2. Exchange rates: parity and the carry trade
Macro 4: Inflation, currencies and commodities
An exchange rate is not the price of a currency: it is the relative price of two, and behind it sit two interest rates pulling in opposite directions. Grasping that mechanism is what separates understanding a currency from having an opinion about it.
First things first: nobody can forecast them in the short run
It is worth starting with the uncomfortable part. In 1983, Meese and Rogoff compared the structural exchange rate models of the day with the dumbest forecast available, namely that tomorrow it will be where it is today. Over horizons of months, the dumb forecast won. Forty years on the result still holds: over the short run an exchange rate looks very much like a random walk, and only over horizons of years do recognizable forces such as convergence toward relative purchasing power emerge.
That does not mean there is no structure. It means the structure lies in the arbitrage relationships, not in the direction.
Covered parity: the equation that does hold
Imagine the one-year rate is 5% in dollars and 3% in euros. You might think it enough to switch euros into dollars, collect the 5% and come back, pocketing 2 points risk-free. It does not work, and the reason is that to remove the risk you have to lock in today's rate for the return leg with a forward contract, a forward.
The price of that forward is not free: arbitrage sets it. If the dollar paid 2 points more and the forward did not offset it, any bank would do the trade in infinite size. That is why the forward quotes the dollar roughly 2% weaker a year out. This is known as covered interest rate parity, and it is the most robust relationship in foreign exchange.
The practical consequence is devastating: an interest rate differential is not free money, it is already in the price of the insurance. Any strategy promising to collect it without risk is either hedging badly or being paid for something else. One caveat: since 2008 covered parity has held with small but persistent deviations, the so-called cross-currency basis, because balance sheet space at the banks doing that arbitrage stopped being free.
Uncovered parity: the one that should hold and does not
If instead of hedging with a forward you take the currency risk, theory says you should on average break even: the high-rate currency ought to depreciate by exactly the differential, offsetting the extra interest. That is uncovered parity.
Empirically, it does not happen. Over long samples, high-rate currencies have depreciated by less than implied, or even appreciated. Fama documented the anomaly in 1984 and it is known as the forward premium puzzle. That gap between what theory predicts and what happens on average is, precisely, the profit of the carry trade.
The carry trade: what you are really selling
The trade is simple: you fund yourself in the cheap currency and put the money to work in the expensive one. In 2007, with Japan around 0.5% and Australia above 6%, the differential ran to some six points a year, and with moderate leverage it turned into a double-digit return that showed up punctually every month.
What you are actually doing is selling insurance. You collect a small, steady premium in exchange for taking on a huge and infrequent loss. The payoff profile has negative skew: many tiny gains and a handful of devastating losses. This carries a statistical implication worth internalizing: through the calm periods, the Sharpe ratio of a carry trade looks extraordinary, and that number does not describe the risk, it conceals it.
Why the ending is always the same
The currency mechanics of the collapse follow a closed logic:
- The position is leveraged and is set up in the same direction by almost everybody, because the differential is public and obvious.
- When currency volatility rises, risk limits force positions to be cut, even though nobody has changed their mind.
- Unwinding the position means buying back the funding currency, which is exactly the one everybody was short.
- That mass buyback pushes the cheap currency up, which deepens the losses of those still in and forces them to close as well.
- The result is the classic asymmetry: carry goes up by the stairs and comes down in the lift.
Notice that none of this requires the Japanese economy to improve. The funding currency appreciates because of its role in the trade, not because of its fundamentals.
2008 and August 2024: the same script twice
In 2008, the yen was the world's funding currency. When volatility exploded, the dollar went from being worth more than 120 yen in mid-2007 to trading below 90 in December 2008, and the Australian dollar against the yen, the carry trade par excellence, lost close to half its value. Japan was sliding into recession while its currency appreciated violently.
August 2024 repeated the pattern with no financial crisis involved. The Bank of Japan raised its rate to 0.25% on July 31 while the Federal Reserve was signaling cuts: the differential was narrowing from both ends at once. The dollar went from around 161 yen in early July to about 142 on August 5, and the Nikkei shed 12.4% in a single session, its worst day since 1987. Weeks later much of the move had reversed.
The lesson: carry does not need a catastrophe to blow up. All it takes is for the differential that justifies it to start closing.