-year stress scenarios that happen with a probability of more than 1% is clearly not enough. If a 1% worst-case happens and a bank becomes insolvent with a probability of 50% conditional on being in the stress scenario, the bank’s unconditional default probability is at least 50%×1%=0.5% — or much more than the AA rating suggests. One would never find out about this if one ignored stress scenarios that only happen with a probability of 1% or less.

Judging from analyst reports and risk reports from before the crisis, it seems that many institutions made exactly this error — i.e., while they knew a housing crash was possible, they did not seriously consider such a scenario, because the probability of a crash was apparently too low.

In one analyst report, for example, a “meltdown” scenario was described but then not discussed, because the probability

Risk models clearly demonstrated
that a crash could happen. Any bank
that wanted to maintain a credit rat-
ing of A or higher should have recog-
nized and responded to this risk.

assigned to it was only 5%.

One therefore should not blame the models — at least for the aggregate housing market studied here. They would have produced scenarios that come close to what finally happened, and these scenarios would have had probabilities large enough for financial institutions to consider.

What else, then, could have gone wrong? Well, it’s possible that some risk managers did not conduct proper stress scenario analyses, or at least failed to communicate the results of such analyses. However, based on the inside views of management processes that internal and public investigations have produced, it seems that many risk managers warned of increased risks. There are also well-documented cases of high-level executives who willingly took larger risks in order to ride the housing bubble. (Fannie Mae and Freddie Mac offer good examples.) This behavior is difficult to reconcile with the prudent risk management policy that managers typically marketed to investors and regulators.

The housing bubble, according to a time-series analysis conducted in 2005, was “most likely” going to continue. However, around that same time, risk models clearly demonstrated that a crash could happen, and any bank that wanted to maintain a credit rating of A or better should have recognized and responded to this risk.

FOOTNOTES

1. N.N. Taleb. The Black Swan. Random House, April 2007. 2. This is why the estimation details are not discussed in the remainder of this article.

Gunter Löffler (PhD) is a Professor of Finance in the department of mathematics and economics at the University of Ulm and the co-author of Credit Risk Modeling Using Excel and VBA (Wiley, June 2007). He can be reached at gunter.loeffler@ uni-ulm.de.