# 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?

• Note that the fx forward is consistent with the currency basis. For example , let's say 3mo usdlibor swaps to euribor minus 10bp. Then the 3 month forward for Eurusd is spot rate * (1+usdlibor)/(1+euribor-10bp). This does not violate interest rate parity because you can't actually borrow or lend easily at libor.
– dm63
Jul 12, 2017 at 4:49
• @Quantuple: I guess my question is: in the presence of a cross-currency basis, how does one derive that the $\tilde{S}_t$ has a drift $r_{EUR}$, based on processes for $S$ and $X$, accounting for the presence of a xccy basis in the process for $X$
– Bram
Jul 12, 2017 at 14:20