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Strategic Financial Management · Foreign Exchange Market

Interest Rate Parity and Purchasing Power Parity for SFM

Updated 11 October 2026 · Fact-checked

Interest rate parity (IRP) links the forward rate to the interest rate gap between two currencies. Purchasing power parity (PPP) links the expected spot rate to the inflation gap. To solve a question, put the home currency in the numerator, multiply spot by the ratio of (1 + rate) or (1 + inflation), and compare with the actual rate.

Understand Interest Rate Parity and Purchasing Power Parity

An exchange rate is the price of one currency in another. Two ideas explain how that price should move. One uses interest rates and gives the forward rate. The other uses inflation and gives the expected future spot rate.

Interest rate parity (IRP) says you should earn the same return whether you invest at home or invest abroad and cover the exchange risk with a forward contract. If the forward rate does not give this result, a risk-free profit exists. Traders take it by covered interest arbitrage, and their trades push the forward rate back to its parity level.

Purchasing power parity (PPP) says the same basket of goods should cost the same in both countries once converted at the exchange rate. In its relative form, the currency of the country with higher inflation is expected to weaken by about the inflation gap. PPP is a forecast of the spot rate, not a risk-free arbitrage condition.

The International Fisher Effect says the expected change in spot rate matches the nominal interest rate gap. The Fisher Effect says nominal rate is about real rate plus expected inflation. Put the two together and you get the chain: inflation gap, interest rate gap, forward premium or discount, expected spot change.

The key difference: IRP uses interest rates and the forward rate, and it holds closely because arbitrage enforces it. PPP uses inflation and the future spot rate, and it holds only loosely, mostly over the long run.

Key rules to remember

Interest rate parity (forward rate)
F ÷ S = (1 + i_quoted currency) ÷ (1 + i_base currency)
For a quote such as ₹ per US$, F = S × (1 + i_₹) ÷ (1 + i_$). Adjust the rates to the forward period, for example 6-month rate = annual rate × 6/12 when simple interest is used.
Forward premium or discount (annualised)
(F − S) ÷ S × 12 ÷ n × 100
n is the forward period in months. A positive result is a premium on the base currency; a negative result is a discount.
Relative PPP (expected spot rate)
E(S1) = S0 × (1 + inflation_quoted currency) ÷ (1 + inflation_base currency)
Use inflation for the same period as the forecast. For a quote such as ₹ per US$, the quoted currency is the rupee.
International Fisher Effect
E(S1) ÷ S0 = (1 + i_quoted currency) ÷ (1 + i_base currency)
Uses nominal interest rates to forecast the future spot rate. It is the same form as IRP but gives an expected spot, not a forward.
Fisher Effect
(1 + nominal rate) = (1 + real rate) × (1 + expected inflation)
Approximation: nominal rate ≈ real rate + inflation.
Covered arbitrage rule
If actual F > parity F, the base currency is expensive forward: borrow the quoted currency, buy the base currency at spot, invest it in the base currency and sell it forward. If actual F < parity F, the base currency is cheap forward: borrow the base currency, convert it to the quoted currency at spot, invest there and buy the base currency forward.
Check by comparing, in the quoted currency at the end of the period, the amount the invest-and-cover route gives with the amount you owe on the loan. The difference is the arbitrage profit.

How to solve Interest Rate Parity and Purchasing Power Parity questions

Use this method for any parity question, whether it asks for a forward rate, a spot forecast or an arbitrage profit.

  1. 1Identify the quote. Mark the base currency (one unit) and the quoted currency (the price). For ₹/US$, US$ is base and ₹ is quoted.
  2. 2Note which data you are given: interest rates (use IRP or IFE) or inflation (use PPP). Do not mix them.
  3. 3Convert annual rates to the period asked. Check whether the question gives simple annual rates, and use the period fraction such as 3/12 or 6/12.
  4. 4Write the formula with the quoted currency's factor on top and the base currency's factor below. Then compute the parity or expected rate.
  5. 5Compare with the actual market forward rate if one is given. If it differs from parity, an arbitrage exists.
  6. 6For arbitrage, borrow where it is cheaper after cover, convert at spot, invest, sell the proceeds forward, then compare the repayment due with the proceeds. The difference is the profit.
  7. 7State the profit in the currency asked and name the direction of the trade in one line.
  8. 8Check that the answer is sensible: the higher-interest or higher-inflation currency should show a forward discount or a weaker expected spot.

Quickest way: Parity factor shortcut

When to use it: Use it when the question asks only for a forward rate, an expected spot rate or whether a given forward rate is fair, and you have little time.

  1. Write the factor: (1 + quoted currency rate for the period) ÷ (1 + base currency rate for the period).
  2. Multiply spot by this factor. The result is the parity forward rate (IRP) or expected spot (PPP or IFE).
  3. Quick sense check: if the quoted currency has the higher rate, the answer must be above spot.
  4. For arbitrage, compare the market forward with the parity forward. State the direction and compute profit on the given amount only if asked.
  5. Use the exact formula, not the approximation, unless the question allows it.

Common mistakes in Interest Rate Parity and Purchasing Power Parity

  • Putting the rates in the wrong way up in the formula.

    Students memorise the formula without noting which currency is base and which is quoted.

    Fix: Always write the quote first. The quoted currency's rate goes on top. For ₹/US$ the rupee factor is the numerator.

  • Using the full annual rate for a 3-month or 6-month forward.

