CFA Level IEconomicsHard
The current spot exchange rate is USD/GBP = 1.3000 (1 GBP = 1.30 USD). Expected inflation over the next year is 2% in the United States and 5% in the United Kingdom. Using relative purchasing power parity, what is the expected spot exchange rate in one year?
- AUSD/GBP = 1.3000
- BUSD/GBP = 1.3390
- CUSD/GBP = 1.2629
- DUSD/GBP = 1.2350
Show answer & explanationAnswer & explanation
Correct answer: C. USD/GBP = 1.2629
Relative PPP states that the currency of the higher-inflation country (UK) should depreciate against the lower-inflation country's currency (US) by approximately the inflation differential. The expected future spot rate is S1 = S0 × (1+π_USD)/(1+π_GBP) = 1.3000 × (1.02/1.05) = 1.3000 × 0.97143 = 1.2629. This reflects the GBP depreciating (fewer USD per GBP) due to its higher inflation rate.
Why the other options are wrong
- A. Incorrect—this assumes no change, ignoring the inflation differential.
- B. Incorrect—this incorrectly appreciates GBP by applying the ratio inverted.
- D. Incorrect—this overstates the depreciation beyond what PPP implies.
Relative Purchasing Power Parity (PPP)
Relative PPP predicts that the exchange rate will adjust so that the currency of the higher-inflation country depreciates by approximately the inflation rate differential relative to the lower-inflation country.
- S1 = S0 × (1+π_price currency)/(1+π_base currency)
- High-inflation currency depreciates
- Long-run FX forecasting tool, imperfect in short run
Memory trick: High inflation, low currency value — PPP evens out purchasing power.