# Carry Trade vs synthetic Carry Trade using forward contracts

When it comes to foreign exchange carry trade strategy, the definition is straightforward: an investor borrows 1 US-\$in the US (low interest country) and invests that \$1 to AU (high interest country). By doing so, his dollar denominated return will be:

$$R_{t+1}^i = \frac{S_{t+1}^i}{S_{t}^i}(1+r_{f,t}^i) - (1+r_{f,t}^{US})$$

where $$S_t$$ is the exchange rate today, and $$S_{t+1}$$ is the exchange rate at time $$t+1$$, $$r_f$$ is the risk-free interest rate in the corresponding country.

However, the literature on the subject suggests using synthesized carry trade using forward contract, that is, buying forward AU currency at time $$t$$ with delivery for $$t+1$$, and then the difference between spot rate at time $$t+1$$ and forward rate would be the return to the investor:

$$R_{t+1}^i = \frac{S_{t+1}^i}{F_{t,t+1}^i} -1 = \frac{S_{t+1}^i (1+r_{f,t}^i)}{S_{t}^i (1+r_{f,t}^{US})} -1$$

Apparently, the latter is a common way FX carry trade is actually implemented.

I want to recall that return to Carry Trade strategy consists of both:

1. Gain on appreciation of investment currency
2. Gain on interest rate differential, that is, that after you borrowed in US and lent in AU, the payments you receive from investing in AU are higher than what you need to pay to the lender of USD.

It seems to me that using forwards approach, you capture the gain on FX appreciation of high-yield currency, but you don't actually capture the gain on interest rate differential.

So, my question is whether these two ways of implementing carry trade give actually different returns, or they are actually equivalent (despite me not seeing that)?

• Keep in mind that the way the forwards are priced is based on the interest rate differential and the CIP condition. So that is how interest rates come in. – noob2 Jul 28 '15 at 16:15
• @noob2 , yeah, I see now. But what about the cases when interest rates change after you bought discounted forward? – forstenn Jul 29 '15 at 13:06
• Well, to earn interest on some cash you have to decide on a maturity. Let's say you decide to roll over treasury bills or bank deposits every 3 months. Then this is equivalent to a carry trade strategy utilizing 3 month forwards. You prefer 1 month, ok, same thing. When they test a carry trade strategy in an article they usually tell you the maturity of the forwards they are using (or what interest rate they are using for the deposits/loans). – noob2 Jul 29 '15 at 15:21
• Great, that makes sense! I am gonna make an answer out of it then (you you can answer?) – forstenn Jul 30 '15 at 11:00