Estimating USD VaR for a EUR/JPY Currency Position

Summary

This question asks how to estimate daily value at risk for a EUR/JPY position held in a USD-base trading account. Returns computed directly from EUR/JPY prices are expressed in yen, so they do not by themselves capture the position’s changing value in the account currency.

The response proposes applying the trading strategy to historical data, converting account equity into USD using historical USD/JPY rates, and then calculating returns and VaR on that USD equity series. It cautions that VaR summarizes a loss threshold rather than the maximum possible loss: a 95% estimate corresponds to a threshold that can be exceeded on a portion of trading days. The brief answer does not specify a VaR model, holding-period assumptions, treatment of costs or leverage, or details of the historical simulation, so those choices remain necessary for implementation.

Key ideas

• Returns for account-level risk should reflect values converted into the account’s base currency.
• The suggested method applies the strategy to historical data and converts equity using historical USD/JPY rates.
• Returns and VaR are then calculated from the resulting USD equity history.
• A 95% VaR threshold can be exceeded on some trading days.
• The response leaves model choices and trading costs unspecified.

Tags

# How to compute returns and daily VaR of a currency position?


# How to compute returns and daily VaR of a currency position?












I have a Forex trading account with a base currency USD. I am holding a position in EUR/JPY and would like to estimate my daily VaR. If I compute the EUR/JPY returns using the historic prices this would not be the right way of doing it, since it would give me returns in JPY which need to be further converted to USD.

What is the correct way for me to compute the VaR and the underlying returns?

## Answer by Sergey Bushmanov (score 2, accepted)

https://quant.stackexchange.com/a/21065

- Apply your trading strategy to history.

- Convert account equity to USD by applying historical USD/JPY rates.

- Calculate VAR/returns as usual.

Remember, VAR calculated in such a way will underestimate the impact of extreme events: i.e. 95% VAR will return you minimum of what you can lose on 5% trading days.

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