Choosing Gross or Net Positions for Foreign Exchange VaR

Summary

The document discusses whether foreign currency value at risk should be calculated on gross asset and liability positions or on their net exposure. It does not present a specific Basel formula or numerical worked example. Instead, it highlights the trade-off between conservatism and recognition of portfolio diversification.

Calculating VaR separately for gross positions and then aggregating them will generally produce a higher estimate and greater economic capital needs. Calculating VaR on a net position can produce a lower estimate because it assumes offsets or diversification across positions. That approach requires evidence that the diversification effect is stable. The response emphasizes that there is no universally correct choice and that authorities expect sufficient conservatism. The appropriate treatment therefore depends on the portfolio and the support for its assumed offsets; the brief discussion does not settle regulatory requirements or explain how to document them in a particular Basel framework.

Key ideas

• Gross asset and liability VaR estimates, when added, generally produce a more conservative capital estimate.
• VaR on a net position can reflect portfolio offsets and usually results in a lower estimate.
• Recognizing diversification through netting calls for evidence that the offsets are stable.
• The document gives no specific Basel calculation method or worked numerical example.

Tags

# How to calculate value at risk in accordance with Basel?


# How to calculate value at risk in accordance with Basel?












I would greatly appreciate if you could let me know whether Value at Risk should be calculated for net open position (foreign currency assets-foreign currency liabilities) or for foreign currency cash?

Could you please introduce me a book regarding Value at Risk measurement in accordance with Basel (including numerical examples)? I already read it.

Thanks in advance.

## Answer by simzoor (score 0, accepted)

https://quant.stackexchange.com/a/46852

Generally, there is no 'right' approach. Bank authorities like to see that your calculations have a sufficient degree of conservatism.

To summarize, you can apply the following:

- If you calculate VaR to the gross positions (asset or liabilities) and add them up, you mostly end up with a higher VaR which implicates a higher need for economic capital to be reserved.

- If you calculate VaR to the net position, you implicitly assume some portfolio level, which might include diversification effects. This results mostly in a lower VaR (i.e. less economic capital to be reserved), but since this approach is 'less conservative' you have additional effort to proof the stability of the underlying diversification effects.

edit: for numerical examples, see e.g. this one

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