The application for VaR finds its applicability, in any type of financial securities market wherever the future cashflows are uncertain and a function of market risks. VAR answers the question : how much can one lose with given probability over a given time horizon. Optimal risk management strategy maximises the net present value of the firms post tax cash-flows while accounting for all capital market imperfections.
Over the last few years, there have been significant developments in conceptualising a common framework for measuring market risk. A well established method of looking at market risks in the banking industry is to forecast earnings under predetermined price/rate market conditions.
There are two two major drawbacks to this methodology :It requires projecting market rate development over extended periods into future.And it supports the illusion that gains and losses occur at the time they show up in accrual acounts The advantages of VaR are that it incorporates the mark to market approach uniformity, and, relies on a much shorter horizon forecast of market variables.
However, a major drawback of this measure, is that it may not be trivial to mark certain transactions to market or even understand their behavior under certain rate environments.
To have a better understanding of measuring VaR we consider here the following example:
An Indian company is importing goods valued USD 100,000 payment due on 181st. day from the date of contract at an agreed price. We would like to evaluate the the VaR over a 6 month horizon for the liability portfolio of USD 100,000 given there is a 5% chance that the realised loss would be greater than what VAR projected. The choice of the 5% probability is discretionary and differs across institutions using the VaR framework.
The first step in calculation is to compute the exposure to market risk (i.e., mark-to-market position) where the exposure is equal to the market value of the position in its base currency, i.e., rupee. let us consider that the foreign exchange 6 monthly forward rate is Rs.42.00/USD (considering the current spot rate at Rs.39.65 & the 6 monthly forward at an annualised 10% level), then the forward market value of the liability portfolio at the end of 6 monthly time horizon is Rs.4.20 mio.
Now since, we would like to measure the VaR for a 6 month horizon, we consider the time series of forward dollar/rupee rates using the 6 monthly forward premia, where the forward rate is obtained by adding the forward premia to the corresponding time series of spot USD/rupee exchange rate.
Moving from the exposure to risk requires an estimate of how much the exchange rate can potentially move. The standard deviation of the return on the 6 monthly Re/USD exchange rate, measured historically can provide an indication of the size of rate movements. Let for example the calculated standard deviation of the time series of 6 monthly forward value of Re/USD is sFX. Now, under the standard RiskMetrics assumption that standardised returns on Re/USD are normally distributed given the value of this standard deviation, VAR is given by 1.65 times the standard deviation, with a 95% confidence level.
This means that the Re/USD exchange rate is not expected to drop more than 1.65c%, 95% of the time. (RiskMetrics provides users with the VAR statistic 1.65s.) In Rupee, the VAR of the exposure is equal to the market value of the position times the estimated volatility or :
FX Risk : Rs.4.2 mioX 1.65sFX. This means that 95% of the time one would not lose more than Rs. Rs.4.2 mioX 1.65sFX over a 6 months period.
We now extend our example considering a situation where an Indian firm has raised an ECB of USD 1 mio. We would like to consider the VAR over a 6 monthly horizon, again, given that there is a 5% chance of understating the realised loss. The only difference with earlier example is that here we have both interest rate risk on the loan and FX risk
resulting from the Dollar exposure. The exposure is still Rs. 4.2 mio. but it is now at risk to two market risk factors.
Here we estimate the standard deviation of 6 monthly LIBOR by taking a historical time series data of 6 monthly LIBOR and then calculate the Interest rate risk : Rs. 4.2 mio X 1.65sFx. Interest rate (where sInterest rate is the standard deviation of 6 monthly LIBOR) ;
FX risk on the other hand is : Rs. 4.2 mioX 1.65sFX
Now, the total risk of the liability portfolio is not simply the sum of the interest rate and FX risk because the correlation between the returns on the 6 monthly Re/USD exchange rate and the 6-monthly LIBOR is relevant. Using a formula common in standard portfolio theory, the total risk of the position can be derived.
VAR is the number that represents the potential change in a portfolios future value. How this change is defined depends on (1) the horizon over which the portfolios change in value is measured and (2) the degree of confidence chosen by the risk manager. VAR calculations can be performed also without using standard deviation or correlation forecasts.
(The author is assistant vice president, Gujarat Securities. The views expressed here are his own.)
