Toomre Capital Markets LLC

Real-Time Capital Markets -- Analytics, Visualization, Event Processing, and Intelligence

UBS Has a "SMALL" VaR Risk Modeling Problem

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.

One such type of security that recently has had a step-like decline in valuation is the so-called super senior CDO tranche sector. These securities were sold to investors on an incremental yield basis and the supposed high quality AAA credit ratings. With the seemingly indiscriminate cut in ratings that have seen some super senior tranches go from AAA to BB in one fell swoop during the past two weeks, this sector has swooned in value. The popular ABX index for AAA-rated CDO bonds has moved from the high 90s to slightly less than 80% in the last few weeks. If UBS has a large concentrated position in super-senior CDO bond classes, it is highly likely that those bond positions have now lost at least ten percent of their value in the last two weeks (less any gains made from hedging activities). Such steep and sudden price drops are not captured by traditional VaR risk management models. Hence, it will be very interesting to read how well the UBS risk management function did in the fourth quarter credit markets swoon.

Toomre Toomre Capital Markets LLC ("TCM") is quite fearful of the forthcoming losses that are still to come in the global fixed-income and structured finance markets. What is so frightening is how the most senior portions of the CDO credit structures are now starting to significantly decline in value. These were the supposedly safe and "no need to think" bond classes that often made up two thirds or more of a CDO capital structure.

These also are the types of CDO bonds that Merrill Lynch, Citigroup, and UBS have touted owning in their recent earnings reports. One wonders what the net exposure to super senior CDOs bonds other global financial institutions might have. What is the net CDO exposure at Goldman Sachs? Deutsche Bank? Barclay's Bank? Morgan Stanley? HSBC? AIG? Lehman Brothers? Munich Re? Swiss Re? GE Capital? BNP Paribas? ABN Amro? MetLife? Prudential Insurance? New York Life?

And this list is not even addressing the supposedly massive holdings among Asian institutions like Bank of China. As Deutsche Bank's Vinod Aachi said in the article Evolution of Asian CDOs in Credit Magazine in December 2005, "the Asian investor base for CDOs is now broad, with insurers, pension funds and banks in Korea, Taiwan, Thailand, Hong Kong, Singapore, India and the Philippines all taking part." The 2005 Credit Magazine article continues with Mr. Aachi's suggestion that "one way forward for CDOs will be along the lines of relative-value strategies and leverage: in other words, the kind of strategies that hedge funds have pursued, but done through credit opportunities funds. "These will allow cross-asset plays and the more intelligent and effective application of arbitrage," says Aachi. "For example, a manager goes long on ABS and short on corporate credits. This is a classic hedge fund strategy, applied to CDOs." And virtually all of these "arbitrage" strategies are now under water!!!

The super senior CDO bond classes are also liberally sprinkled in many incremental spread investment strategies, including those pursued by Special Investment Vehicles, commercial banks, hedge funds, insurance companies, foreign banks, foreign finance companies tapping bank lines and those organizations involved in the Yen carry trade. Virtually all of these incremental yield investment strategies are now underwater and these organizations are looking to unwind their positions into a virtually non-existent market. Perhaps they are learning to truly become "investors"? The anger and frustration from such steep losses have not yet been fully played out and are unlikely to do so until at least mid-year 2008.

BE PREPARED FOR SOME VERY SURPRISING NEWS ON HOW THE CDO CREDIT LOSSES WILL AFFECT THE GLOBAL FINANCIAL SYSTEM. Liquidity truly will be king for the next period of time. Reader comments and thoughts are most welcome.