Strategic Financial Management · Foreign Exchange Risk Management

Exchange Rate Determination and Parity Theories for CMA Final

Updated 11 October 2026 · Fact-checked

Parity theories link exchange rates to inflation and interest rates. Purchasing power parity ties the expected spot rate to inflation differences. Interest rate parity ties the forward rate to interest rate differences. Write the rate as home currency per unit of foreign currency, apply the ratio of (1 + home rate) to (1 + foreign rate), and compare with the quoted rate.

Understand Exchange Rate Determination and Parity Theories

An exchange rate is the price of one currency in terms of another. Over time it moves because countries differ in inflation and in interest rates. Parity theories turn these differences into numbers you can use to forecast or to price a forward contract.

Purchasing power parity (PPP) says the same basket of goods should cost the same in two countries once converted at the exchange rate. If India's prices rise faster than US prices, the rupee should weaken by about the inflation gap. PPP is a forecasting tool for the expected spot rate. It works better over the long run than the short run.

Interest rate parity (IRP) is about the forward rate, not the future spot rate. A currency with the higher interest rate trades at a forward discount. If it did not, you could borrow in the low-rate currency, invest in the high-rate currency, cover with a forward contract and earn a risk-free profit. That trade is covered interest arbitrage. It pushes the forward rate back to the IRP value.

Fisher effect says the nominal interest rate equals the real rate plus expected inflation. The International Fisher Effect (IFE) extends this: the currency with the higher nominal interest rate is expected to depreciate by the interest differential. So the Fisher effect compares interest and inflation within one country. The IFE links interest rates to the expected change in spot rate across two countries.

Keep the four ideas apart. PPP uses inflation and gives an expected spot rate. IRP uses interest rates and gives a forward rate. IFE uses interest rates and gives an expected spot rate. Fisher links interest to inflation. Questions often combine them, so first decide what is asked: a forward rate, a future spot rate, or an arbitrage profit.

Key rules to remember

Purchasing power parity (relative form): S1 = S0 × (1 + Ih) ÷ (1 + If); S is home currency per unit of foreign currency. Ih is home inflation, If is foreign inflation, for the same period. S1 is the expected spot rate.
Interest rate parity: F = S0 × (1 + rh) ÷ (1 + rf); rh and rf are the home and foreign interest rates for the forward period. For a period shorter than a year, use rate × months ÷ 12 (simple interest) unless the question gives effective rates.
Forward premium or discount (annualised): (F − S0) ÷ S0 × 12 ÷ n × 100; n is the forward period in months. A positive result is a premium on the foreign currency, a negative result is a discount.
Fisher effect: (1 + nominal rate) = (1 + real rate) × (1 + expected inflation); Approximation: nominal rate ≈ real rate + inflation. Use the exact form when the question asks for precision.
International Fisher effect: S1 = S0 × (1 + rh) ÷ (1 + rf); Same algebra as IRP but the result is the expected future spot rate, not the forward rate. It assumes equal real rates across countries.
Covered interest arbitrage test: Compare quoted forward F with IRP forward; If quoted F is above the IRP forward: borrow home currency, buy foreign currency at spot, invest it abroad, and sell the foreign currency forward. If quoted F is below the IRP forward: borrow foreign currency, convert it to home currency at spot, invest at home, and buy the foreign currency forward.

How to solve Exchange Rate Determination and Parity Theories questions

Use this method for PPP, IRP, Fisher and arbitrage questions.

1Fix the quote. Write every rate as home currency per one unit of foreign currency (for example ₹ per US$). Convert if the question gives the reverse.
2Decide what is asked: expected spot (PPP or IFE), forward rate (IRP), or an arbitrage gain.
3Note the period. Match inflation or interest rates to that period. Annual rates for a 3-month forward need adjusting to 3 ÷ 12.
4Apply (1 + home rate) ÷ (1 + foreign rate) to the spot rate, with the rate quoted as home per foreign unit. The higher-rate currency will be at a forward discount or will depreciate.
5Compute the theoretical rate and compare it with any quoted rate or market rate.
6For arbitrage, borrow where the money is cheap, convert at spot, invest, cover forward, and compute the end-period profit in the same currency.
7State the result with its meaning: premium or discount, profit or no profit, and a clear conclusion.

Quickest way: Ratio shortcut for parity questions

When to use it: Use when the question gives a spot rate, two rates for the same period and asks for a forward or expected spot rate.

Write the factor (1 + home rate) ÷ (1 + foreign rate) for the period.
Multiply spot by this factor. The answer is the forward (interest rates) or expected spot (inflation).
A factor above 1 means the home rate is higher, so the foreign currency trades at a forward premium and the home currency at a discount. A factor below 1 means the reverse.
For arbitrage, compare the quoted forward with your answer. The gap shows the direction. Then compute profit on a round amount like 10,00,000 units.

