Exchange Rates and Interest Parity Concept Card Template

Exchange Rates and Interest Parity Concept Card: [Your course, currency pair or exposure]

A concept card for exchange rates as an MBA core course and a treasury team use them: spot and forward quotes, covered interest parity (CIP), uncovered interest parity (UIP), purchasing power parity (PPP, absolute and relative), the three kinds of currency exposure (transaction, translation and economic) and hedging with forwards and options. It is for MBA students in a global economy or corporate finance course and for managers who buy, sell or invest across currencies. Source basis: Keynes (1923) on forward exchange, Cassel (1918) on purchasing power parity, Fama (1984) on forward and spot rates, Garman and Kohlhagen (1983) on currency option values, Adler and Dumas (1984) on exposure, and Du, Tepper and Verdelhan (2018) on CIP deviations, all written up in original words. Every rate, price and company number is fictional (Northfield Outdoor Co., Corvane Robotics, the Republic of Avelin); nothing here is a market quote, a forecast or financial advice. Replace every [bracketed] value and every row marked Example.

Document control

When to use it

Use this card whenever a decision involves a cash flow, asset or competitor in another currency:

• A supplier invoice or customer receivable in foreign currency (transaction exposure): Northfield Outdoor Co. owes a European supplier EUR 4.0 million in 180 days.
• Consolidating a foreign subsidiary (translation exposure): Corvane Robotics owns a euro area subsidiary whose net assets are translated into US dollars every quarter.
• Long-run competitiveness (economic exposure): a stronger home currency makes exports dearer and imports cheaper for years, whatever the firm hedges this quarter.
• Pricing a cross-border deal or valuing a foreign project: forward rates convert foreign cash flows consistently with interest rates (mba/mba-dcf-valuation-card).
• Country analysis: inflation and interest differentials explain much of the long-run path of a currency (mba/mba-macro-indicators-card).

The idea in plain language

Quotes. An exchange rate is the price of one currency (the base) in units of another (the quote currency). EUR/USD 1.0850 means 1 euro costs 1.0850 US dollars. If the number rises, the euro has strengthened. A spot trade settles in two business days for most pairs; a forward fixes today the rate for a later date. The difference between forward and spot, quoted in pips (0.0001), is the forward points.

Covered interest parity. If you can borrow dollars, convert them to euros, deposit the euros and sell the euro proceeds forward, all today, the result must equal simply depositing dollars. Otherwise there is a riskless profit. So the forward rate is fixed by the spot rate and the two interest rates: the currency with the higher interest rate trades at a forward discount. The forward is not a forecast: it is the price that removes the riskless profit. Keynes (1923) set out this reasoning; since the 2008 crisis small, persistent deviations (the cross-currency basis) have been documented for major currencies (Du, Tepper and Verdelhan 2018), so a corporate treasurer will see quotes a few pips away from the textbook formula.

Uncovered interest parity. If investors were risk neutral, the expected future spot rate would equal the forward rate, so high-interest currencies would be expected to depreciate by the interest differential. In the data, the opposite has often happened over short horizons (Fama 1984): high-interest currencies have tended to hold up or appreciate, which is the "forward premium puzzle" and the basis of carry trades. UIP is a neutral planning assumption, not a forecast.

Purchasing power parity. Absolute PPP says a basket of goods should cost the same in two countries once converted at the exchange rate (Cassel 1918). Relative PPP says the exchange rate changes over time to offset inflation differences: the currency with higher inflation depreciates. The evidence supports relative PPP over long horizons, with deviations that take years to halve (Rogoff 1996). The Economist's Big Mac index, published since 1986, is a well-known light-hearted teaching illustration of absolute PPP: compare the local price of one standardised burger. This card uses invented prices instead of its data.

Exposure and hedging. A hedge does not make a firm richer on average; it changes which outcomes are possible. A forward locks a rate: no loss and no gain from currency moves. An option sets a worst case for a premium paid today and keeps the upside. The right choice depends on how certain the cash flow is and how much a bad outcome would hurt.

Formulas and notation

Quote convention in every formula: $S$ and $F$ are domestic (quote) currency per one unit of foreign (base) currency. For EUR/USD, domestic = USD, foreign = EUR.

