CMA Final · Strategic Financial Management

Foreign Exchange Risk Management: formula sheet

Full chapter guide

Key formulas

Direct and indirect quote: Indirect quote = 1 ÷ Direct quote; For bid and ask, reverse them: Indirect bid = 1 ÷ Direct ask, and Indirect ask = 1 ÷ Direct bid.
Bid-ask spread (absolute): Spread = Ask − Bid; Always positive. Quoted in paise or pips.
Bid-ask spread (percentage): Spread % = (Ask − Bid) ÷ Ask × 100; Some questions use bid or the mid-rate as the denominator. Follow the question; if silent, state your base.
Cross rate (both quoted against common currency as base): A/C = (A/B) × (B/C); Cancel the common currency B. Bid × bid gives the cross bid; ask × ask gives the cross ask.
Cross rate (common currency is the base in one and quote in the other): A/C = (B/C) ÷ (B/A); For bid, divide the bid of B/C by the ask of B/A. For ask, divide the ask of B/C by the bid of B/A.
Forward premium or discount (annualised): (Forward − Spot) ÷ Spot × (12 ÷ n) × 100, where n is months; Positive means the base currency is at a premium; negative means a discount. For days, use 365 ÷ days.
Forward rate from points: Forward = Spot + Premium points (or − Discount points); Quote points are added when ascending (bid points lower than ask points) and subtracted when descending.
Rupee value of a foreign currency item: ₹ amount = Foreign currency amount × Exchange rate (₹ per unit); Use the correct quote: bid for the bank buying from you, ask (offer) for the bank selling to you.
Transaction gain or loss on a receivable: Gain/(Loss) = FC amount × (Settlement rate − Booking rate); For a receivable, a higher settlement rate is a gain. For a payable, the sign reverses.
Transaction gain or loss on a payable: Gain/(Loss) = FC amount × (Booking rate − Settlement rate); A higher settlement rate means you pay more rupees, so it is a loss.
Translation gain or loss on net exposed assets: Change = (Net assets in FC) × (Closing rate − Opening rate); Net exposed assets = exposed assets − exposed liabilities. Positive net assets gain if the foreign currency strengthens.
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.
Net exposure in a currency: Net exposure = Receivables in currency − Payables in currency; Positive means long, so a fall in that currency hurts. Negative means short, so a rise in that currency hurts.
Multilateral netting position of a company: Net position = Total receivable from all others − Total payable to all others; Convert all amounts to one currency at one agreed rate before netting. The net positions of all companies sum to zero.
Gain or loss from leading or lagging: Net benefit = Rupee saved on settlement rate − Interest cost or gain on timing change; Compare the payment at the expected future rate with the payment at today's rate, then adjust for interest on the days moved.
Rupee value of a foreign-currency flow: ₹ amount = Foreign currency amount × Exchange rate (₹ per unit); Use the bid rate when you sell the currency and the ask rate when you buy it, if both are given.
Forward rate from interest rate parity: F = S × (1 + r(INR) × t) ÷ (1 + r(FC) × t); S and F are in ₹ per unit of foreign currency. t is in years. Simple interest is used unless the question says otherwise.
Annualised forward premium or discount: (F − S) ÷ S × (12 ÷ n) × 100; n is the number of months. A positive result is a premium. A negative result is a discount.
Forward hedge: receivable: ₹ received = Foreign amount × forward BID rate; The bank buys foreign currency from you, so it uses the lower rate of the two-way quote.
Forward hedge: payable: ₹ paid = Foreign amount × forward ASK rate; The bank sells foreign currency to you, so it uses the higher rate of the two-way quote.
Money market hedge: receivable: Borrow FC amount ÷ (1 + r(FC borrow) × t). Sell at spot BID. ₹ at due date = proceeds × (1 + r(INR deposit) × t); If the firm has INR debt, use the INR borrowing rate, since repaying that debt is the saving.
