Why VaR Is Zero for Equal Long and Short Futures Positions

Summary

The document considers a portfolio holding equal long and short positions in the same futures contract and expiry at the same traded price. It explains that under this setup, the positions offset one another, leaving the portfolio with no net exposure to movements in that contract. A full-revaluation profit-and-loss calculation therefore produces zero VaR, consistent with the answers discussed.

The explanation is limited to the stated case of matching positions in the same contract and maturity. It does not examine mismatched quantities, different contracts or expiries, basis risk, transaction costs, margin requirements, liquidity, or other risks that could remain in a real portfolio. The zero result should therefore be understood as a consequence of the assumed complete hedge, rather than a general claim that offsetting positions always eliminate every source of risk.

Key ideas

• Equal and opposite positions in the same futures contract and maturity cancel their market exposure under the stated assumptions.
• A full-revaluation profit-and-loss calculation gives zero VaR when the portfolio value remains unchanged across scenarios.
• The conclusion depends on the positions matching fully and does not account for other portfolio or trading risks.

Tags

# Value At Risk for Long and short position with same maturity and same traded price


# Value At Risk for Long and short position with same maturity and same traded price












I am not a quant geek.I always have doubt what should be the VaR output for portfolio contains long and short of the same maturity @ same traded price. e.g. CME corn future of sept expiry

## Groundwork

I was using the full revaluation with PnL approach at 95 percentile. The output was coming as zero.

## Answer by Neeraj (score 1, accepted)

https://quant.stackexchange.com/a/24947

If your portfolio has both long and short position, it means it is completely hedge. Under such scenario, VaR would become zero, as there is no risk involve in portfolio.

## Answer by SmallChess (score 1)

https://quant.stackexchange.com/a/24948

VaR is a method for simulating value of your future portfolio. If your portfolio is always zero, this is like not investing anything. Thus, there's no risk and VaR must always be zero.

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