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.
        o Equity risk
        o Interest rate risk
        o Currency risk
        o 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.
        o Issue risk
        o Issuer risk
        o 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.

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