The nonsense of VaR

Value at Risk - Just a few short years ago it was all the rage. The question on the trading floor was not 'how big is your position', but 'What's your VaR?'. Over the past couple of years, VaR has taken a battering from many who have pointed out that VaR is all very well for dealing with day-to-day volatility, it is truly useless for understanding worst-case scenarios because it is reported to a confidence level, usually 95 or 99%, and thus deliberately excludes the 'fat tail' or abnormal deviations that are the really important and interesting part of risk management. Being told that your portfolio has a daily VaR of $10 million, with 99% confidence is all very well, but what does it actually mean, in real terms? Risk management shouldn't primarily be about fluctuations in value (i.e. volatility), but about permanent impairment of wealth - i.e. rare, cataclysmic events that wreck portfolios terminally, not the daily back-and-forth. VaR is just another volatility-based definition of 'risk' - relevant perhaps, but not the kind of risk that a portfolio manager or trader should focus on. However, I want to focus on another serious flaw in the VaR measurement, one that has been overlooked. This is that it measures volatility using past data as its input. More specifically, through there are differences in calculation, VaR typically uses the past x days of a market as typical of the volatility in that market, and uses this figure to derive its confidence levels. This in turn means that VaR is always behind the curve as market volatility changes. Think this is a theoretical argument? Well, allow me to make it a very real one. Using figures culled from Bear Stearns annual reports over the past decade, we can see what this really means. Over the nine and a half years between Q1 1998 and the end of Q2 2007, Bear's traders experienced just 5 days of loses above the 95% daily VaR limit. In Q3 2007, however, BSC succumbed to 10 such days. In Q4 they had 16, and in Q1 2008 (just before BSC went the way of the dodo), they experienced a further 8. That's 34 days where the day's trading loss exceeded the firm's 95% confidence level in a mere 9 months. Assuming a 21 trading day month, that implies that loses exceeded the VaR limit 18% of the time in a 9 month period. Equally worryingly, it came after just 5 such days in nearly the entire previous decade. Figures from Goldman Sachs, Morgan Stanley and Lehman Brothers show similar rapid increases in the number of days where VaR limits were exceeded. The problem then is that not only does VaR fail to account for the really crucial 'fat tail' risk, but, as conventionally configured, it isn't even that good at quantifying volatility due to an over-reliance on the near past. Bad, VeRy bad!