= Solution
For a Dollar investor, the Euro bank account has Dollar value $e^{r_Et}/Y_t$. After Dollar discounting, it is $e^{(r_E-r_D)t}/Y_t$. Its conditional mean growth exponent is $r_E-r_D+\sigma^2-\mu$, so the <martingale> requirement gives
$$
\boxed{\mu=r_E-r_D+\sigma^2\quad\text{under }Q_D.}
$$
With equal rates, $Y^{-1}$ is a <martingale> under $Q_D$ by part (a), whereas $Y$ has positive drift $\sigma^2$ and is not a <martingale> when $\sigma\ne0$. In the degenerate zero-volatility case, both exchange rates are constant and both are <martingales>; the asserted nonmartingale conclusion implicitly requires a genuinely risky exchange rate.
Back to article page
