Value at risk

Value at risk (VaR) is the amount of money that one would expect to gain or lose over a specific time (the holding period) to a certain level of probability assuming normal market conditions[?]. It is routinely calculated on the portfolio of assets owned by securities houses or investment banks to estimate how much money they have to put aside on the rare occasions when daily trading generates a loss. VaR is not a measure of the maximum amount that could be lost because this is potentially infinite.

VaR calculation standardly involves the use of historical changes in market data as a proxy for future changes. Common methods are (i) historical simulation (ii) variance covariance (VCV) (iii) Monte Carlo method.

Historical simulation is the simplest and most transparent method of calculation. This involves running the current portfolio across a set of historical price changes to yield a distribution of profits and losses, and computing a percentile (the VaR). The benefits of this method are its simplicity to implement, and the fact that it does not assume a normal distribution of market price returns[?]. Drawbacks are the requirement for a large market database, and the computationally intensive calculation. Variance covariance involves the use of a covariance matrix derived from market data to compute the standard deviation of the portfolio. VaR can then be estimated from standard deviation. Benefits are the use of a more compact and maintainable data set (the VCV matrix) which can often be bought from third parties, and the speed of calculation. Drawbacks are the assumption that the portfolio is linear, and the assumption of a normal distribution of market price returns. Monte Carlo techniques usually involve principal components analysis of the VCV matrix, followed by random simulation of the components. Benefits are those of the VCV method, plus a more accurate assessment of non-linear risk factors. Drawbacks are the the assumption of normal distribution, as well the inherently opaque nature of Monte Carlo calculation, and the computationally intensive process.

The typical holding period is one day, although ten days are required to compute capital requirements under the European Capital Adequacy Directive (CAD). Confidence levels vary from 1% (usually, but misleadingly, referred to as 99%) to 5% (95%).

Risk is often broken down into different types according to the type of banking activity. These are usually:

• Market risk is the risk arising from changes in equity prices and market rates.
  • Equity risk
  • Interest rate risk
  • Currency risk
  • Commodity risk
• Credit risk is the risk arising from the bank's positions in other companies where those companies may become bankrupt e.g. a loan to Enron.
  • Issue risk
  • Issuer risk
  • Counterparty risk
• Liquidity risk arises from situations in which a bank cannot sell an asset because nobody in the market wants to trade that asset.
• Operational risk is caused by failures of the infrastructure within a bank, such as a critical computer system crashing.
• Legal and regulatory risk sometimes governments change the law in a way that adversely affects a bank's position.