Sunday, May 04, 2008

Bank Value-at-Risk Reporting

I'm a big Value at Risk fan. As a method to report risk for a desk with diverse financial factors, and accommodating fat tails, it is unsurpassed. Many of the criticisms are of deficiencies 'within the box'. Indeed, many claim that VaR assumes normality, but nothing could be further than the truth. A particular modeler can assume normality, but he shouldn't. And because the VaR focuses on the tail--usually a 95% or 99% event--it teases out nonlinear exposures that are not shown in things like standard deviations. So it isn't ignorant of nonlinear exposures and extreme events, it was designed with them in mind. Most importantly, it replaced the old method of reporting, which was a myriad of stress tests particular to various products, such as 5% moves in currencies, or 100 basis point shifts for bonds, and puts them in a standard, common denominator. Riskmetrics was the pioneer of this risk reporting, and they continue to put out a great deal of common sense on this topic.

But there are two large holes in VaR. First, banks are reluctant to apply this to nontraded assets, because banks traditionally treat assets in their 'banking book' different than in their mark-to-market book: in the former it is kept at book value, in the latter it is marked to market quarterly. Secondly, credit risk is very cyclical, so you have several years, if not decades, of low or zero defaults, but then a big boom in defaults. In this case, your horizon should really be not days, but rather years, and instead of using historical data for a particular asset class, they should use a variety of similar producs. In a sense, estimating credit risk, is like estimating country default risk: you don't look at the daily time series of, say, Greek defaults (zero, every day this century!), to estimate their future default rate. Instead, you look at a panel of data, that has both a cross section (many countries) and a time-series aspect to it.

But for a desk, it is a great way to get a 'little' top down view. That is, if you are very parochial desk, trading, say, convertible bonds, you have a handful of sensitivities you monitor: yield curve shifts, twists, credit spread shocks, implied volatility shocks, realized volatility shocks, stock market shocks. But if you have a handful of these desks, VaR sums them up, and allows you to see, day to day, if any significant new exposures were put on. But it only aggregates so well. The problem with the Value-at-Risk reported in major bank's annual reports are farcical. The big 7 US money center banks (Goldman, Citi, etc.) show an average daily VaR (99%) of about $120MM, which annualizes to about $1.9B. But the average market value decline in those same banks over the past 12 months has been about $42B, a 22 fold difference. A seemingly reasonable interpretation, that VaR measures a once in 100 year scenario as applied to the bank, is clearly not reasonable, not by a longshot.

But of course, if you read the fine print, you'll find that the VaR was actually pretty good. The problem is that banks tend to apply VaR only to their market making operations, and so, in the recent case, all those subprime mortgages were simply off the radar screen. Quite the asterisk. Further, given most market making operations are more like selling widgets than speculating on risk factors, these activities generate insanely high pnl/VaR numbers, so if the annualized trading revenue is $20B, and the annualized VaR $2B, the ridiculous Sharpe ratio implies that the VaR doesn't matter. Double the VaR, and the bank would do exactly the same thing, because it's like an internal ROE of 56%--well over the hurdle rate. VaR is not constraining, or directing, capital. It is merely measuring incidental risk taking by a select subset of its inventory. It's like measuring the cost of electricity at headquarters--not without interest, surely better minimized, but generally not a strategic issue. Indeed, if you are going to exclude the major risks from a top-down number, it is misleadingly irrelevant. Mid-level management should know the VaR of trading operations, to monitor significant changes to their books, but until they include most, if not 'almost all' risks within a VaR-type approach, don't even report a top-level VaR.

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