Common mistakes in Exchange Rate Determination and Parity Theories

Putting the foreign rate on top of the ratio.
Students memorise the formula without checking the quote direction.
Fix: With the rate as home per foreign, home rate goes on top. Test: the higher-rate currency must show a discount.
Using annual rates for a 3 or 6-month forward without adjusting.
The period is in the question text but not in the formula students recall.
Fix: Scale each rate by months ÷ 12 before applying the ratio, unless effective period rates are given.
Mixing up IRP and IFE.
Both use the same interest ratio.
Fix: IRP gives today's forward rate and is enforced by arbitrage. IFE gives an expected future spot rate and is only a forecast.
Using the wrong bid or offer rate in arbitrage.
Students use one mid rate for all legs.
Fix: Use the rate the bank actually offers you for each transaction. If only one rate is given, state that assumption.
Stopping at the arbitrage direction without a profit figure.
Students think identifying the trade is enough.
Fix: Run the full cycle to the end date and show the net gain in rupees.
Treating PPP as always exact.
Textbooks present it as an equation.
Fix: Write that PPP is a long-run forecast and that actual rates can differ. Add a one-line comment in written answers.

Worked examples

Example 1

The spot rate is ₹83.00 per US$. Expected inflation for the next year is 6% in India and 2% in the USA. Using purchasing power parity, find the expected spot rate after one year and the expected percentage change in the rupee value of the dollar.

Show the solution

Quote is ₹ per US$, so home is India.
S1 = 83.00 × (1.06 ÷ 1.02).
1.06 ÷ 1.02 = 1.039216.
S1 = 83.00 × 1.039216 = ₹86.2549, about ₹86.25.
Change = (86.2549 − 83.00) ÷ 83.00 = 3.92%.

Answer: Expected spot rate is about ₹86.25 per US$. The dollar is expected to appreciate by about 3.92% against the rupee, so the rupee depreciates.

Example 2

The spot rate is ₹80.00 per US$. Annual interest rates are 8% in India and 4% in the USA. The six-month forward rate quoted is ₹83.00 per US$. Is there a covered arbitrage opportunity? Show the gain for a US$10,00,000 transaction.

Show the solution

Six-month rates: India 8% × 6 ÷ 12 = 4%; USA 4% × 6 ÷ 12 = 2%.
IRP forward = 80.00 × 1.04 ÷ 1.02 = ₹81.5686.
The quoted forward ₹83.00 is above the IRP forward ₹81.57, so the dollar is overpriced forward. Borrow rupees, buy dollars at spot, invest them and sell them forward.
Borrow ₹8,00,00,000 at 4% for six months. Amount to repay: ₹8,00,00,000 × 1.04 = ₹8,32,00,000.
Buy US$10,00,000 at spot (₹8,00,00,000 ÷ 80.00) and invest in the USA at 2% for six months: US$10,00,000 × 1.02 = US$10,20,000.
Sell US$10,20,000 forward at ₹83.00: 10,20,000 × 83.00 = ₹8,46,60,000.
Gain = ₹8,46,60,000 − ₹8,32,00,000 = ₹14,60,000.

Answer: Yes. Because the quoted forward (₹83.00) exceeds the IRP forward (₹81.57), borrow rupees, buy dollars at spot, invest them in the USA and sell forward. The risk-free gain is ₹14,60,000 on a ₹8,00,00,000 start (US$10,00,000 at spot).

Exam tips

Write the quote direction and the period at the top of your working. Many marks go for this alone.
In MCQs, check whether the question asks for a forward rate (IRP) or an expected spot rate (PPP or IFE).
In arbitrage answers, show each leg in order: borrow, convert, invest, cover, repay, profit.
Add one line of interpretation, such as which currency is at a discount and why. Case-style answers reward this.
If the question gives bid and offer rates, use them leg by leg and say so.

Practice questions from Foreign Exchange Risk Management

Exchange Rate Determination and 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.

Exchange Rate Determination and Parity Theories: frequently asked questions

What is the difference between the Fisher effect and the international Fisher effect?

The Fisher effect links a nominal interest rate to the real rate and expected inflation within one country. The international Fisher effect says the interest rate differential between two countries is approximately equal to the expected change in the spot rate. Exactly, the expected spot rate is S0 × (1 + rh) ÷ (1 + rf). It assumes real rates are the same across the two countries.

How do I decide between PPP and IRP in a numerical?

If the data are inflation rates, use PPP for the expected spot rate. If the data are interest rates and the question asks for the forward rate, use IRP. If it asks for the expected spot from interest rates, that is the international Fisher effect.

How do I solve covered interest arbitrage?

Calculate the IRP forward rate and compare it with the quoted forward. Then run the borrow, convert, invest and cover cycle in the profitable direction, and show the net gain in rupees at the end date.

Does the higher interest rate currency trade at a premium or discount?

Under interest rate parity, the currency with the higher interest rate trades at a forward discount. The gain from the higher interest is offset by the lower forward value of the currency.