Forward Rates Using Inflation
If prices rise faster in one country than another, its currency should lose value so purchasing power stays roughly equal. Relative purchasing power parity turns that idea into a formula for the expected future exchange rate. If forward rates are unbiased forecasts, that same number is your forward rate estimate.
Forward exchange rates from inflation, explained simply
Relative purchasing power parity says a currency with higher inflation should lose value: E(S₁) = S₀ × (1 + i_A) ÷ (1 + i_B). If forward rates are unbiased forecasts, that's also the forward rate. In the example, ¥150 per $1 with 1% Japanese and 3% US inflation gives about ¥147.09 per $1 in a year.
What this inflation and exchange rates lesson covers
- Why higher inflation tends to weaken a currency
- The relative PPP formula for the expected future spot rate
- How to set up the quote so the formula points the right way
- How the expectations theory links expected spot and forward rates
- Why PPP works better over long horizons than short ones
Purchasing power parity formulas, explained
- S₀
- spot rate today, in units of currency A per 1 unit of currency B
- E(S₁)
- expected spot rate in one year, same quote
- i_A
- expected inflation in country A
- i_B
- expected inflation in country B
- F₁
- one-year forward exchange rate, same quote
How to estimate a future exchange rate step by step (worked example)
The spot rate is ¥150 per $1. Expected inflation is 1% in Japan and 3% in the US. Estimate the exchange rate one year from now.
- Quote is yen per dollar, so currency A = yen and currency B = dollar.
- E(S₁) = 150 × (1.01 ÷ 1.03).
- 1.01 ÷ 1.03 = 0.98058, so E(S₁) = 150 × 0.98058 = ¥147.09 per $.
- By the expectations theory, the one-year forward rate should also be about ¥147.09.
Answer: About ¥147.09 per dollar. The yen is expected to strengthen because Japan's inflation is lower, so each dollar buys fewer yen.
Absolute vs relative purchasing power parity
| Absolute PPP | Relative PPP | |
|---|---|---|
| Says | The same basket costs the same everywhere | Exchange rates change with inflation gaps |
| Formula | S = P_A ÷ P_B | E(S₁) = S₀ × (1 + i_A) ÷ (1 + i_B) |
| How well it holds | Poorly in the short run | Better over longer periods |
Harder inflation and exchange rate questions
What if US inflation were 5% instead of 3%?
E(S₁) = 150 × 1.01 ÷ 1.05 ≈ ¥144.29 per $. The wider the inflation gap, the more the higher-inflation currency is expected to weaken.
Which currency goes on top of the ratio?
The currency the rate is quoted in. Here the rate is yen per dollar, so Japan's inflation goes on top and the US's below. Mixing them up is the most common exam mistake.
Common inflation and exchange rate questions
How does inflation affect exchange rates?
Over time, a country with higher inflation tends to see its currency weaken, because each unit buys less at home and foreign goods look relatively cheaper. Relative PPP says the exchange rate should move by roughly the inflation gap between the two countries each year.
What is relative purchasing power parity?
Relative PPP says the expected change in an exchange rate is set by the ratio of one plus each country's inflation rate: E(S₁) = S₀ × (1 + i_A) ÷ (1 + i_B), with S quoted as currency A per unit of currency B. It is a forecasting rule, not a guarantee.
What is the difference between absolute and relative PPP?
Absolute PPP says identical goods should cost the same everywhere once converted at the exchange rate, like the Big Mac index. Relative PPP is weaker: it only says exchange rates change in line with inflation differences. Relative PPP is the version used to forecast future rates.
Is the forward rate a good predictor of the future spot rate?
The expectations theory says forward rates equal expected future spot rates on average, so they are a reasonable unbiased guess. In practice actual exchange rates bounce around a lot, and PPP holds much better over several years than over a few months.