# Value at Risk (VaR)

Value at Risk (VaR, pronounced to rhyme with bar) is a measure of tail risk. For example if you invest £10,000 then if the 5% daily VaR is £200 you would expect to lose £200 or more on one day out of 20. The one in twenty comes from the level of VaR that you choose, hence 5% is 1 / 20, 1% VaR would be a one in one hundred day loss (1 / 100) and so on. This VaR is daily because it is based on daily returns. Just like volatility, VaR scales as the square root of time, so to convert daily VaR to annual you would multiply by the square root of the number of trading days in a year, which is roughly 16 (square root of 252 trading days). This is the rule of 16.

If you plot the daily returns of an asset they usually form a bell-shaped distribution but the tails of the distribution, which represent the most extreme losses and gains, tend to be very large for shares and corporate bonds. In the diagram below we can see the daily returns over a 30 year period for the FTSE 100. The FTSE 100 lost 1.62% or more with a probability of 5%, so we would say that the daily VaR of the FTSE 100 is 1.62%.

To calculate a VaR you have to choose a loss level (5%) and a time period (daily). VaR is commonly used by banks and asset managers to gauge the risk of their assets. The robo investor Scalable Capital uses a VaR-based algorithm to decide which assets to buy and sell for their clients. Alternative risk measures are volatility and drawdown. See our article on the best way to measure risk. 