Historical VaR for an Equity Portfolio Hedged with Futures
Summary
The document explains a historical simulation approach to estimating Value-at-Risk for an equity portfolio hedged with futures. For each observation in a chosen historical window, apply the equity return and futures return from the same past period to today’s respective positions, then calculate the resulting portfolio dollar profit or loss. Repeat across the window and take the selected lower-tail loss percentile as the VaR estimate. The example suggests a one-year window of 250 observations and a 5% tail, but these are illustrative choices.
Because the method replays joint historical returns, it does not require an assumed return distribution or a separate correlation estimate between the equity portfolio and futures. Its main limitation is that it relies on past market behavior and the relationship between the hedged assets remaining relevant. The passage names parametric and Monte Carlo alternatives, but does not describe their implementation or compare their performance. It also gives no empirical backtest or guidance on window selection, rebalancing, or stress scenarios.
Key ideas
- Historical simulation applies paired historical equity and futures returns to current positions.
- The portfolio profit or loss is calculated for each past observation in the selected window.
- VaR is read from the chosen lower-tail percentile of the resulting losses.
- This approach avoids specifying a return distribution or estimating correlation separately.
- The estimate assumes historical market behavior remains informative about future risk.
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Full text
# How to compute the Value-at-Risk of an equity portfolio hedged using futures contracts? # 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? ## Answer by Woraphon T (score 2) https://quant.stackexchange.com/a/32337 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. - Choose number of windows. For example, 250 cases (1 year) VaR of today position (t) is based on historical data - collect historical return of equity and return of futures on t-1 - 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 - repeat 2-3 but change t-1 to t-2 - do 4 (by changing t-2 to t-3 and so on) until you have 250 cases - Choose your significance level, say 5% - 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.
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