# Mapping Futures/Forward Positions to Risk Factors

We have learned about how various complex positions can be broken down into elementary blocks which can be further mapped to risk factors. The four such elementary blocks/instruments are Spot FX positions, Equity Positions, Zero-coupon bonds, and Future/Forward positions.

In this article we will look at mapping futures/forward positions.

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.

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