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What is VaR
Value at Risk, VaR, is a statistical tool to measure risk. Value-at-risk (VaR) is a statistical technique used to measure and quantify the level of financial risk within a firm or investment portfolio, over a specific time frame. This metric is most commonly used by investment and commercial banks to determine the extent and occurrence ratio of potential losses in their institutional portfolios. VaR calculations can be applied to specific positions or portfolios as a whole or to measure firm-wide risk exposure. (Investopedia)
Using this tool one can measure the likely loss in a fund for a given period of time. Further it also shows the probability of suffering such a loss, whether it is high or low.For example, a financial firm may determine an asset has a 3% one-month VaR of 2%, representing a 3% chance of the asset declining in value by 2% during the one-month time frame. The conversion of the 3% chance of occurrence to a daily ratio places the odds of a 2% loss at one day per month. (Investopedia)
One must use VaR with caution. There are no standard procedures to determine portfolio, asset or enterprise wide risks. Statistics gathered during periods of stability, periods with low volatility, may not reveal any risk. Yet there could be potentially risky investments which are simply not on the radar of this metric. Similarly, analysis using standard distribution probabilities would not be able to predict extreme events. The technique shows the lowest quantum of risk for a range of outcomes. For example, a VaR determination of 95% with 20% asset risk represents an expectation of losing at least 20% one of every 20 days on average. In this calculation, a loss of 50% still validates the risk assessment.(Investopedia). Such analyses were exposed in the 2008 Financial crisis, when the computations tended to underplay the likelihood of risk events posed by subprime mortgages.
How to Calculate VaR
VaR is a metric that is general to all asset classes, unlike other measures like duration, beta or Greeks. It is calculated as the probability distribution for a fund portfolio's market value. Writes Glyn Holton on his website; 'all liquid assets have uncertain market values, which can be characterized with probability distributions. All sources of market risk contribute to those probability distributions. Being applicable to all liquid assets and encompassing, at least in theory, all sources of market risk, value-at-risk is a broad metric of market risk.'
This general nature makes the metric all the moredifficult to calculate. For example,firstly the probability distribution of a portfolio's market value must be determined. Obviously, the more diversified a portfolio is,the more challenging will be computation.
VaR should be thought of as follows. Firstly, it is a computation by which one calculates a portfolio's value-at-risk. Secondly it is one's interpretation of the output of VaR. For example, a VaR with a 90% USD is defined as a probability, a time range and a currency. This VaR measures a certain amount of money,the portfolio, in a particular currency, namely the USD, in such a manner as to show the probability of the portfolio loosing that money over the given time period.In technical parlance this is called a quantile. Hence a one day 90% USD VaR is just the .90 quantile of a portfolio's one day loss. This is worth emphasizing: value-at-risk is a quantile of loss. The task of a value-at-risk measure is to calculate such a quantile. (Glyn Holton)
Let time 0 be now, so time 1 represents the end of thetime horizon. We know a portfolio's current market value0p. Its market value 1P at the end of the horizon is unknown. Define portfolio loss 1L as
1L = 0p - 1P
By its very nature the metric is probabilistic and as such must handle random financial variables. In general these variables can be grouped as portfolio value, asset value and key factors. Portfolio value refers to the value of a portfolio at the end of the value-at-risk time horizon. Asset value means the accrued value of the individual assets like bonds, stocks, options, futures and other assets, comprising the portfolio, at the end of the time horizon. Key factors are the financial variables like interest rate, exchange rates, commodity prices and implied volatilities that are used to value the assets at the end of the given time horizon. Further it is useful to realize that every risk has two components, uncertainty and exposure. According to Glyn Holton, 'in the context of market risk, we are uncertain if we don't know what will happen in the markets. We are exposed if we have holdings in instruments traded in those markets. A value-at-risk measure must combine those two components to measure a portfolio's market risk, and it does so with a transformation procedure.'
In sum, VaR is a valuable tool to study the risks associated with investing. Like any measure it is as good as the inputs given and the analysis with which the results are interpreted.
In a study, RBI estimated 5 percent 1-day-VaR for both BSE-SENSEX and NSE-NIFTY daily return using univariate GARCH model with proper mean specification as estimated in section 4.2 and following the FHS approach for VaR estimation (Model A). The study also estimated 5 percent VaR for both BSE-SENSEX and NSE-NIFTY daily return using ARMA-GARCH-FHS model (Model B). To estimate the model parameter we have used the daily data from 2nd January 2003 to 30th October 2009 and forecasted dynamically 1-day VaR for the period 2nd November 2009 to 24thDecember 2009, i.e., for 39 days. Actual returns and forecasted VaR based on both Model A and Model B for BSESENSE and NSE-NIFTY are given in Chart 2 and Chart 3, respectively. Out of 39 forecasts of VaR for BSE and NSE, only in one occasion, actual return was less than the VaR estimate (failure rate 1/39) for both model A and model B.
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