Mapping Futures/Forward Positions to Risk Factors

A forward contract is an agreement to buy a specific asset, a commodity or a financial asset, at a fixed price on a fixed future date. While a forward contract is an OTC instrument and is customized for every transaction, a futures contract is a standardized contract and is traded on exchanges. For the purpose of understanding the mapping, let’s assume that they both are the same.

Similar to spot positions, the futures/forward positions also provide daily returns based on the price movement. Let’s say that we have n futures contracts each valuing V in our portfolio. Assume that the futures returns follow a normal distribution with a standard deviation (σ) and a mean of 0. As a certain confidence level (Zα), the VaR of the portfolio can be calculated as follows:

VaR = -ZασnV

At 99% confidence level, a portfolio with 10 futures contracts each valuing $10,000, and a standard deviation of 20%. will have a VaR of.

VaR = -2.33*0.20 * 10 * 10000 = -$46,600

The calculation is quite straightforward; the only practical issue is to estimate the standard deviation. Typically we will have pre-estimates for some time horizons, and for the inbetween time horizons we will interpolate the volatilities.