# covered interest arbitrage - formula, please?

I seem to routinely get the wrong answer on covered interest arbitrage, and I’d like to memorize a formula, rather than a whole series of steps (borrow in this currency, sell short this currency in the forward market, etc). For instance, given: Rb = interest rate in country B(ase) Rc = interest rate in country C(ounter) S = spot in B:C F = forward in B:C I’ve seen one answer in a Schweser practice exam (#120 on exam 2) essentially compute: (1+Rc) - (1+Rb)(F/S) and multiply this factor times the notional amount in C’s currency. But in the Schweser online class, essentially the formula was: (1+Rb)F - (1+Rc)S and multiply this factor times the notional amount in B’s currency. I knew that in the process of typing this question it would finally start to come together. C’s currency is related to B’s currency by a factor of 1/S, and the formulas above are equivalent multiplying through by -(1/S). Well, I wonder if anyone else has a helpful mechanism to remembering how to solve this sort of question. May only be one question exam day, but I might be taking Level 3 this June but for one or two questions

I don’t know what all those equations you posted up are but this probably all you need to know: S0 DC/FC * (1+rDC/1+rFC) I’m curious to see a question if possible.

Honestly, the best way to think about this is not with a formula, however I totally understand where you’re coming from. “covered” in the Covered Interest Arbitrage simply means you are covering your currency investment with a forward contract. This means you are buying foreign currency, for why would you need to long a forward contract on domestic currency? Look for where the arbitrage is, and buy low, sell high. That’s it. Remember to adjust for your time period, if less than 1. Typically, a broker quotes a forward price with a higher exchange rate than what is suggested by interest rate parity. You sell that, which means you long a forward to exchange foreign currency to domestic currency at the end of the contract date. You borrow at domestic risk free rate, invest the foreign currency at the foreign risk free rate, repatriate the foreign currency to domestic using the forward and pay back the original loan interest plus principal.