• # Value at Risk (VAR)

Value at Risk (VaR) is one of the most widely used risk management methodology. This method is used for market risk calculation which uses probability to calculate risk and is widely used in the financial world. Value at Risk (VaR) is used as a risk measurement technique to calculate the risk of losing money in a specific portfolio of financial assets.

Value at Risk (VAR) provides both the maximum amount of expected loss with the probability of its occurrence.

Like an example, if the VAR is stated as “there is a 95% probability that a portfolio will not lose more than 10% of its value over the next month.”

In this example, the investor is provided with both the maximum risk value and the probability that it will occur. However, the measure is done only based on the historical value which does not give any guarantee for the future.

Drawbacks of VAR method

• VAR is usually estimated based on the historical data, which does not guarantee its usefulness for the future data.
• VAR is applicable only for returns which are normally distributed, for any other distribution it does not provide the effective result.
• VAR method requires huge historical data to make the returns normally distributed, which may not be possible for a relatively new fund.

In spite of these drawbacks, VAR is a very popular method to calculate risk and widely used in the world.

To Calculate VAR we need the following

• A well defined portfolio: The VAR of a portfolio is not the same as the sum of the VAR of individual assets
• A well-defined period of time: Most investors calculate a VAR over a day.
• A defined confidence level: For example, 95% VAR is the minimum amount of loss you would expect to make on 5 days out of a 100day investment period.
• Once we have the portfolio, we also need:

–        The MTM value of the portfolio.

–        The risk of the portfolio: the forecasted standard deviation of portfolio returns.

• For traded securities, the MTM value is readily calculated. If there are non-traded or OTC assets in the portfolio, use the mark-to-model value of the assets.
• For traded securities, returns variance can be forecasted out of estimated models. For non-traded and OTC assets, the variance will have to be modeled separately – mostly using asset pricing theories.
• If the one day rupee profit on a portfolio is x; and it has has a probability distribution function (pdf) f (x); then the VaR v at a 95% level is:

VAR Example

• Suppose the firm invests Rs.1000 crore in the Dowjones Index.
• The variance of this investment was about 1.02% daily.
• At a confidence level of 99%, the VAR is calculated to be Rs.24 crore.
• In comparison, the investment in Nifty has a 99% daily VAR of Rs.30 crore.
• Therefore, for the investor investing in DowJones index offer lower risk than investing in Nifty
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