Key takeaways
– Relative purchasing power parity (RPPP) links changes in inflation differentials between two countries to changes in their exchange rate over time.
– The basic idea: the currency of the country with higher inflation should depreciate relative to the currency of the country with lower inflation by roughly the inflation differential.
– RPPP is a dynamic (change-over-time) version of absolute PPP (APPP). APPP compares levels; RPPP compares rates of change.
– RPPP is most useful as a long‑run guide. Short‑run exchange rates can deviate substantially due to interest rates, capital flows, policy, and market sentiment.
– Source: Investopedia (Julie Bang) and supporting price-index data (e.g., Numbeo for purchasing‑power indexes).
Understanding Relative Purchasing Power Parity (RPPP)
Relative PPP is an extension of the law of one price and absolute PPP. Whereas absolute PPP says a given basket of goods should cost the same in two countries once prices are converted at the exchange rate, relative PPP says changes in price levels (inflation rates) between two countries will be reflected in changes in the exchange rate.
In plain terms: if Country A’s inflation is higher than Country B’s by x percentage points in a period, Country A’s currency should depreciate by approximately x% relative to Country B’s currency over that period.
Why this matters
– It links inflation expectations to expected currency movements.
– It can be used for long‑term forecasting of exchange rates, for valuation adjustments, and for real-return calculations on cross‑border investments.
– It helps explain why high‑inflation countries often see persistent currency weakness.
Purchasing power parity in theory
– Law of one price: identical tradable goods should have the same real price across countries once exchange rates are applied (ignoring transport costs, tariffs, and other frictions).
– Absolute PPP formula (level version): S = P_domestic / P_foreign
• S = spot exchange rate (domestic currency per unit of foreign currency)
• P_domestic, P_foreign = price levels (same basket) in each country
– Relative PPP (rate-of-change version): percentage change in the exchange rate ≈ inflation_domestic − inflation_foreign.
RPPP formula (practical expression)
– Define e as the domestic price of one unit of foreign currency (domestic currency per foreign currency). Then:
Δe / e ≈ π_domestic − π_foreign
where π = inflation rate over the same period.
– Equivalently, expected depreciation of domestic currency ≈ domestic inflation − foreign inflation.
– Example rearrangement for forecasting a future spot: e_t+1 ≈ e_t × (1 + π_domestic − π_foreign) (for small rates; for large rates use multiplicative exact form e_t+1 = e_t × (1 + π_domestic)/(1 + π_foreign)).
Example of RPPP
– Suppose U.S. inflation over the coming year is forecast at 3% and Mexico’s at 6% (a 3‑point differential).
– RPPP implies the Mexican peso should depreciate about 3% against the U.S. dollar. Put another way, the U.S. dollar should appreciate ≈ 3% vs. the peso.
– If the current rate is 20.00 MXN per USD, the RPPP‑implied one‑year rate ≈ 20.00 × (1 + 0.03) ≈ 20.60 MXN per USD (approximate using the differential). Using the exact multiplicative form: 20.00 × (1.03/1.06) ≈ 19.43 would be the implied domestic price of foreign currency depending on your e convention — so always be careful to define which currency is the numerator.
Dynamics of RPPP — when it works and when it doesn’t
– RPPP tends to be more informative over longer horizons (years) than in the short run.
– Short-run exchange rates are strongly affected by:
• Interest rate differentials and capital flows
• Speculative trading and market sentiment
• Trade barriers, transportation costs, and nontradable goods
• Differences in the composition of price baskets and measurement issues
– Over decades, cross-country inflation differentials are an important driver of exchange‑rate trends, but they are not the only factor.
Limitations of RPPP
– Measurement: comparing “the same” basket across countries is difficult (quality differences, different consumption patterns).
– Nontradables: many prices (services, local housing) do not arbitrage internationally, so PPP does not hold for those components.
– Short‑run deviations: interest rates, capital flows, and risk premia cause persistent short‑ and medium‑term deviations.