Covered interest parity with money market (simple) rates and day-count fractions:

Uncovered interest parity (expectations under risk neutrality):

Purchasing power parity:

Garman and Kohlhagen (1983) call on the foreign currency (written with the forward and discount factors):

Hedged outcomes for a foreign currency payable of $Q$ units at date $T$:

Translation (current rate method): cumulative translation adjustment for the period $\Delta CTA = NA_f \times (S_{\text{close}} - S_{\text{open}})$ for constant foreign net assets.

Assumptions and limits

1. CIP assumes free capital movement, no default risk and equal access to funding. Capital controls, credit risk, bank balance-sheet costs and quarter-end effects create a basis. A non-deliverable forward (NDF) market prices restricted currencies differently.
2. Day counts matter. USD and EUR money markets use ACT/360, GBP uses ACT/365. Mixing them moves a 270-day forward by several pips.
3. UIP assumes risk neutrality and rational expectations. Risk premiums and slow-moving capital break it in the short run.
4. PPP assumes identical tradable goods and no trade costs. Non-traded services (rent, local labour), taxes, tariffs and quality differences keep price levels apart. Richer countries tend to have higher price levels.
5. Option pricing assumes lognormal rates with constant volatility. Real FX markets show volatility smiles; banks quote premiums from market volatility surfaces.
6. A hedge needs a forecastable exposure. Hedging a cash flow that does not happen creates a new open position.
7. Accounting is separate from economics. Translation gains and losses go to other comprehensive income under the current rate method (IAS 21; ASC 830 for US GAAP reporters) and do not change cash; hedge accounting under IFRS 9 or ASC 815 needs documentation at inception (see finance/hedge-designation-documentation).

Worked example A (fully solved): Northfield's EUR payable

Setting (fictional). Northfield Outdoor Co. reports in USD. It ordered tents from a European supplier and owes EUR 4,000,000 in 180 days. Market data today (fictional): spot EUR/USD 1.0850; 180-day USD rate 4.20%; 180-day EUR rate 2.40%; both ACT/360. EUR/USD volatility 8% a year.

Step 1: the CIP forward.

Excel: =1.0850*(1+4.2%*180/360)/(1+2.4%*180/360) = 1.094649, rounded to 1.0946. Forward points = +96.5 pips (=(F-S)*10000). The euro trades at a forward premium of 0.889% for the period (1.779% annualised on ACT/360) because euro interest rates are lower than dollar rates.

Step 2: is a quote of 1.0990 an arbitrage? Suppose a bank quoted 1.0990 for 180 days (above parity). Sell euros forward at the high price and buy them spot with borrowed dollars:

In practice the gap would be closed by banks within seconds, and transaction costs, credit lines and balance-sheet charges would absorb small differences. The point for a manager: a forward quote far from parity signals a pricing error or a large spread.

Step 3: three choices for the payable.

• Unhedged: pay $4{,}000{,}000 \times S_T$, unknown today.
• Forward: lock $4{,}000{,}000 \times 1.0946 =$ USD 4,378,400 whatever happens. Excel =4000000*1.0946.
• EUR call option, strike K = 1.1000, 180 days (T = 0.5 years). Garman and Kohlhagen with the CIP forward: $d_1 = -0.0579$, $d_2 = -0.1145$, $N(d_1) = 0.4769$, $N(d_2) = 0.4544$, premium USD 0.0217 per EUR (0.021721 before rounding to a four-decimal quote), or USD 86,800 paid today; carried to the payment date at the USD rate, USD 88,622.80. Excel: =(1/(1+4.2%*0.5))*(F*NORM.S.DIST(d1,TRUE)-1.1*NORM.S.DIST(d2,TRUE)) with d1 = (LN(F/1.1)+0.5*0.08^2*0.5)/(0.08*SQRT(0.5)).

