Risk-Neutral Drift of Unhedged Foreign Equity in a Cross-Currency Basis

Summary

The document raises a risk-neutral valuation question for a euro-denominated fund holding US stocks without currency hedging. The fund’s euro value depends both on the dollar equity holdings and on converting those holdings at the prevailing EUR/USD exchange rate.

It contrasts an intuition based on the euro risk-free rate with a look-through approach that combines dollar equity dynamics and FX forwards. Under interest rate parity, the forward adjustment would reconcile the two currency perspectives; with a cross-currency basis, that relationship no longer holds in the same simple way. The text frames the issue but provides no answer, derivation, or market evidence, so it does not establish which drift applies. Resolving it requires specifying the pricing measure, FX quote convention, and treatment of the basis in the model.

Key ideas

• An unhedged euro fund holding US stocks has exposure to both equity returns and exchange-rate movements.
• A currency conversion connects dollar-denominated asset values to the fund’s euro value.
• Interest rate parity links risk-neutral drifts across currencies through FX forwards.
• A cross-currency basis complicates that link, and the document leaves the question unresolved.

Tags

# Risk neutral drift in presence of xccy basis


# Risk neutral drift in presence of xccy basis












Suppose I invest in an EUR denominated fund. This fund invests fully in USD stocks and doesn't hedge it's FX exposure (i.e. the EUR value of this fund is just equal to the USD value of the holdings converted to EUR based on the daily rate).

On one hand, I would like to think that since I've invested a EUR amount, my risk-neutral drift should be equal to the EUR risk-free rate. On the other hand, if I look through the fund at the underying assets, then they have a risk neutral drift equal to the USD risk-free rate corrected by the FX forward. Without a xccy basis, that drift would correct the risk neutral drift back to the EUR drift (based on interest rate parity), but in the presence of a xccy basis, that relation breaks down.

So which one is correct?

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