## Value at Risk (VaR) for Asset Managers

**Ashish Sharma** | August 02,2014 10:53 pm IST

**Overview:- **

Value at Risk (VaR) is a portfolio based metric for quantifying the market risk of assets and portfolios. VaR is often used as an approximation of the "maximum reasonable loss" over a chosen time horizon.

Its primary appeal - widespread amongst commercial bankers, derivatives dealers, and corporate treasury risk managers - is its ease of interpretation as a summary measure of risks as well as its consistent treatment of risk across different financial instruments and asset classes. The earlier popular approaches used for risk measurement such as sensitivity and volatility are being rapidly replaced by VaR. VaR concentrates on the worst case loss unlike sensitivity which measures change in portfolio due to change in market factors (interests rates, exchange rates etc.) or volatility which measures the variance of portfolio returns on either side of the mean returns. Value at Risk has become essential toolkit of risk managers because it provides a quantitative measure of downside risk.

**What is VaR?**

VaR is generally considered as a probability based measure of loss potential. This definition is very general however and we need something more specific. More formally, VaR is the loss that would be exceeded with a given probability over a specified period of time. This definition has three important elements. First, we see that VaR is a loss that could be exceeded. Hence, it is a measure of a minimum loss. Second, we see that VaR is associated with a given probability. Thus, we would state that there is a certain percent chance that a particular loss would be exceeded with a given probability. Finally, VaR is defined for a specific period of time. Therefore, the loss that would be exceeded with a given probability is a loss that would be expected to occur over a specified time period.

Consider the following example of VAR for an investment portfolio: The VaR for a portfolio is Rs. 15 million for one day with a probability of 0.05. Consider what this statement says: There is a 5 percent chance that the portfolio will lose at least Rs. 15 million in a single day. The emphasis here should be on the fact that the loss is a minimum, not a maximum.

Value at risk is a statistic that summarizes the exposures of an asset or portfolio to market risks. VaR allows managers to quantify and express risk. In other words, VaR is a measure of the maximum potential change in the value of a portfolio of financial instruments with a given probability over a pre-set horizon. Thus, the value of VaR depends on: -

**• **The Horizon over which the portfolio's change in value is measured. **• **The degree of confidence chosen for the measurement.

VaR is often considered a useful summary measure of market risk for several reasons. One feature of VaR is its consistency as a measure of financial risk. VaR facilitates direct comparison of risk across different portfolios and distinct financial products. Also it allows the managers or investors to examine potential losses over a particular time horizon with which they are concerned. Another relative advantage of is that it is largely tactical neutral. In other words, VaR is calculated by examining the market risks of the individual instruments in a portfolio, not using actual historical performance.

**Mechanics of VaR Estimation**

Establishing a VaR measure involves a number of decisions. Two important ones are the choice of probability and the choice of the time period over which the VaR will be measured. Once these parameters are chosen, one can proceed to actually obtain the VaR estimate. The mechanics of VaR estimation can be described as a 5-step process, which is explained with the help of an example: -

**Steps in Constructing VaR**

Assume, for instance, that we need to measure the VaR of Rs. 500 cr equity portfolio over 10 days at the 99 percent confidence level. The following steps are required to compute VaR: -

**• **Mark-to-market of the current portfolio (e.g., Rs. 100 cr) **• **Measure the Variability of the risk factors(s) (e.g., 15 % annum) **• **Set the time horizon, or the holding period (e.g., adjust to 10 business days) **• **Set the confidence level (e.g., 99% which yields a 2.33 factor assuming a normal distribution) **• **Report the worst loss by processing all the preceding information (e.g., a Rs. 7 cr VaR)

This is a very simple method of calculating VaR for a given portfolio but in reality the calculation of VaR for general, parametric and other complex distribution is more complicated and different methods are used for calculating VaR which are explained in detail in the subsequent part of the report.

**VaR Methods**

There are three different methods for calculation of VaR namely: -**1. **Analytic Method **2. **Historical Method **3. **Monte Carlo Simulation Method

**Analytic Method**

The analytic method follows the variance/ covariance approach, which uses historic volatility and correlation data to predict the way markets are likely to move in future. By assuming that underlying market factors follow normal distribution, the VaR estimate can be calculated analytically for any confidence interval.

There are essentially two types of analytic method: -

**• **Delta-Normal Method: This method involves linear approximation of the price changes. It is mainly suitable when the portfolio does not contain non-linear products and when the movements in the risk factors are small. This method can accommodate a large number of assets and is simple to implement.**• **Delta-Gamma Method: This method improves upon the linear approximation in the Delta-Normal Method by taking into account the second order term also. However, inclusion of this term skews the distribution of changes in portfolio values. Hence the simplicity of the Delta-Normal approach is lost.

Risk metrics methodology is based on the analytic method. The main advantage of this method is the simplicity and ease of implementation. This method is easy to communicate because of standardization.

Delta Gamma method performs well provided the Greeks are stable. Thus, it is not a good measure of risk for At the money option, Near maturity money options, barrier options where the price is close to the barrier etc.