Value at Risk (VaR)

VaR is a widely used risk measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, probability and time horizon, VAR is defined as a threshold value such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value (assuming normal markets and no trading in the portfolio) is the given probability level.

For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day in 20.

Reference: http://en.wikipedia.org/wiki/VAR

Although the focus is often on a single number the "Global VaR", Banks generally measure VAR on many levels in the organizational structure. VAR is often broken down further (or attributed) to different risk factors; for example interest rates, FX, commodities and equities.

Historical simulation is a robust technique for measuring VaR. This methodology generates potential future scenarios by applying historic rate movements to today's rates. Advantages of this technique are that historic correlation between rates is automatically captured along with the non-normal "fat tailed" distributions often seen in financial markets rate movements.

Monte Carlo is another powerful technique for calculating VaR. It's advantages are that it can explore a great number of possible future scenarios, and recent changes in the volatility or correlation of market parameters can be included.


Expected Shortfall (ES)

ES is similar to VaR but instead of using a single value at the confidnece level we average the losses in the tail of the distribution (falling outside the confidence interval). The calculation is one-tailed in the same style as VaR.

This measure is increasingly being favoured by regulators (in particular for FRTB) because it takes into account the non-normality (or fat tails) typical of market rate movements; where rates will move very little for long periods and then suddenly "shock" to another level altogether.