Value at Risk

In a league table of the most misunderstood investment tools of all time, Value at Risk (VaR to its friends), is probably the bookies’ favourite for a medal. VaR emerged in the 1990s as the then latest über-clever risk management tool that boldly sought to quantify, in terms of pounds and pennies, the amount a portfolio or trader has on the proverbial casino table.

The exact definition of VaR is quite subtle and lends itself to misinterpretation, so please sit comfortably and follow closely: VaR estimates the losses that are expected to be exceeded over a specified time period with a given level of probability. This can be illustrated by way of an example – consider:

“The one-day VaR for my portfolio is £20,000 with a probability of 5%”

That statement means that there is an estimated 5% chance of the portfolio losing at least £20,000 in one day. Or equivalently, and more reassuringly, there is a 95% chance that the portfolio’s one-day losses will be less than £20,000. I hope you are still with me so far.

The VaR recipe has three key ingredients: the time period, the probability level, and the approach used to model the likely losses. Any discussion of the numerous models available to estimate losses fills textbooks; here we simply offer a broad outline of two methods. The easiest, the Historical approach, assumes the future will mirror the past: line up yesteryear’s returns and calculate your VaR based on the one that sits 5% up from the bottom. As Sergei used to say, ‘Simples’. The Analytical method is not so user-friendly and unavoidably takes us into forbidden statistical-jargon-land. In calculations that only a risk manager could love, it assumes a ‘normal’ distribution of returns and needs an ‘expected volatility’. It gets even worse for the non-mathematically minded, as our 5% probability is now a –1.65 ‘standard deviation’ move.

VaR calculation can hypnotically lead to a misplaced sense of security. A common abuse is in interpreting it as a “worst case” or “maximum loss” number – it is not and woe betide the risk manager who considers a 95% probability as a comfort. In a year of 252 trading days, our example VaR tells us the portfolio is expected to lose at least £20,000 on 12 days, and potentially a lot more. VaR does not tell us how much more; it could be £20,001 but it could be £200,000.

VaR is in the charlatan business of measuring the immeasurable. “Known-unknowns” can perhaps be factored into models but, by definition, the same cannot be said of “unknown-unknowns”. The Black Monday crash of 1987, for example, was a move equivalent to 20 standard deviations. To put that into context, a move of 7 standard deviations should occur once in a period five times the length of time that has elapsed since multicellular life first evolved on this planet. A 20 standard deviation event was, according to the models, impossible. But on the 19th of October 1987 the Dow Jones Industrial Average fell by 22.6%. Even in 1929 the worst daily fall was only 13.5%.

Nonetheless, and provided its multifarious limitations are considered, VaR is still considered to have uses. It is pertinent for those trading on leverage in order to gauge the likelihood of a margin-call when everything goes horribly wrong. For those of us engaged in sensible multi-asset portfolio management, it should va va voom into a different world.