ACCA Applied Skills · Financial Management

Causes of exchange rate differences and interest rate fluctuations: formula sheet

Full chapter guide

Key formulas

Quote format: Base/Quote currency = Bid - Offer (lower rate first); The bid is the rate at which the bank buys the base currency. The offer is the rate at which the bank sells it.
Spread: Spread = Offer − Bid; Can be expressed in pips, the last decimal place quoted, or as a percentage of the rate.
Spread as a percentage: Spread % = (Offer − Bid) ÷ Bid × 100; Some questions use the mid-point as the denominator. Use the method the question implies, and state it.
Mid-rate: Mid-rate = (Bid + Offer) ÷ 2; Use only when the question asks for a mid-market rate. Real transactions use bid or offer.
Converting with the base currency: Customer buys base currency: pay quote currency = base amount × Offer. Customer sells base currency: receive quote currency = base amount × Bid.; The bank sells base currency at the offer and buys it at the bid.
Reciprocal of a quote: Rate for the reverse pair: Bid = 1 ÷ Offer of original; Offer = 1 ÷ Bid of original; Bid and offer swap when you invert. The lower rate must stay first.
Relative PPP forecast of future spot rate: S1 = S0 × (1 + hc) ÷ (1 + hb); S0 = current spot, quoted as units of currency C per 1 unit of currency B. hc = inflation of the country of currency C (the quoted/top currency). hb = inflation of the country of currency B (the base/one-unit currency). Both are for the same period.
Multi-year forecast: S(n) = S0 × [(1 + hc) ÷ (1 + hb)]^n; Use when inflation is stable each year. If the rates differ by year, apply each year's ratio in turn.
Absolute PPP: S0 = Price level in country C ÷ Price level in country B; Theory only. It assumes identical goods, no trade costs and free trade. It rarely holds exactly.
Rule of direction: Higher inflation ⇒ that currency depreciates; Use this to check your answer. The top (quoted) currency's inflation sits in the numerator.
Interest rate parity (forward rate): F₀ = S₀ × (1 + iᶜ) ÷ (1 + iᵇ); S₀ and F₀ are quoted as units of the counter currency (c) per 1 unit of the base currency (b). iᶜ is the interest rate of the counter currency. iᵇ is the interest rate of the base currency. Both rates are for the period to the forward date.
Interest rate for part of a year: Period rate = annual rate × (months ÷ 12); Time-apportion the annual rate (annual rate × months ÷ 12) unless the question states otherwise.
Direction rule: Higher interest rate currency → forward discount; lower interest rate currency → forward premium; Use this to check your answer. The forward rate must move in the right direction from spot.
Multi-year forward rate: F₀ = S₀ × [(1 + iᶜ) ÷ (1 + iᵇ)]ⁿ; Use it for n years with annual rates, if the question gives the same annual rate each year.
Fisher Effect (exact): (1 + i) = (1 + r) × (1 + h); i = nominal (money) rate, r = real rate, h = expected inflation. Rearrange to find any one of the three.
Fisher Effect (approximation): i ≈ r + h; Only a rough guide. Use the exact form unless the question says otherwise.
International Fisher Effect: S1 = S0 × (1 + i of currency in numerator) ÷ (1 + i of currency in denominator); For a quote of A per 1 B, S1 = S0 × (1 + iA) ÷ (1 + iB). Uses interest rates for the period.
Purchasing power parity: S1 = S0 × (1 + h of currency in numerator) ÷ (1 + h of currency in denominator); Same layout as IFE but with inflation rates. Part of the four-way equivalence.
Interest rate parity: F0 = S0 × (1 + i of currency in numerator) ÷ (1 + i of currency in denominator); Gives the forward rate. Same layout as IFE, but the result is the forward rate, not the expected spot rate.
Expectations theory: Forward rate (time t) = Expected future spot rate (time t); Forward rate is an unbiased predictor, not a perfect one.
Forward rate from interest rates (interest rate parity): F = S × (1 + i quoted currency) ÷ (1 + i base currency); Use rates for the period to the forward date. Base currency is the one that appears as 1 in the quote.
Expected spot rate from inflation (purchasing power parity): S1 = S0 × (1 + h quoted currency) ÷ (1 + h base currency); h means inflation rate. It explains long-run movements.
Direction of movement rule: Higher inflation or lower interest rates → currency weakens; trade surplus or capital inflow → currency strengthens; Other things being equal. State this condition in answers.
Long-term rate under pure expectations: (1 + r₂)² = (1 + r₁) × (1 + f); r₁ is the one-year spot rate, r₂ is the two-year spot rate and f is the expected one-year rate in a year's time. Rearrange to find f.
Implied forward rate: f = (1 + r₂)² ÷ (1 + r₁) − 1; This is the rate the market expects for year 2 under pure expectations theory. It is a general method, not always given in the FM exam, so check the question.
Liquidity preference: Long-term yield = expected average short-term rate + liquidity premium; The premium normally increases with maturity. This is a conceptual rule, not a calculation you will usually be given numbers for.
Components of a nominal rate: Nominal rate ≈ real rate + expected inflation + risk premium; A simple way to list causes of rate differences. It is an approximation.

