In a league table of the most misunderstood investment tools of all time, value at risk (VaR to its friends) is one of the bookies’ favourites 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 across a specified time period with a given level of probability. This can be illustrated by way of an example: The one-day VaR for my portfolio is £20,000 with a probability of 5 per cent.
That statement means that there is an estimated 5 per cent chance of the portfolio losing at least £20,000 in one day.
Or equally, and more reassuringly, there is a 95 per cent 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 per cent up from the bottom.
The ‘analytical’ method is not so user-friendly and unavoidably takes us into the 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 per cent probability is now a -1.65 standard deviation move.
Standard deviation is, in its simplest terms, a measure of the dispersion of a set of data from its mean.
The VaR calculation can hypnotically lead to a misplaced sense of security.
A common abuse is in interpreting VaR as a worst-case or maximum-loss number.
It is not, and woe betide the risk manager who considers a 95 per cent 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 in 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 seven 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 October 19 1987 the Dow Jones Industrial Average fell by 22.6 per cent.
Even in 1929, the worst daily decline was only 13.5 per cent.
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.
Jim Wood-Smith is head of research at Hawksmoor Investment Management
