The Real Value-at-Risk

The Economist had a special report on international banking a few weeks back (May 17th, 2008). I particularly enjoyed the article on risk management ("Professionally gloomy"), despite the fact that the author has the wrong date for the concept of Value-at-Risk - it was developed by JPMorgan in the 1990s, not the 1980s, as the magazine itself noted correctly in a January 22nd, 2004 article, "Too Clever by Half". The definition of "the maximum amount of money a bank can expect to lose" isn't the clearest available out there, but it's better than nothing, and the rest of the article goes to some length to clarify the concept. VaR receives quite a bit of attention in the mainstream media because it has now become "a staple of the risk-management toolkit and is embedded in the new Basel 2 regime on capital adequacy."

The article points out that the VaR calculations, which use historical data from the previous three to four years, let banks take more aggressive positions "the longer things go smoothly", for the same total amount of money set aside. Then, when there is a crash, prices that showed little volatility and correlation become extremely volatile and correlated: suddenly, the bank loses a lot more money than the VaR it had calculated. (See also Buttonwood's column, February 17, 2004, and the article titled "The Coming Storm", February 19, 2004 and "Uphill work", September 6, 2007) Common sense, however, suggests that "the risk of a blow-up will increase, not diminish, the farther away one gets from the last one." VaR also "acts as an amplifier" by triggering sell orders in times of crisis, which depress prices further and trigger additional sell orders from other companies. The last issue mentioned in the article is that "VaR captures how bad things can get 99% of the time, but the real trouble is caused by the outlying 1%."

It is interesting to note that "VaR breeds complacency" is not a new observation - the same theme can be found in the January 2004 article mentioned above, for instance, and yet banks don't seem to have taken advantage of the previous four and a half years to address this flaw. A difficulty is to determine how many years of data banks should use - how much of what was true five or eight years ago remains true today? This is for instance the case for computer-based trading: if you used different computer systems back then, or relied more on traders' judgment, the sell-offs might exhibit different characteristics that limit their present usefulness in predicting asset price behavior. Using historical data to compute VaR, quite simply, might not be the right way to approach the problem; someone at PriceWaterHouseCoopers suggested to start with given amounts of money (say, $1 billion) and "work backwards to think about what events might lead to that kind of hit."

To compensate for the limitations of historical data, banks run stress tests, which are discussed in "Eggheads and long tails," May 17th, 2007. (The most hilarious sentences of the day: "[UBS's approach to risk is described as:] zero tolerance for fiefs; beware of tail risks, risk concentrations, illiquid risks and legacies; avoid risks that cannot be properly assessed or limited; and never be hostage to a single transaction or client. [...] Indeed, it is sometimes criticised for not taking large enough punts. Earlier this year [a prominent investment banker] left the firm, reportedly because he felt it was too conservative in using its own capital in private-equity deals." To understand why it's hilarious, recall the recent UBS meltdown, which I wrote about here.) The "eggheads" article also mentions some interesting assumptions behind Goldman Sachs's scenario planning, such as the need to protect against liquidity risk and the hypothesis for stress-testing purposes that "the firm is unable to hedge or sell positions and must hold them from peak to trough. One of its fixed-income tests is a replay of the 1998 LTCM and bond-market meltdown. In its equity division it uses a “supercrash test” that assumes an instantaneous fall in the price of equities of 50%." Details of the simulations, however, are scarce. A footnote in the "Trading places" graph in the "Coming Storm" article, showing how VaR has increased in every bank from 2002 to 2003, puts the discussion in perspective: "Figures are calculated differently by different banks." That doesn't exactly inspire confidence in Wall Street's risk management abilities.