# construct portfolio offering risk free profit

Have trouble understanding this question, seems quite open ended.

Assume that $S(0)$ is the current rate of exchange for foreign currency. Assume that and $K_n$ and $K_f$ are rates of return on home and foreign currency if it is invested over a period $T$.

Assume that the forward rate of exchange $F > S(0)\frac{1+K_n}{1+K_f}$. Construct a portfolio that offers a risk free profit.

I'm not quite sure what I'm asked to do here...

Specifically, given the assumption above, if there were no arbitrage the inequality above could not hold. However, given the inequality, it would be optimal to borrow in the foreign currency at rate of $K_f$, convert that cash flow into the local currency at the spot rate, lend the local cash flow at $K_n$ and enter into a forward contract to convert the future local cash flows into the foreign currency to pay off the initial debt. This is because the true forward price (converting local currency into foreign currency) is more expensive than the synthetic forward price. Therefore, it is optimal to be on the side that is converting the foreign currency into local currency.
• so if the opposite inequality exists $F<S(0)\frac{1+K_n}{1+K_f}$ then it is optimal to be on the side converting local into foreign currency? Basically a reversal of the steps you took earlier. Commented Feb 17, 2016 at 18:08