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:
- Gain on appreciation of investment currency
- 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)?
