Risk, What Risk?

In its April 26th issue, The Economist summarizes a report on  UBS's spectacular $38 billion loss on American mortgage-backed assets ("Wealth Mismanagement"). I was particularly interested in the section describing the mistakes made in calculating risk, but since the article was a bit vague for my taste, I just downloaded the actual 50-page report from the UBS website.  The report is written in surprisingly clear, accessible language, compared to the usual press releases to shareholders. The losses in the US subprime residential mortgage market are not due to a single business unit and do not have one single cause, but the collateralised-debt obligation (CDO) desk was responsible for two-thirds (p.7).

One quarter of the CDO desk's losses can be ascribed to the "CDO warehouse" (p.14), which is where UBS keeps the risky positions [residential mortgage-backed securities] while it waits to combine all of them into a CDO (which is made of layers of those, with various degrees of risk and hence return to suit various investors' tastes); the report states on p.13 that "there was typically a lag of between 1 and 4 months between initial agreement with a collateral manager to buy assets, and the full ramping of a CDO warehouse." During that time, "these positions would be on UBS's books with exposure to market risk."

The remaining three quarters of the losses of the CDO desk, ironically, are due to the super-senior tranches of the CDOs - the ones rated AAA, which were supposed to have the smallest degree of risk. These tranches remained on UBS's books, rather than being sold to a third party, because they were viewed as a source of easy profit. The report distinguishes between three types of super-senior positions (p.14):

1. negative basis super-seniors - a monoline (i.e., bond) insurer provided to the owner of the AAA-rated CDO (here, UBS) 100% protection against default; the difference between bond cash-flows and the insurance payment is booked as risk-free money, but a ton of problems arises if the insurer is downgraded, forcing the bank to unwind the trades it had already put on its books (see Section 6.2.2 p.30 of the report, or this New York Times article); those "represented approximately 10% of the super-senior losses,"
2. amplified mortgage portfolio super-seniors - they "contributed approximately 63% of total super-senior losses," so their study is particularly meaningful here. As expected, the size of the losses is due to mistakes in the underlying mathematical models. The report states on p.14: "the risk of losses was initially hedged through the purchase of protection on a proportion of the nominal position (typically between 2 and 4% though sometimes more); this level of hedging was based on statistical analyses of historical price movements that indicated that such protection was sufficient to protect UBS from any losses on the position." (Also read Section 6.3.6.1 p.38) In other words, this was supposed to be a perfect hedge, just like the negative basis super-seniors. Later (p.30, Section 6.2.3), the report's authors deadpan: "The cost of hedging through a NegBasis trade was approximately 11bp [basis points], whereas the cost of hedging through an AMPS trade was approximately 5-6 bp. The reason for the differential pricing of hedging strategies that from a risk metrics perspective were deemed to be equivalent appears not to have been closely scrutinised at desk or other levels." If it really had been a perfect hedge, it should have been as expensive as a NegBasis trade.
3. unhedged super-seniors -  they "contributed approximately 27% of total super-senior losses." The risk inherent to unhedged super-seniors is plain to see, and I won't discuss it in detail here.

On p.20, we learn another important weakness of the methodology, related to the assumptions underlying the VaR (value-at-risk) calculations. (The 95% Value-at-Risk of a portfolio is the value such that there is only a 5% chance of falling below that threshold, so we can say with 95% confidence that the portfolio value will exceed that threshold.) "VaR methodologies relied on the AAA rating of the Super Senior positions. The AAA rating determined the relevant product-type time series to be used in calculating VaR. In turn, the product-type time series determined the volatility sensitivities to be applied to Super Senior positions. Until Q3 2007, the 5-year time series had demonstrated very low levels of volatility sensitivities. As a consequence, even unhedged super-senior positions contributed little to VaR utilisation." Furthermore, there were issues with the quality of the data collected by the front office, as important features such as FICO scores were not tracked. Also (p.30), the risk of AMPS super-seniors was not included in VaR, since the position was believed to be fully hedged, i.e., carry zero risk: "For AMPS trades, the zero VaR assumption subsequently proved to be incorrect as only a portion of the exposure was hedged, although it was believed at the time that such protection was sufficient." That meant they did not "utilise VaR limits" (if VaR is viewed as a capacitated resource, they did not use any of it.) Overall, the methodology as implemented by UBS "had not appropriately captured the risk inherent in the businesses having subprime exposures" (p.34).

While the whole situation has had tragic consequences for UBS, it also allows for an unusually candid account of a top investment bank's risk management practices - I doubt any firm would have bothered to describe its strategies in such detail to its shareholders if it had not been faced with losses of that magnitude. That report, with its emphasis on the series of erroneous assumptions that were made and not corrected in time, should be required reading in financial engineering classes. At least it will be in mine.