FX Spot Rates, Forward Rates, and Interest Rates

Exactly.

Suppose you're watching the news, and the topic of discussion is a change in exchange rates between your home domestic currency (d) and some foreign currency (f).

The arbitrage-free condition would include a higher borrowing cost abroad than what you'll earn at home, since you'll be gaining on the forward rate over spot. Then the whole thing works out. Mathematically, this is expressed as: $$\displaystyle F_{f/d} = S_{f/d} \left( \frac{1 + r_f}{1 + r_d} \right) $$

To summarize: [[summary]]

No, the foreign rate (the one you're paying, since you are borrowing there) will be higher.

If you're planning a trip to the foreign country, you might want to see a stronger domestic currency right now, so that your money can buy more souvenirs when you travel. The __spot rate__ is the exchange rate available right now, and that's the one you want to see move in your favor. What spot rate would you want to see rise, in terms of the base and price currencies?

That's right!

No, this spot rate is the foreign currency as a base, priced in your domestic currency. You wouldn't want to see that go up, since that would mean a relatively stronger foreign currency, and therefore a relatively weak domestic currency. The value of your domestic currency is measured in terms of _f/d_.

Spot transactions are executed at the spot rate, and settle in two days. It can take that long for funds to be delivered through the banking systems and to account for the different time zones. But since there's so much liquidity in the foreign exchange market, agreeing to a spot rate takes only seconds. The __forward rate__ is a rate which can be locked in right now at some future date. For example, maybe your big trip is in 12 months, and you want to take advantage of the 12-month forward rate, and not have to worry about what will happen in the forex markets between now and then (that might make the vacation even more relaxing).

Now suppose you saw that the spot rate, again in terms of f/d, was exactly 1.00. Then the 12-month forward rate is 1.05. That looks good; you can lock in a better future rate for your currency. If you decided to go a step further, and really take advantage of that difference, you might choose to borrow a bunch of money, exchange it, and then exchange it back at the forward rate. To profit, which currency would you borrow?

No, the foreign currency. Note that it's the domestic currency that is appreciating, so you would want to borrow the foreign currency and move it to the currency that's appreciating.

Yes.

Of course, you don't borrow for free. You have to pay interest on the foreign loan. That's okay, since you can also lend it at home and earn interest. So if the interest rates in both countries is the same, then this is an __arbitrage__ opportunity. Arbitrage is riskless profit, and if you can borrow and lend at the same rate in both countries, then this is a great opportunity. But if something sounds too good to be true, it probably is. Other people chase after arbitrage opportunities until they are gone, and they will here as well. So the interest rates are going to "eat up" your profits if you try this. That means that which interest rate has to be higher?

So in this case, you might have a 2% interest rate at home. With a little algebra, you can solve for any piece of this equation, which in this case would be: $$\displaystyle r_f = (1 + r_d) \left( \frac{F_{f/d}}{S_{f/d}} \right) - 1 = 1.02 \left( \frac{1.05}{1.00} \right) - 1 = 7.1 \% $$ No currency can have it all. If the spot rates and forward rates suggest that one currency will appreciate, then it will offer a lower interest rate. High interest rate currencies will have forward rates which suggest depreciation.

$$ S_{f/d} $$

$$ S_{d/f} $$

The foreign currency

The domestic currency

The foreign rate

The domestic rate

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