Quick revision

FM quote convention: a rate of X/Y means units of X per 1 Y. Y is the base currency, the one that is 1 unit. To convert Y into X, multiply by the rate. To convert X into Y, divide by the rate.
Spot rates are quoted bid and offer. Check which rate the bank uses for your transaction.
PPP: future spot X/Y = spot X/Y × (1 + inflation of the currency in the numerator, X) ÷ (1 + inflation of the currency in the denominator, Y).
The currency with the higher inflation is expected to weaken.
IRP: forward X/Y = spot X/Y × (1 + interest rate of the numerator currency, X) ÷ (1 + interest rate of the denominator currency, Y), for the same period.
IRP uses interest rates for the forward rate. PPP uses inflation for the future spot rate.
Fisher effect: (1 + nominal rate) = (1 + real rate) × (1 + inflation).
International Fisher effect: expected future spot X/Y = spot X/Y × (1 + nominal interest rate of X) ÷ (1 + nominal interest rate of Y). The currency with the higher nominal interest rate is expected to depreciate.
Use the same time period for rates and the exchange rate forecast. Adjust annual rates for part years.
Expectations theory: the forward rate is an unbiased predictor of the future spot rate.
Other causes: trade flows, capital flows, government intervention, speculation and political events.
Yield curve: an upward slope is the normal shape. An inverted curve means short-term rates exceed long-term rates.

Common mistakes

Using the bid rate when the customer is buying the base currency. Fix: Always ask what the bank is doing. The bank sells base currency at the offer, so a customer buying base pays the offer.
Multiplying when you should divide, or the reverse. Fix: To convert a known base amount into quote currency, multiply. To convert a known quote amount into base currency, divide. Then choose bid or offer by what the bank does with the base currency. Write the currency labels beside every number.
Putting the inflation rates the wrong way round. Fix: Always put the inflation of the country whose currency is the number in the quote on top. Then do the direction check.
Subtracting inflation rates instead of using the ratio. Fix: Use (1 + h) ÷ (1 + h) as the exam does. Use the approximation only for a quick sense check.
Putting the interest rates the wrong way round Fix: Always put the counter currency's rate on top. Then check the direction rule: the higher interest rate currency is at a forward discount.
Using the full annual rate for a period under a year Fix: Multiply each annual rate by months ÷ 12 before using it in the formula.
Adding real rate and inflation instead of multiplying Fix: Use (1 + i) = (1 + r)(1 + h) every time unless told to approximate. Options in objective tests are often set to catch the shortcut.
Putting the rates upside down in the IFE fraction Fix: Write the quote as A per 1 B first. The rate of A goes on top. Then check the direction: higher rate means weaker currency.
Saying the forward rate is a guaranteed or accurate forecast. Fix: Say it is an unbiased predictor: it is right on average but usually wrong on any one occasion.
Putting the interest rates the wrong way round in the forward rate formula. Fix: Quoted currency rate goes on top and base currency rate on the bottom. Check the direction with the discount rule.

Exam tips

Write Bid - Offer on your scratch paper before you touch the numbers, and label each rate with its currencies.
In OT questions, the wrong options are usually the answers you get from using the wrong rate or the wrong operation. Work it out first, then match, and do not pick the first number that looks close.
Check which currency is the base. The pair 'USD/EUR' and 'EUR/USD' give different rates and need different operations.
If a question gives a quote in the form 'X per Y', note which currency is Y. That is your base.
In Section C, show the rate you used and say why, for example 'bank sells dollars at the offer'. Method marks depend on this.
Circle the quote format in the question before doing any maths. Most lost marks come from putting inflation the wrong way round.
In objective tests, use the direction check to remove two options at once. An answer that moves the wrong way is always wrong, since marking is all or nothing.
Read whether inflation is given per year or for the whole period. Do not compound a figure that is already a total.