    Students forget to scale the rate to the period.

    Fix: Multiply the annual rate by n/12 before adding 1. Do this as the first calculation step.

  • Using interest rates in a PPP question or inflation rates in an IRP question.

    The two formulas look alike, so students treat them as the same.

    Fix: Ask what is given. Inflation gives PPP and expected spot. Interest rates give IRP and forward rate.

  • Calling PPP a risk-free arbitrage and claiming a certain profit from it.

    Students carry over the idea from covered interest arbitrage.

    Fix: Say that PPP is a forecasting theory. Only IRP deviations give a covered arbitrage profit.

  • Showing arbitrage profit without a comparison, or in the wrong currency.

    Students stop once they see the forward rate differs from parity.

    Fix: Lay out each step with amounts: borrow, convert, invest, sell forward, repay. Then show the net gain in the currency the question asks for.

  • Taking the forward premium or discount sign the wrong way.

    The sign depends on which currency is the base.

    Fix: If F is above S, the base currency is at a premium. If F is below S, it is at a discount.

Worked examples

Example 1

The spot rate is ₹83.00 per US$. The 6-month interest rate is 4% per annum in the US and 8% per annum in India (simple interest, annual rates). (a) Find the 6-month forward rate under interest rate parity. (b) If the market quotes a 6-month forward at ₹84.50, say which side gains from arbitrage and find the gain per US$ 1,00,000 borrowed.

Show the solution
  1. Convert the annual rates to 6 months. India: 8% × 6/12 = 4%. US: 4% × 6/12 = 2%.
  2. IRP forward = 83.00 × 1.04 ÷ 1.02 = 83.00 × 1.019608 = ₹84.6275 per US$ (rounded to 4 decimals).
  3. The market forward ₹84.50 is below the parity forward ₹84.6275, so the US$ is cheap forward. Borrow US$, convert to ₹ at spot, invest in ₹ and buy US$ forward at ₹84.50 to repay the loan.
  4. Borrow US$ 1,00,000 and repay in 6 months: 1,00,000 × 1.02 = US$ 1,02,000.
  5. Convert at spot: 1,00,000 × 83 = ₹83,00,000. Invest in India at 4% for 6 months: ₹83,00,000 × 1.04 = ₹86,32,000.
  6. Buy US$ 1,02,000 forward at ₹84.50 = ₹86,19,000.
  7. Net gain = ₹86,32,000 − ₹86,19,000 = ₹13,000.

Answer: (a) Parity 6-month forward = ₹84.6275 per US$. (b) Market forward is too low, so borrow US$, convert at spot, invest in rupees and buy US$ forward. Gain = ₹13,000 on US$ 1,00,000 borrowed.

Example 2

The spot rate is ₹80 per euro. Expected inflation over the next year is 6% in India and 2% in the euro area. Using relative PPP, forecast the spot rate after one year and state the expected change in the rupee.

Show the solution
  1. Rupee is the quoted currency, so its inflation goes on top.
  2. E(S1) = 80 × (1.06 ÷ 1.02).
  3. 1.06 ÷ 1.02 = 1.039216.
  4. E(S1) = 80 × 1.039216 = ₹83.14 per euro (rounded).
  5. The euro's price in rupees rises from ₹80 to about ₹83.14, so the euro is expected to appreciate by about 3.92% in rupee terms (1.039216 − 1).
  6. The rupee's value in euro terms falls by 1 − 1/1.039216 ≈ 3.77%. The 3.92% rise in the euro's rupee price and the 3.77% fall in the rupee's euro value are two views of the same change.
  7. The rupee therefore depreciates against the euro, because India has higher inflation.

Answer: Expected spot after one year ≈ ₹83.14 per euro. The euro is expected to appreciate by about 3.92% in rupee terms, and the rupee's value in euro terms is expected to fall by about 3.77%. These are two views of the same change.

Exam tips

  • Write the quote, base and quoted currency in the first line of your answer. Examiners award marks for showing direction clearly.
  • In arbitrage numericals, set out each step with amounts. Marks are given for the process even if the final figure has a small error.
  • Read the question for simple or compound rates and for the period. Scale rates first.
  • When the question asks to compare PPP with IRP, state three points: input used (inflation or interest), output (expected spot or forward), and whether arbitrage enforces it.
  • In MCQs, check the direction of the answer first. The currency with the higher interest rate or inflation should be at a forward discount or weaker expected spot. This removes two options quickly.

Practice questions from Foreign Exchange Market

Interest Rate Parity and Purchasing Power Parity in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Interest Rate Parity and Purchasing Power Parity: frequently asked questions

What is the difference between PPP and IRP?

IRP links the forward rate to the interest rate gap. Arbitrage enforces it, so it holds closely. PPP links the expected spot rate to the inflation gap. It is a forecasting theory and holds only loosely, mostly over long periods.

How do I know if a covered interest arbitrage is possible?

Compute the parity forward rate from spot and the interest rates. If the market forward rate is different, an arbitrage opportunity exists. Compare the two routes in rupees at the end of the period to confirm.

Do I use the full annual rate in the IRP formula?

Only when the forward period is one year. For a 3-month or 6-month forward, scale the annual rate by the period fraction first, using the method the question states.

What is the International Fisher Effect?

It says the expected change in the spot rate equals the nominal interest rate gap between two countries. The currency with the higher nominal rate is expected to weaken. It has the same form as IRP, but it forecasts the future spot rate.