USD cost at the payment date for six possible spot rates:

Reading the result. The forward removes all uncertainty at USD 4.378m. The call caps the cost at USD 4.489m (the strike plus the carried premium) and lets Northfield benefit if the euro falls; it beats the forward when the spot at payment is below 1.0724 (=1.0946-88622.8/4000000) and costs at most USD 110,223 more than the forward when the euro rises. A half hedge (50% forward, 50% open) would cost between USD 4,189,200 at 1.00 and USD 4,589,200 at 1.20. The choice is a policy decision about risk tolerance, set out in Northfield's hedging policy (finance/fx-interest-rate-hedging-policy), not a view on where the euro is going.

Step 4: translation exposure (Corvane Robotics). Corvane's euro area subsidiary has net assets of EUR 25m. Over the quarter EUR/USD falls from 1.0850 to 1.0400. Under the current rate method the translated net assets change by $25{,}000{,}000 \times (1.0400 - 1.0850)$, a loss of USD 1,125,000, recorded in other comprehensive income (Excel =25000000*(1.04-1.085)). No cash moved; many firms do not hedge this, or hedge it only with foreign currency debt (a net investment hedge) when the board's policy says so.

Step 5: economic exposure. Northfield sells EUR 12m a year through its European e-commerce site at euro prices, with USD 9m of US-based costs. Operating profit in USD at three exchange rates (prices and volumes held constant):

A 10% fall in the euro cuts profit by almost a third. A one-year forward programme cannot protect this for long: economic exposure is managed with operations (sourcing in euros, pricing, where to produce). Adler and Dumas (1984) define exposure as the sensitivity of a firm's value to the exchange rate, which is why it reaches beyond contracts.

Step 6: PPP with invented burger prices. A standard burger costs USD 5.80 in a US city and AVL 410 in the Republic of Avelin; the market rate is AVL 82 per USD.

• Implied PPP rate: $410 / 5.80 = 70.69$ AVL per USD. Excel =410/5.8.
• At the market rate the Avelin burger costs $410/82 =$ USD 5.00.
• Valuation: $70.69 / 82 - 1 = -13.8\%$: on this measure the AVL is undervalued against the USD. Excel =(410/5.8)/82-1.
• Relative PPP: Avelin inflation 6.0%, US inflation 2.5%: expected rate in one year $82 \times 1.06/1.025 = 84.80$ AVL per USD, a 3.41% AVL depreciation (the approximation gives 3.5%). Excel =82*(1+6%)/(1+2.5%).

A single burger is a weak price index: local rent and wages are a large part of its cost, so poorer countries tend to look "undervalued" by construction.

Step 7: UIP as a planning rate. Under UIP the expected EUR/USD rate in 180 days equals the forward, 1.0946: the euro is expected to rise 0.889%, offsetting its lower interest rate. Northfield's budget may use the forward as the planning rate because it is the rate it could lock today, not because it predicts the future.

Worked example B (half solved): USD/CHF forward for a Swiss supplier

Setting (fictional). Corvane Robotics (USD reporting) must pay CHF 2,500,000 to a Swiss component maker in 90 days. Spot USD/CHF 0.8800 (CHF per USD). 90-day CHF rate 0.50%, USD rate 4.20%, both ACT/360.

1. In USD/CHF the base (foreign) currency is [ ] and the quote (domestic) currency is [ ].
2. $F = 0.8800 \times \dfrac{1 + 0.005 \times 90/360}{1 + 0.042 \times 90/360} =$ [ ]. Excel =0.88*(1+0.5%*90/360)/(1+4.2%*90/360).
3. Forward points = [ ] pips. Is the USD at a forward premium or discount against the CHF? [ ].
4. USD cost of the payable if Corvane buys CHF forward: $2{,}500{,}000 / F =$ [ ]. Excel =2500000/F.
5. Explain in one sentence why the higher-yielding currency trades at a forward discount: [ ].

Exercise C (unsolved): GBP receivable

Corvane will receive GBP 2,500,000 from a UK customer in 270 days. Spot GBP/USD 1.2700 (USD per GBP). 270-day USD rate 4.20% (ACT/360), GBP rate 3.90% (ACT/365). A GBP put option with strike 1.2500 costs USD 0.0180 per GBP, paid today.