Money market hedge: payable: Deposit FC amount ÷ (1 + r(FC deposit) × t). Buy at spot ASK. ₹ at due date = cost × (1 + r(INR borrow) × t); If the firm has surplus cash, use the INR deposit rate, the interest it gives up.
Quote rule: Bank buys foreign currency at BID. Bank sells foreign currency at ASK.; Always read the quote from the bank's side.
Number of futures contracts: Contracts = Foreign currency exposure ÷ Contract size; For USD-INR the contract size is USD 1,000. Round to a whole number of contracts and state any unhedged balance.
Gain or loss on futures: Long: (Exit price − Entry price) × Contract size × Contracts. Short: (Entry price − Exit price) × Contract size × Contracts; Importer is long. Exporter is short. Assume futures converge to spot at expiry unless the question gives an exit price.
Call option buyer payoff: Max(Spot − Strike, 0) − Premium, per unit; Exercise only if spot is above strike. Maximum loss is the premium.
Put option buyer payoff: Max(Strike − Spot, 0) − Premium, per unit; Exercise only if spot is below strike.
Effective rate with a call (importer): Maximum cost per unit = Strike + Premium. If spot is below strike, cost = Spot + Premium; Add interest on the premium only if the question asks for it.
Effective rate with a put (exporter): Minimum receipt per unit = Strike − Premium. If spot is above strike, receipt = Spot − Premium; This is the floor. Above strike the exporter keeps the upside, less the premium.
Break-even against a forward: Put: option is better if Spot − Premium > Forward rate. Call: option is better if Spot + Premium < Forward rate; Use this to say at which spot rates each alternative wins.
Total gain from comparative advantage: Total gain = | (Fixed-rate spread between A and B) − (Floating-rate spread between A and B) |; Spread means B's rate minus A's rate in each market. Subtract the smaller from the larger. If a bank or dealer takes a fee, deduct it before sharing.
Net borrowing cost of a party: Net cost = Interest paid to own lender + Interest paid under swap − Interest received under swap; Compare this with the cost of borrowing directly in the desired form. The difference is the saving.
Interest on a swap leg: Interest = Notional × Rate × (Days ÷ Day-count basis); For a full year it is Notional × Rate. Use the day-count the question gives (360 or 365).
Net settlement in an interest rate swap: Net payment = Notional × (Fixed rate − Floating rate) for the period; The fixed-rate payer pays this if positive and receives it if negative. Only the net amount moves.
Currency swap principal: Home-currency principal = Foreign-currency principal × Spot rate (home per foreign); The same rate is used again to re-exchange principal at maturity.
Cross rate: A/C = (A/B) × (B/C); Convention used on this page: X/Y means units of Y per 1 unit of X. So GBP/USD is dollars per pound and USD/INR is rupees per dollar. Multiply so that the common currency B cancels: GBP/INR = GBP/USD × USD/INR. Check the direction of every quote before multiplying.
Inverse of a quote: B/A = 1 ÷ (A/B); Use this when the quote is in the opposite direction to the one you need. For example, INR/USD = 1 ÷ (USD/INR).
No-arbitrage condition: Quoted cross rate = Implied cross rate; If they differ, a triangular arbitrage profit exists.
Bid and ask rule: You buy at the ask (offer) rate; you sell at the bid rate; The bank does the reverse. Bid is always lower than ask.
Two-point arbitrage profit per unit: Profit = Sell rate (bid) at dearer centre − Buy rate (ask) at cheaper centre; Multiply by the amount of foreign currency traded.
Regulatory rule: Hedge only a genuine underlying exposure, through an authorised dealer, under FEMA and RBI directions; Use as the framework for descriptive answers.

