Value at risk:

We deal with an important concept related to market risk, called the value at risk.. Value at risk, usually denoted by VaR (not to be confused with variance in statistics!) is a measure of how the market value of an asset or portfolio of assets is likely to decrease over time under usual circumstances. Value-at-risk (VaR) is a category of risk metrics that describe probabilistically the market risk of a trading portfolio.  We shall discuss it and see how it can be employed as a strategy to guard against market risk.

We have seen in an earlier unit (Unit 3) that there are some widely used measure of risk, for example, in the case of a portfolio of stocks, the variance of this  portfolio. However, in many contexts it helps to have a measure of risk that is easily understandable and is a single index. Moreover, if the measure is such that it can widely applied in a large number of cases like firms, banks etc, many  organisations will benefit. The VaR is such a measure. Moreover, the variance or standard deviation do not specify the direction of deviation from the mean. Volatility can be in either direction. But sometimes investors or organisations like banks may be specifically interested in knowing the maximum loss they can possibly make in a particular period; they may be concerned with the worst-case scenario about their portfolio. This is where VaR comes in.

This measure is related to the probability of making large losses. Its power is its generality. Unlike other market risk metrics like duration, VaR is general. It is based on the probability distribution of a security's or portfolio's market value. The uncertain market values have a probability distribution, and all the types of risks that affect the market value have an impact on  that probability  distribution. Being applicable to all liquid assets and encompassing, at least in theory, all sources of market risk, VaR is
an all-encompassing measure of this risk.  In order to measure market risk in a portfolio using VaR, some means must be found for determining the probability distribution of that portfolio's market value.

VaR has two parameters: the time horizon for which the estimate is made because the asset is typically held for that 'holding period', usually being one day: and the confidence level at which the estimate is made (this is the usual confidence level used in statistical estimation).  VaR, with the parameters: holding period w days; confidence level x%, defines the likelihood that a given portfolio's losses will exceed a certain amount on a normal market conditions over a given period. Value at Risk (VAR) calculates the maximum loss expected (or worst-case scenario) on an investment, over a given time period and given a specified degree of confidence. Suppose we are interested in large losses of a given portfolio, and specifically, in those losses that are not likely to  occur not more than once in hundred trading days. We say that we are interested in the 99% confidence level and in a daily value at risk. Daily value at risk at a 99% confidence level is the smallest number x for which the probability that the next day's portfolio loss will exceed x is not more than 1%.