Comparing Borrowed-Currency and Forward-Based FX Carry Returns
Summary
The document compares two ways to express a foreign exchange carry trade. In the funded version, an investor borrows in a lower-rate currency and invests in a higher-rate currency; the resulting return reflects both the exchange-rate move and the difference between the countries’ interest rates. In the synthetic version, the investor buys the higher-yield currency forward and measures the return by comparing its later spot value with the agreed forward rate.
The displayed equations connect the forward-based return to spot exchange rates and the two risk-free rates, illustrating why the forward price embeds the interest-rate differential. The question raises a useful implementation distinction: the forward payoff does not show an interest payment as a separate cash flow, even though the rates enter through the forward price. The document poses the equivalence question but supplies no answer, empirical comparison, or treatment of funding, transaction costs, collateral, or other market frictions.
Key ideas
- A funded FX carry position borrows in one currency and invests in another.
- Its return combines the investment currency’s exchange-rate change with the interest-rate differential.
- A forward-based carry position expresses the currency exposure through a forward price that incorporates interest rates.
- The document asks whether the funded and synthetic implementations are equivalent but does not resolve the question.
Tags
Full text
# Carry Trade vs synthetic Carry Trade using forward contracts
# 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:
- 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)?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.