Advanced Financial Management · International Financial Management

Foreign Exchange Rate Parity Theories for CA Final AFM

Updated 5 October 2026 · Fact-checked

Parity theories link exchange rates to inflation and interest rates. Purchasing power parity forecasts the future spot rate from inflation differentials. Interest rate parity fixes the forward rate from interest differentials. The international Fisher effect forecasts spot from interest differentials. Multiply spot by (1 + home rate) ÷ (1 + foreign rate) for the period.

Understand Foreign Exchange Rate Parity Theories

An exchange rate is the price of one currency in terms of another. Parity theories say this price cannot drift freely. If it did, someone could make a risk-free profit by buying in one market and selling in another. Three theories describe how the rate is tied to inflation and interest rates.

Purchasing power parity (PPP) is about goods. In its absolute form, the same basket of goods should cost the same in both countries once converted at the exchange rate. In its relative form, which is what exams use, the currency of the country with higher inflation weakens by roughly the inflation gap. So if India's inflation is higher than US inflation, the rupee is expected to depreciate against the dollar. PPP gives you a forecast of the future spot rate.

Interest rate parity (IRP) is about money markets. It says the forward rate is set so that you earn the same return whether you invest at home, or convert to a foreign currency, invest there, and cover the proceeds with a forward contract. The currency with the higher interest rate trades at a forward discount. The currency with the lower interest rate trades at a forward premium. IRP gives you the forward rate, not a forecast. If the quoted forward differs from the IRP rate, a covered arbitrage profit exists.

International Fisher effect (IFE) builds on the Fisher equation, which splits a nominal interest rate into a real rate and expected inflation. If real rates are the same across countries, the nominal rate gap equals the inflation gap. So the interest rate gap also predicts the change in the spot rate. IFE gives you a forecast of the future spot rate using interest rates instead of inflation.

The three tie together. A higher inflation rate goes with a higher nominal interest rate, a forward discount and an expected fall in the currency. In exams, the real skill is picking the right theory from the data given, then using the right ratio direction.

Key rules to remember

Relative PPP (forecast of spot rate): S₁ = S₀ × (1 + Ih) ÷ (1 + If); S is in units of home currency per one unit of foreign currency (for example ₹ per $). Ih and If are inflation rates for the same period. Home inflation goes on top.
Absolute PPP: S = Ph ÷ Pf; Price of the same basket at home divided by its price abroad. Holds only if there are no transport costs, barriers or taxes.
Interest rate parity (forward rate): F = S₀ × (1 + ih × n) ÷ (1 + if × n); ih and if are annual rates, n is the period in years (for example 0.5 for six months). Use compounding instead if the question says so. Same quote direction as S₀.
Forward premium or discount (annualised): (F − S₀) ÷ S₀ × (12 ÷ months); A positive result means the foreign currency is at a forward premium. A negative result means a discount.
Fisher equation: (1 + i) = (1 + r) × (1 + π); i is the nominal rate, r is the real rate and π is expected inflation. The shortcut i ≈ r + π is only an approximation.
International Fisher effect (forecast of spot rate): S₁ = S₀ × (1 + ih) ÷ (1 + if); Uses nominal interest rates for the same period. Assumes equal real rates in both countries.

How to solve Foreign Exchange Rate Parity Theories questions

Use this method for any parity question. It stops you from using the wrong theory or flipping the ratio.

1Read what is asked: a forward rate, a future spot rate, an arbitrage profit, or a premium or discount.
2Match the data to the theory. Inflation rates point to PPP. Interest rates with a forward rate point to IRP. Interest rates with a request for expected spot point to the international Fisher effect.
3Write the quote as home currency per one unit of foreign currency, for example ₹ per $. If the quote is the other way, invert it first.
4Adjust the rates to the period asked. For a six-month forward on annual rates, use half of the annual rate unless the question says compounding.
5Put the home rate on top and the foreign rate below, then multiply by spot. Compute step by step and keep at least four decimals in the ratio.
6If a quoted forward is also given, compare it with your IRP forward. If they differ, set up covered arbitrage: borrow where it is cheap, invest where it is dear, and cover with the forward contract.
7Work out the arbitrage profit in the home currency by comparing the final inflow and the loan repayment, both at the end of the period.
8State the conclusion in words: which currency appreciates or depreciates, or whether an arbitrage gain exists.

Quickest way: One-ratio shortcut

When to use it: Use when the question gives a single period and asks for a forward rate or an expected spot rate, and you do not need to show the arbitrage working.

Compute the ratio (1 + home rate) ÷ (1 + foreign rate) for the period.
Multiply spot by this ratio. The same calculation serves PPP (inflation), IRP (interest) and IFE (interest).
Check the sign: if the home rate is higher, the answer must be above spot, meaning the home currency weakens.
Only if a market forward is quoted, compare it with your answer. Forward above the parity value means the home currency is cheap in the forward market. Borrow home currency, convert and invest abroad, and sell the foreign currency forward.

Common mistakes in Foreign Exchange Rate Parity Theories

Putting the foreign rate on top and the home rate below.
Students memorise the formula without fixing the quote direction.
Fix: Always write the quote as home currency per one unit of foreign currency first. Then home rate goes on top. Check the sign afterward: the higher-rate currency must weaken.
Using the full annual interest rate for a three-month or six-month forward.
Students rush and forget to scale the rate to the period.
Fix: Multiply the annual rate by n (months ÷ 12) before using it, unless the question specifically gives a compound rate for the period.
Using PPP to find the forward rate or IRP to forecast spot.
Both formulas look the same, so the purpose gets lost.
Fix: Remember: IRP gives the forward rate from interest rates. PPP gives expected spot from inflation. IFE gives expected spot from interest rates.
Using the approximation (difference in rates) when an exact answer is needed.
The shortcut is quick and often close.
Fix: Use the ratio form (1 + rate) ÷ (1 + rate) in numerical answers. Use the approximation only if the question says so or only a rough estimate is wanted.
Stopping at the IRP forward rate and not showing the arbitrage steps.
Students treat parity as a formula only.
Fix: When a market forward is given, show the borrow, convert, invest and cover legs in order, then the profit at the end of the period.
Taking ₹ and $ rates in the wrong currency during arbitrage, such as borrowing dollars when the rupee is the cheap currency.
The direction of arbitrage is guessed rather than derived.
Fix: Compare the market forward with the IRP forward. If market forward is higher than IRP, the foreign currency is expensive forward, so sell it forward after investing in it. Check by computing the final amounts in both routes.