– Policy and restrictions: capital controls, FX interventions, and taxes distort exchange rates away from PPP predictions.
– Data lags and forecasting errors in inflation undermine accuracy for forward-looking uses.
RPPP vs. APPP (Relative vs Absolute)
– Absolute PPP (APPP): compares price levels at a point in time and implies a level exchange rate that equates price levels of an identical basket across countries (S = P_dom / P_for).
– Relative PPP (RPPP): compares changes in price levels (inflation rates) and implies exchange rate adjustments over time according to inflation differentials.
– APPP is a stronger condition and typically fails in practice because of nontradables, transaction costs, and market imperfections. RPPP is weaker and more realistic as a long‑run relationship.
Practical steps — how to apply RPPP (for analysts, treasurers, investors)
1) Define your exchange‑rate convention
• Decide whether you use domestic currency per unit foreign (e = domestic/foreign) or the reverse. Keep the convention consistent in calculations.
2) Gather inflation data
• Use comparable price indices (e.g., consumer price index CPI or GDP deflator) for both countries.
• For forecasting, use central bank/consensus inflation forecasts or build your own forecast model.
3) Compute the inflation differential
• π_diff = π_domestic − π_foreign (same horizon and periodicity).
4) Convert differential to expected exchange rate change
• For small rates: expected % change in exchange rate ≈ π_diff.
• For exact multiplicative: E[e_t+1] = e_t × (1 + π_domestic)/(1 + π_foreign).
5) Produce a forecasted exchange rate
• Apply the expected change to the current spot to get the RPPP‑implied future rate.
6) Adjust for real‑world factors
• Add overlays for risk premia, expected interest rate changes, capital flows, policy risk, and market sentiment.
• Consider ranges/scenarios rather than a single point.
7) Use for decision making
• Hedging: determine whether forward rates or hedges are attractive relative to RPPP expectations.
• Valuation: adjust foreign cash‑flows for expected currency moves to compute real returns.
• Strategic planning: budget for likely currency trends when inflation differentials are persistent.
8) Monitor and update regularly
• Inflation forecasts and market conditions change — update inputs and monitor deviations.
Practical examples of use cases
– Corporate treasury: Decide whether to hedge a three‑year revenue stream in a currency of a high‑inflation market.
– FX strategist: Build a long‑run fair‑value model combining RPPP with interest parity and risk premia.
– Portfolio manager: Estimate expected currency returns for international equities when evaluating real returns.
Important considerations and best practices
– Always be explicit about the exchange‑rate convention and price indices used.
– Use comparable baskets or broad indices (CPI or GDP deflator); avoid one‑off goods that are not representative.
– Treat RPPP as a long‑run guide, not a short‑term trading signal.
– Combine RPPP with other models (interest rate parity, PPP-implied misalignment measures, fundamental econometric models) for richer forecasts.
– Be cautious in countries with weak statistics, active FX controls, or volatile capital flows.
Fast facts and context
– PPP is commonly used to compare living standards: institutions like the IMF and World Bank provide PPP‑adjusted GDP to compare real output across countries.
– Crowdsourced cost‑of‑living indices (e.g., Numbeo) and institutional PPP datasets can provide context — for example, Numbeo’s 2023 purchasing power index listed Luxembourg, Qatar, and UAE among the highest (Numbeo, 2023). (Investopedia also references U.S. purchasing power metrics.)
The bottom line
Relative purchasing power parity provides a simple, intuitive link between inflation differentials and expected currency depreciation/appreciation. It is most reliable as a long‑run equilibrium anchor and a component of valuation and hedging decisions, but it must be applied with care: measurement issues, nontradables, policy interventions, and capital flows can all cause large deviations in the short and medium term. Use RPPP as one tool among many, and always pair it with scenario analysis and adjustments for real‑world market drivers.
Sources
– Investopedia, “Relative Purchasing Power Parity (RPPP),” Julie Bang.
– Numbeo, “Purchasing Power Index by Country 2023.”
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.