Quick revision

Direct quote gives rupees per unit of foreign currency; indirect quote gives foreign currency per rupee.
Bank buys at the bid and sells at the ask; the customer deals at the opposite side.
Forward premium or discount follows the interest rate difference between the two currencies.
Interest rate parity, for a direct quote (₹ per unit of foreign currency): forward rate = spot × (1 + home rate) ÷ (1 + foreign rate), with rates for the same period. For an indirect quote, the rates are inverted: forward rate = spot × (1 + foreign rate) ÷ (1 + home rate).
Purchasing power parity, for a direct quote (₹ per unit of foreign currency): expected spot = spot × (1 + home inflation) ÷ (1 + foreign inflation). For an indirect quote, the formula is inverted: expected spot = spot × (1 + foreign inflation) ÷ (1 + home inflation).
Transaction exposure arises from specific contracted cash flows. Translation exposure is an accounting effect on consolidated statements. Economic exposure affects future operating cash flows and firm value.
A money market hedge for a foreign receivable means borrowing the present value of the receivable in foreign currency now (discounted at the foreign borrowing rate) and converting it at spot (the bid rate). The rupees are invested, or used to reduce rupee borrowing, at the home interest rate. The foreign loan is repaid from the receivable when it arrives. The future value of the rupee proceeds at the receipt date is then compared with the forward and other alternatives.
A money market hedge for a foreign payable means converting rupees at spot (the ask rate) into only the present value of the payable, discounted at the foreign deposit rate. You deposit that amount at the foreign rate so it grows to the payable amount, and the deposit pays the liability when it falls due. The rupee cost today is carried forward to the payment date at the home rate (the financing cost). That rupee outflow is compared with the forward and other alternatives.
A forward fixes the rate; an option gives the right but not the obligation, at the cost of a premium.
Compare hedges on the rupee amount at the same date, and recommend the one that is best for the firm's position.
Cross rates are found by combining two quotes against a common currency, using bid and ask carefully.
A currency swap exchanges principal and interest in different currencies; an interest rate swap exchanges interest payments only.

Common mistakes

Using the bid when the customer buys the base currency. Fix: The bid and ask belong to the dealer. A customer buying the base currency pays the ask; a customer selling it receives the bid.
Inverting a quote without swapping bid and ask. Fix: Indirect bid = 1 ÷ direct ask and indirect ask = 1 ÷ direct bid. Check the new ask is bigger than the new bid.
Treating translation loss as a cash loss. Fix: Remember no cash is exchanged on consolidation. It is an accounting effect unless the subsidiary is actually sold or funds are remitted.
Reversing the sign for payables and receivables. Fix: Ask first whether you receive or pay. A rise in the rate helps a receiver and hurts a payer.
Putting the foreign rate on top of the ratio. 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. Fix: Scale each rate by months ÷ 12 before applying the ratio, unless effective period rates are given.
Treating netting and matching as the same thing Fix: Say netting is offsetting dues between two or more parties, mainly group companies. Matching offsets your own inflows and outflows in one currency.
Using the wrong direction for leading and lagging Fix: For payables, pay early if the foreign currency will rise. For receivables, collect early if it will fall. Work out who gains from the move, then choose the timing.
Using the wrong side of the two-way quote, for example the ask rate for an export receivable. Fix: Remember that the bank always gains from the spread. For a receivable it buys at the lower rate (bid). For a payable it sells at the higher rate (ask).
Using annual interest rates without scaling them for the period. Fix: Multiply each annual rate by months ÷ 12 before using it in any formula.

Exam tips

Write bid and ask in a small table at the start of each answer and mark the dealer's side. Examiners award method marks for this.
In MCQs, test options quickly: ask must exceed bid, and a cross rate must lie in a sensible range from the two inputs.
State the base currency every time you say premium or discount. Marks are lost for ambiguity.
Show the annualisation step separately in forward premium questions, because the periodic figure and annualised figure are often both tested.
Keep four decimals in intermediate rates and round only the final answer, as small rounding differences can change the final MCQ option.
In theory answers, define each exposure in one line, add one Indian example, and state whether it affects cash or reported figures.
Section A MCQs usually test classification: practise spotting the keyword that identifies the exposure type.
In numerical questions, write 'long' or 'short' first. It protects you from sign errors.