Why doesn't the high-yield currency fall the way theory says it should?
Covered interest parity is arithmetic and it holds. Its unhedged cousin is a theory about expectations, and it fails — persistently, measurably, and in the same direction for decades. That failure has its own name in the literature, and it is the reason the carry trade exists at all.
The claim
Uncovered interest parity (UIP) says that the expected change in the spot rate equals the interest differential:
E[ΔS] ≈ i_terms − i_base
In words: on average, the high-interest currency depreciates by exactly its rate advantage, so an investor is indifferent between the two currencies. Combine this with CIP and you get the compact version: the forward rate should be an unbiased predictor of the future spot rate.
It is what "no free lunch" would look like if investors were risk-neutral.
What the data says
The standard test, from Fama in 1984, regresses the realised change in the spot rate on the forward premium:
Δs = α + β × (f − s) + ε
UIP predicts β = 1. Across major currency pairs and long samples, estimated β came out near zero, and frequently negative — often in the region of −0.5 to −1. That is not a small miss. A negative coefficient says the high-yield currency tended, on average, to appreciate slightly rather than depreciate. This result is known as the forward premium puzzle, or the Fama puzzle, and it survived thirty years of attempts to make it go away.
The arithmetic of what that means
Return to AUD/JPY at 100.00 with a one-year forward of 96.17. UIP says the expected spot in one year is 96.17 — the Australian dollar should fall 3.83% and hand back the entire 4.0 point interest advantage.
Suppose instead the pair ends the year unchanged at 100.00. The carry holder keeps the full 4.0%. Suppose it ends at 101.00. They keep 4.0% plus a 1.0% currency gain — 5.0%. Repeat that outcome across many currencies and many years and you have both the empirical puzzle and, straightforwardly, the carry trade's historical return.
Four explanations, none of them complete
- A time-varying risk premium. The extra return is compensation for bearing a real risk — precisely the crash risk of Unit 1, lesson 3. On this reading UIP is not violated; it is misspecified, because it assumed risk-neutrality.
- The peso problem. A rare, enormous devaluation that investors correctly fear may simply not appear in the sample. The measured excess return then looks like free money right up until the sample includes the event.
- Limits to arbitrage. Capital that would close the gap is slow, constrained by risk limits, and withdraws exactly when the opportunity is largest.
- A convenience yield. Investors accept a lower return on the safest, most liquid currencies for reasons that have nothing to do with the interest rate — a theme Unit 4 takes up for the dollar.
The honest current picture
Two qualifications matter. First, UIP performs considerably better at long horizons — five to ten years — and in samples dominated by high-inflation economies, where the interest differential really is mostly an inflation differential and really does show up in the exchange rate. Second, several studies find the anomaly has weakened or changed sign in post-2008 samples. A regularity that held for thirty years is not guaranteed to hold for the next thirty, and treating a documented historical average as a rule about the future is exactly the error this course is written to prevent.
What survives is more useful than a trading rule: the market's forward price is not its expectation, the difference between the two is a risk premium, and that premium is paid for carrying a specific and asymmetric risk.
Try it now
- Pick a pair with a persistent rate gap. AUD/JPY is the classic, and it is below: switch the chart to Monthly and take the ten years to August 2026. Take the two policy rates from the central banks' own pages, both public with their full history: the Reserve Bank of Australia's cash rate target and the Bank of Japan's policy interest rate. Note that a parity test is only as good as the rate series you can actually source.
- For each year in the window, compute what UIP predicted the pair would do (the differential) and what it actually did.
- Count how many of those years went the way UIP said. Write one neutral sentence about the count — and one about why a favourable count is not a reason to expect the next one.