FINM8007 Chap.5 International Parity Conditions
International Parity Conditions
Arbitrage arguments that tie four markets together
The parity conditions link spot and forward exchange rates, interest rates and inflation.
This chapter builds them in turn: the law of one price and the Big Mac index, absolute and relative purchasing power parity and why tests rarely confirm them, forward rates and premiums, and interest rate parity.
Using and breaking parity
It works through covered interest arbitrage step by step, explains why parity can fail with spreads, controls and taxes, contrasts the uncovered carry trade and its risks, and adds the Fisher effect and the forward rate as an unbiased predictor, showing how all the conditions fit together.
Where marks are won and lost
The parity solutions use the exact formulas, not only the approximations, and they end every forecast by saying which currency appreciates.
In the relative PPP tutorial, the expected rate is the spot rate times one plus the exact inflation differential over one plus the foreign rate.
In the Week 7 interest rate parity practice, the question asks for four things in order: the test against parity, the direction of the trade, every cash flow at time zero and at maturity, and an explanation of how the arbitrage restores parity.
How it connects
Parity is the hinge of the course.
Chapter 6 tests the forward rate and fundamentals as forecasts and treats covered arbitrage alongside locational and triangular arbitrage, Chapter 7 uses parity to judge competitive exposure, and Chapter 8 shows that a forward hedge and a money market hedge cost the same exactly when interest rate parity holds.
What this chapter covers
- 01
Law of one price
- 02
Absolute and relative PPP
- 03
Forward premium and discount
- 04
Interest rate parity
- 05
Covered interest arbitrage
- 06
Why parity can fail
- 07
Carry trades
- 08
Fisher effect
- 09
Forward rate as predictor
Worked example · free
Test interest rate parity and lock in a covered profit
- 1Parity forward: 1.0800 × (1 + 0.05 × 180/360) ÷ (1 + 0.03 × 180/360) = 1.0906.
- 1The market forward of 1.0950 is higher, so the euro is dear forward: buy euros spot and sell them forward.
- 1Borrow $1,000,000, buy €925,925.93, deposit it to receive €939,814.81 in 180 days.
- 1Sell €939,814.81 forward at 1.0950 for $1,029,097.22.
- 1Repay $1,025,000, leaving a riskless profit of $4,097.22.
Key terms
- Law of One Price
- The rule that an identical good sells for the same price in two competitive markets.
- Relative PPP
- The prediction that exchange rates change by roughly the inflation gap between two countries.
- Forward Premium
- The annualised percentage by which a currency’s forward rate exceeds its spot rate.
- Carry Trade
- Borrowing a low-interest currency to invest in a high-interest one without covering the rate.
- Fisher Effect
- The relation that nominal interest equals the real rate plus expected inflation.
- Unbiased Forward Predictor
- The view that today’s forward quote is, on average, where the spot rate will be on that date.
- Eurocurrency Deposit
- A deposit in a currency held at a bank outside that currency’s home country.
International Parity Conditions FAQ
Why does PPP hold better in high-inflation countries?
With high inflation, price gaps across borders open quickly and are large, so cross-border price arbitrage pays well and prices return to parity faster. Over short horizons in low-inflation economies, trade costs, non-tradable services and quality differences dominate.
Which currency sells forward at a discount?
The one with the higher interest rate. Interest rate parity says its forward discount offsets the extra interest, so an investor who covers the conversion earns the same in either currency.
Is a carry trade a form of arbitrage?
Not in the strict sense, because the conversion back is left open. The trade profits only if the high-yield currency does not fall by more than the interest gap, and leverage magnifies the loss when it does.
How do the parity conditions fit together?
Relative PPP links expected spot changes to inflation gaps, the Fisher effect links inflation gaps to interest gaps, interest rate parity links interest gaps to forward premiums, and an unbiased forward links the premium back to the expected spot change.
Should I use the exact or the approximate parity formula?
Use the exact form whenever the numbers are given, as the tutorial solutions do, and quote the approximation only to explain the intuition. With low inflation or interest rates the two barely differ, but with double-digit rates the approximation can move your answer by a meaningful margin.
Exam move
Learn each condition as a sentence, a formula and a direction. Then run the covered arbitrage routine on three invented quotes until the profit and the four restoring pressures come without notes. Close each session by writing the four restoring pressures of covered arbitrage from memory and checking them against your worked example.
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