Annexure-IV

Definition:

VaR is defined as an estimate of potential loss in a position or asset/liability or portfolio of assets/liabilities over a given holding period at a given level of certainty.

VaR measures risk.

Risk is defined as the probability of the unexpected happening - the probability of suffering a loss. VaR is an estimate of the loss likely to suffer, not the actual loss. The actual loss may be different from the estimate. It measures potential loss, not potential gain. Risk management tools measure potential loss as risk has been defined as the probability of suffering a loss. VaR measures the probability of loss for a given time period over which the position is held. The given time period could be one day or a few days or a few weeks or a year. VaR will change if the holding period of the position changes. The holding period for an instrument/position will depend on liquidity of the instrument/ market. With the help of VaR, we can say with varying degrees of certainty that the potential loss will not exceed a certain amount. This means that VaR will change with different levels of certainty.

The Bank for International Settlements (BIS) has accepted VaR as a measurement of market risks and provision of capital adequacy for market risks, subject to approval by banks' supervisory authorities.

VAR can be arrived as

The expected loss on a position from an adverse movement in identified market risk parameter(s) with a specified probability over a nominated period of time.

Volatility in financial markets is usually calculated as the standard deviation of the percentage changes in the relevant asset price over a specified asset period. The volatility for calculation of VaR is usually specified as the standard deviation of the percentage change in the risk factor over the relevant risk horizon.

The following table describes the three main methodologies to calculate VaR:$

There are three main approaches to calculating value-at-risk: the correlation method, also known as

1. the variance/covariance matrix method;

2. historical simulation

3. Monte Carlo simulation.

All three methods require a statement of three basic parameters

• holding period

• confidence interval and

• the historical time horizon over which the asset prices are observed.

Under the correlation method, the change in the value of the position is calculated by combining the sensitivity of each component to price changes in the underlying asset(s), with a variance/covariance matrix of the various components' volatilities and correlation. It is a deterministic approach.

The historical simulation approach calculates the change in the value of a position using the actual historical movements of the underlying asset(s), but starting from the current value of the asset. It does not need a variance/covariance matrix. The length of the historical period chosen does impact the results because if the period is too short, it may not capture the full variety of events and relationships between the various assets and within each asset class, and if it is too long, may be too stale to predict the future. The advantage of this method is that it does not require the user to make any explicit assumptions about correlations and the dynamics of the risk factors because the simulation follows every historical move.

The Monte Carlo simulation method calculates the change in the value of a portfolio using a sample of randomly generated price scenarios. Here the user has to make certain assumptions about market structures, correlations between risk factors and the volatility of these factors. He is essentially imposing his views and experience as opposed to the naive approach of the historical simulation method.

At the heart of all three methods is the model. The closer the models fit economic reality, the more accurate the estimated VAR numbers and therefore the better they will be at predicting the true VAR of the firm. There is no guarantee that the numbers returned by each VAR method will be anywhere near each other.

VaR is used as a MIS tool in the trading portfolio in the trading portfolio to "slice and dice" risk by levels/ products/geographic/level of organisation etc. It is also used to set risk limits. In its strategic perspective, VaR is used to decisions as to what business to do and what not to do. However VaR as a useful MIS tool has to be "back tested" by comparing each day's VaR with actuals and necessary reexamination of assumptions needs to be made so as to be close to reality. VaR, therefore, cannot substitute sound management judgement, internal control and other complementary methods. It is used to measure and manage market risks in trading portfolio and investment portfolio.

VaR uses past data to compute volatility. Different methods are employed to estimate volatility. One is arithmetic moving average from historical time series data. The other is the exponential moving average method. In the exponential moving average method, the volatility estimates rises faster to shocks and declines gradually. Further, different banks take different number of days of past data to estimate volatility. Volatility also does not capture unexpected events like EMU crisis of September 1992 (called "event risk"). All these complicate the estimation of volatility.

VaR should be used in combination with "stress testing" to take care of event risks. Stress test takes into account the worst case scenario.

Why Backtest

Backtests compare realized trading results with model generated risk measures, both to evaluate a new model and to reassess the accuracy of existing models. Although no single methodology for backtesting has been established, banks using internal VaR models for market risk capital requirements must backtest their models on a regular basis. Banks should generally backtest risk models on a monthly or quarterly basis to verify accuracy. In these tests, they should observe whether trading results fall within pre-specified confidence bands as predicted by the VaR models. If the models perform poorly, they should probe further to find the cause (e.g., check integrity of position and market data, model parameters, methodology). The BIS outlines backtesting best practices in its January 1996 publication "Supervisory framework for the use of 'backtesting' in conjunction with the internal models approach to market risk capital requirements

$ Risk Management: A Practical Guide, RiskMetrics Group, J.P. Morgan, August, 1999* Philip Best: "Stress Testing", Marc Lore & Lev Borodovsky (ed)-The Professional's Handbook of Financial Risk Management, Global Association of Risk Professionals (GARP), 2001