Worked examples

Example 1

A treasury manager notes the spot rate at ₹83.00/$. The six-month interest rate is 7% p.a. in India and 3% p.a. in the US. A bank quotes a six-month forward rate of ₹85.00/$. Find the IRP forward rate. If the quote differs, show the covered arbitrage profit on a loan of ₹83,00,000. Use simple interest.

Show the solution

Period n = 0.5 year. Rupee rate for the period = 7% × 0.5 = 3.5%. Dollar rate for the period = 3% × 0.5 = 1.5%.
IRP forward = 83.00 × 1.035 ÷ 1.015 = 83.00 × 1.019704 = ₹84.635 (rounded to 84.64).
The quoted forward of ₹85.00 is higher than ₹84.64. So the dollar is expensive in the forward market, and a gain can be made by investing in dollars and selling them forward.
Borrow ₹83,00,000 in India for six months. Repayment after six months = 83,00,000 × 1.035 = ₹85,90,500.
Convert at spot: ₹83,00,000 ÷ 83.00 = $1,00,000.
Invest $1,00,000 in the US for six months at 1.5%: $1,00,000 × 1.015 = $1,01,500.
Sell $1,01,500 forward at ₹85.00: 1,01,500 × 85 = ₹86,27,500.
Profit = 86,27,500 − 85,90,500 = ₹37,000.

Answer: The IRP six-month forward rate is about ₹84.64/$. Because the quoted ₹85.00 is higher, borrow rupees, invest in dollars and sell dollars forward. The riskless profit is ₹37,000 on ₹83,00,000.

Example 2

The spot rate is ₹82.00/$. Expected inflation for the next year is 6% in India and 2% in the US. One-year nominal interest rates are 10% in India and 4% in the US. (a) Forecast the spot rate after one year using PPP. (b) Forecast it using the international Fisher effect. (c) State what the results tell you about the rupee.

Show the solution

(a) PPP: S₁ = 82.00 × 1.06 ÷ 1.02. The ratio 1.06 ÷ 1.02 = 1.039216.
S₁ = 82.00 × 1.039216 = ₹85.2157, which is about ₹85.22/$.
(b) IFE: S₁ = 82.00 × 1.10 ÷ 1.04. The ratio 1.10 ÷ 1.04 = 1.057692.
S₁ = 82.00 × 1.057692 = ₹86.7308, which is about ₹86.73/$.
(c) Both forecasts are above ₹82.00, so the rupee is expected to depreciate. PPP implies a fall of about 3.92% in the rupee's value (1.039216 − 1). IFE implies about 5.77% (1.057692 − 1).
The two answers differ because the interest rate gap (10% vs 4%) is larger than the inflation gap (6% vs 2%), so real rates are not equal in the two countries. The IFE assumption does not hold exactly here.

Answer: PPP forecast: about ₹85.22/$. IFE forecast: about ₹86.73/$. In both cases the rupee is expected to weaken because India has higher inflation and higher interest rates.

Exam tips

Read the data first and name the theory: inflation data means PPP, interest data with a forward means IRP, interest data with a spot forecast means IFE. Write this in one line, as the examiner looks for it.
Write the quote direction at the start of your answer (for example ₹ per $) and use it throughout. Most lost marks in this topic come from a flipped ratio.
If a market forward is given, always compare it with the IRP value. A numerical question that gives both nearly always expects an arbitrage profit.
Show the period conversion of rates separately. Marks are often given for correctly adjusting an annual rate to months.
In theory answers, a short comparison of PPP and IRP works well: PPP links spot to inflation and forecasts the future, IRP links forward to interest and is enforced by arbitrage.

Practice questions from International Financial Management

Foreign Exchange Rate Parity Theories in other exams

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

Foreign Exchange Rate Parity Theories: frequently asked questions

What is the difference between PPP and IRP?

PPP links the exchange rate to inflation differentials and is used to forecast the future spot rate. IRP links the forward rate to interest rate differentials and is enforced by covered arbitrage. PPP is an expectation. IRP is a no-arbitrage condition.

How do I forecast an exchange rate using inflation differentials?

Multiply the current spot rate by (1 + home inflation) ÷ (1 + foreign inflation) for the period. With the quote in home currency per foreign unit, higher home inflation gives a higher future rate, meaning the home currency depreciates.

What is the international Fisher effect?

It says the expected change in the spot rate equals the nominal interest rate differential, because real rates are assumed equal across countries. The currency with the higher nominal rate is expected to depreciate. The forecast uses S₁ = S₀ × (1 + ih) ÷ (1 + if).

Which currency trades at a forward discount under IRP?

The currency with the higher interest rate trades at a forward discount. The currency with the lower interest rate trades at a forward premium. This offsets the extra interest earned, so investors gain nothing from moving money across borders when covered.

Should I use simple or compound interest in IRP problems?

Follow the question. For periods up to one year, ICAI-style questions commonly use simple interest scaled to the period, for example 6/12 of the annual rate. If the question gives compound rates or multi-year periods, use (1 + rate) raised to the number of years.