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Historical VaR for Offseting Long and Short Forward Positions

Article Quant Q&A · Author: user1131338
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Summary

The document discusses how to estimate historical Value at Risk for a portfolio containing long and short forward contracts. Its central example is an equal-sized purchase and sale of the same delivery-month contract, and whether their separate VaR figures should be added or offset. The replies distinguish a matched position in the same contract from positions in different assets, where correlations affect portfolio risk.

The practical guidance is to calculate VaR from the portfolio’s combined historical profit and loss rather than summing standalone VaRs mechanically. Equal and opposite exposures to the same contract eliminate market-price sensitivity when quantities match, though the second reply notes that different trade prices can leave an economic position whose P&L changes. The brief exchange does not specify a historical sampling method, confidence level, horizon, or treatment of basis and operational risks, so it is not a complete VaR procedure.

Key ideas

  • Standalone VaRs generally cannot be added or netted without considering portfolio dependence.
  • Historical VaR should be estimated from combined portfolio profit and loss.
  • Equal and opposite quantities of the same contract remove price exposure under a matched-position assumption.
  • Different trade prices can leave residual economic exposure despite offsetting contract quantities.
  • The post does not define the VaR horizon, confidence level, or data procedure.

Tags

Risk managementStatisticsFutures
Full text
# How to compute the historical VaR for a portfolio with long and short positions?


# How to compute the historical VaR for a portfolio with long and short positions?












I would like to calculate historical Value at Risk for a portfolio that includes both long and short positions in forward contracts.

The part that confuses me is that I wonder whether the VaR of the different positions should better netted or summed up.

For example, I purchased a December contract and sold another contract for same delivery month. If VaR on the long position is 1000 usd and sales is also 1000 usd, can I net them?

## Answer by SRKX (score 2)

https://quant.stackexchange.com/a/15760

I must say that I'd advise you not to use this kind of concepts if you don't really understand what VaR is and how it should be used, which seems to be the case here.

In short, if you bought and sold the same amount of the same contract then obviously you are not exposed to market risk anymore. So intuitively you expect you risk (and hence your VaR) to be 0.

However, this doesn't mean that you can net the VaR of different position in all cases. In fact you can't most of the time when you're not talking about the same asset. The reason is simply that correlation gets in the picture. What you need to do is to consider your global portfolio and estimate VaR from historical results.

## Answer by Carlo Longo (score 0)

https://quant.stackexchange.com/a/55792

Hi I think that if you buy dec contract and sell the same contract for the same quantity, but with a different Trade Price, you still have an exposure, so your P&L can be affected.So your VaR is not zero.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.