1. Compute the CIP forward rate to four decimals.
2. Compute the USD proceeds under no hedge, a forward hedge and a put hedge (premium carried to the receipt date at the USD rate) if spot at T is 1.20, 1.27 and 1.34.
3. Which hedge would you recommend if the receivable is contractually certain, and which if the customer may cancel? Explain in three sentences.

How managers use it in practice

• Exposure register. Treasury lists each exposure with currency, amount, date and certainty, then applies the hedge ratios in the board-approved policy, often layered (for example, more of the next quarter hedged than of the fourth quarter out). See finance/fx-interest-rate-hedging-policy and finance/treasury-policy.
• Budget rates. The budget uses forward rates (or a policy rate) so that sales and procurement are judged on volumes and prices, not on currency luck.
• Pricing and contracts. Invoicing currency, price adjustment clauses and natural hedges (matching revenue and cost currencies) often do more than derivatives.
• Project valuation. Convert foreign cash flows at forward rates implied by interest differentials, or discount in foreign currency at a foreign rate and convert at spot; both give the same answer when CIP holds (mba/mba-dcf-valuation-card).
• Dealing discipline. Get two or three quotes, compare with the CIP forward and the mid-market rate, record the spread paid, and keep hedge documentation from day one if hedge accounting is wanted.

Connections to other cards

• mba/mba-macro-indicators-card: inflation, policy rates and the yield curve that drive interest differentials.
• mba/mba-options-real-options-card: the option logic behind the currency call and put.
• mba/mba-capm-wacc-card and mba/mba-dcf-valuation-card: currency consistency between cash flows and discount rates.
• mba/mba-global-immersion-plan and mba/mba-exchange-semester-plan: personal budgets in foreign currency.
• finance/fx-interest-rate-hedging-policy, finance/hedge-designation-documentation, finance/treasury-policy: the governance documents a company actually uses.

Common mistakes and misconceptions

1. Inverting the quote. EUR/USD 1.0850 is USD per EUR. Using it as EUR per USD gives a forward on the wrong side.
2. Reading the forward as a forecast. CIP makes the forward a price set by interest rates; it predicts the future spot poorly.
3. Expecting the higher-yield currency to strengthen in the forward. It trades at a forward discount.
4. Ignoring day counts. ACT/360 against ACT/365 matters for long tenors.
5. Treating UIP as an arbitrage. UIP is uncovered: it involves risk, and it fails often in the short run.
6. Using a burger index as a trading signal. It is a teaching illustration of absolute PPP; non-traded costs bias it.
7. Hedging uncertain cash flows with forwards. If the sale is lost, the forward becomes a speculative position.
8. Comparing a hedge with the realised spot after the fact. A hedge is judged by whether it met the policy objective, not by whether it "made money".
9. Forgetting the option premium or its timing. Compare all strategies at the same date, with the premium carried at the domestic rate.
10. Confusing translation with cash. Translation adjustments sit in other comprehensive income; they do not change cash unless the subsidiary is sold or funds are repatriated.

Self-test

1. EUR/USD moves from 1.0850 to 1.1000. Which currency strengthened?
2. State CIP in words and explain why the forward is not a forecast.
3. If the domestic interest rate is higher than the foreign rate, does the foreign currency trade at a forward premium or discount (domestic per foreign quote)?
4. What is the forward premium puzzle?
5. A basket costs 300 in currency A and 60 in currency B. The market rate is 4.5 A per B. Compute the PPP rate and say whether A is over- or undervalued.
6. Expected inflation is 8% at home and 3% abroad. By how much should the domestic currency depreciate under relative PPP (exact)?
7. Name the three kinds of currency exposure and one management tool for each.
8. Why might a firm prefer an option to a forward for a tender bid in foreign currency?
9. Where do translation gains and losses go under the current rate method?
10. A 90-day forward quote is 50 pips away from the CIP value computed from mid rates. Give two legitimate reasons.

