Toomre Capital Markets LLC ("TCM") would like to highlight a couple of items from UBS's 3rd quarter 2007 earnings report that was released on Tuesday, October 30th, 2007. Buried in the earnings report (a copy of the pdf file is attached to the bottom of this posting) is a discussion about the investment bank's market risk. The report states that "Investment Bank Value at Risk ["VaR"] (VaR-10-day, 99% confidence based on 5 years of historical data) ended the quarter at CHF 676 million, up from CHF 454 million at the end of the prior period end." Apparently the approximately 49% increase in VaR during the 3rd quarter was driven primarily by increased market volatility. As the report states, "The largest contributor to Investment Bank VaR at quarter end was credit spread on mortgage-related positions."
The earnings report continues with "'Backtesting' compares 1-day VaR calculated on positions at the close of each business day with the revenues arising from those positions on the following business day (excluding intraday trading revenues, fees and commissions)… When backtesting revenues are negative and greater than the previous day's VaR, a 'backtesting exception' occurs." The report then makes the rather startling admission: "In the third quarter [of 2007] we suffered our first backtesting exceptions in total – 16 in total – since 1988."
That is right folks! UBS's investment banking unit had losses on 16 days [Yes that is right sixteen days!!!] of the third quarter that it exceeded the Value-at-Risk calculated by its own risk management function. As an M.I.T.-trained engineer and the son of a mathematics professor no less, Lars Toomre is a little fuzzy with statistics and math. However, 16 out of 63 third-quarter 2007 trading days does make it seem like the losses at UBS exceeded it supposed daily VaR 25.3968% of the time!!!
Under a normal Gaussian distribution (bell-shaped statistical curve fitting that many are familiar with), a 99th percentile event is some 2.58 standard deviation units from the mean measurement and is meant to represent extremely unlikely events. In insurance terms, the 99th confidence interval is often used to represent that realized losses from all events but that single extremely unusual one in a hundred year event will be less than the stated amount. UBS' VaR modeling did not even capture greater than one standard deviation events (i.e. less than 84.13% of the time).
Clearly, UBS' realized experience during the 3rd quarter of 2007 greatly exceeded the losses that they estimated would occur only 1% of the time. Some of this variation no doubt can be attributed to the sharp pick up in volatility, and particularly in the seemingly one-way movement of sub-prime mortgage and other structured finance securities. And yes, some market sectors did have an almost step like decline in valuations. However, Toomre Capital Markets would suggest that the volatility in structured finance prices already was increasing in both the first and second quarters. Did not the UBS security prices reflect the sharp declines in the various ABX indices that started in the fourth quarter of 2006? Why were there no backtesting exceptions during earlier accounting periods?
So while several of the 'backtesting exception' days can be excused, an outside observer might be very accurate in observing that either the risk management process itself and/or the data feeding it was flawed, or more likely, UBS had extremely concentrated positions that declined in value relative to the historical volatility of their prices.
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