# How to compute the Value-at-Risk of an equity portfolio hedged using futures contracts?

I would like to have your opinions about how to calculate the VaR of a hedged portfolio using futures contracts.

I have tried several "black box" softwares and none of them make too much sense. The idea is that I have a 100% Equity Portfolio and a 100% coverage with futures that might no be very well correlated to the Portfolio itself. How would you calculate the VaR? With what model?

• Couldn't you just simulate the daily performance over a past historical period and take the 95-th percentile? Feb 9, 2017 at 3:42

There are 3 main methods for VaR Calculation: Historical, Parametric and Monte Carlo (see here). All 3 can be performed on simple softwares like Excel or Matlab.

Parametric and Monte Carlo requires a few assumptions including return distribution on equity, futures and rates.

A Simple parametric VaR and Historical VaR can be done in one small page of spreadsheet, really.

I will present an example on Historical VaR, as I'm most familiar with.

1. Choose number of windows. For example, 250 cases (1 year)

VaR of today position (t) is based on historical data

2. collect historical return of equity and return of futures on t-1

3. apply that return of equity on t-1 to today equity position and return of futures on t-1 to today futures position and record dollar P&L
4. repeat 2-3 but change t-1 to t-2
5. do 4 (by changing t-2 to t-3 and so on) until you have 250 cases
6. Choose your significance level, say 5%
7. Rank those 250 P&L and get 5%th lowest percentile (top 5% most negative P&L)

This method doesn't require assumption on return distributions or correlation of equity and futures.

It, though, assumes that past characteristic and relationship will keep continuing in the future.

• I also assume 250 points are enough to estimate what's in the tails of the distribution.
– SRKX
Feb 9, 2017 at 5:36