My notes and next steps

Sources and further reading

Primary works:

• Keynes, J. M. (1923). A Tract on Monetary Reform. Macmillan.
• Cassel, G. (1918). Abnormal deviations in international exchanges. Economic Journal, 28(112), 413-415.
• Fama, E. F. (1984). Forward and spot exchange rates. Journal of Monetary Economics, 14(3), 319-338.
• Garman, M. B. and Kohlhagen, S. W. (1983). Foreign currency option values. Journal of International Money and Finance, 2(3), 231-237.
• Adler, M. and Dumas, B. (1984). Exposure to currency risk: definition and measurement. Financial Management, 13(2), 41-50.
• Rogoff, K. (1996). The purchasing power parity puzzle. Journal of Economic Literature, 34(2), 647-668.
• Du, W., Tepper, A. and Verdelhan, A. (2018). Deviations from covered interest rate parity. Journal of Finance, 73(3), 915-957.

Accounting standards (names only; check the current official text): IAS 21 The Effects of Changes in Foreign Exchange Rates; IFRS 9 Financial Instruments (hedge accounting); ASC 830 and ASC 815 for US GAAP reporters.

Teaching illustration: The Economist, Big Mac index (published since 1986), economist.com. No data reproduced here.

Textbooks (further reading): Krugman, Obstfeld and Melitz, International Economics: Theory and Policy; Berk and DeMarzo, Corporate Finance (international chapters); Hull, Options, Futures, and Other Derivatives. Open resource: OpenStax, Principles of Macroeconomics 3e (CC BY-NC-SA 4.0), chapters on exchange rates, openstax.org.

Answer key

Worked example B. (1) Base USD (foreign), quote CHF (domestic). (2) $F = 0.88 \times 1.00125 / 1.0105 = 0.871945$, so 0.8719. (3) Forward points = -80.6 pips: the USD trades at a forward discount against the CHF. (4) USD 2,867,301.30 (=2500000/0.8719). (5) Otherwise investors could borrow the low-yield currency, invest in the high-yield one and sell it forward for a riskless profit; the forward discount exactly offsets the interest advantage.

Exercise C. (1) $F = 1.2700 \times (1 + 0.042 \times 270/360) / (1 + 0.039 \times 270/365) = 1.273272$, so 1.2733. (2) Premium USD 45,000 today, USD 46,417.50 at T. Proceeds (USD):

(3) Certain receivable: a forward fixes USD 3,183,250 at no premium, the usual policy choice. Possible cancellation: a put sets a floor without creating an obligation to deliver GBP that might never arrive; the premium is the cost of that flexibility.

Self-test.

1. The euro (one euro buys more dollars).
2. Borrowing at home, converting, investing abroad and selling forward must earn the same as investing at home, so the forward is set by spot and the two interest rates; it removes arbitrage and carries no information beyond those rates.
3. Premium: $F > S$ when $i_d > i_f$.
4. Under UIP, high-interest currencies should depreciate by the interest differential; in the data they have often not, or have appreciated (Fama 1984).
5. PPP rate = 300 / 60 = 5.0 A per B. Market 4.5 A per B buys fewer A per B than PPP implies, so A is overvalued by 5.0 / 4.5 - 1 = 11.1% (equivalently, B is undervalued).
6. 1.08 / 1.03 - 1 = 4.85%.
7. Transaction (forwards, options, invoicing currency), translation (net investment hedge, foreign currency debt, or accept), economic (sourcing, pricing, production location, diversification).
8. If the bid is lost, a forward leaves an open position; an option's loss is limited to the premium.
9. Other comprehensive income (cumulative translation adjustment in equity), recycled to profit or loss on disposal.
10. A bid-offer spread or credit and balance-sheet charges; a cross-currency basis (CIP deviation) in funding markets; different interest rates from those used (bank funding rates instead of the quoted mid rates).

Revision history

Standard and licence note

Based on the covered and uncovered interest parity relations (Keynes 1923), purchasing power parity (Cassel 1918), the Garman and Kohlhagen (1983) currency option model and the exposure definitions of Adler and Dumas (1984), with IAS 21, IFRS 9, ASC 830 and ASC 815 named only. The text, examples and numbers are original and fictional; they are not affiliated with or endorsed by any school, bank, publisher or The Economist. Market conventions and accounting standards change: check the current official texts and your company's hedging policy before you rely on any statement here. This is learning material, not financial advice. Template licence: MIT.