CA Final · Advanced Financial Management

Foreign Exchange Exposure and Risk Management: formula sheet

Full chapter guide

Key formulas

Net exposure in a currency: Net exposure = Foreign currency inflows (receivables, foreign assets) − Foreign currency outflows (payables, liabilities); Inflows include receivables and other foreign currency assets. Outflows include payables and foreign currency loans. Positive means long position and you lose if the foreign currency weakens. Negative means short position and you lose if it strengthens.
Transaction gain or loss: Gain or loss (₹) = Foreign amount × (Settlement rate − Booking rate); For a receivable, a positive result is a gain. For a payable, the sign reverses: a positive result is a loss.
Translation exposure (exposed net assets): Exposed net assets = Assets translated at closing rate − Liabilities translated at closing rate; Exposed net assets are measured at the closing rate. Under Ind AS 21 the year's profit or loss is translated at transaction-date or average rates, and the exchange difference goes to OCI for foreign operations. So the OCI difference also reflects the gap between average and closing rates on that profit.
Change in translated net assets: Change = Net assets in foreign currency × (Closing rate − Opening rate); Use ₹ per unit of foreign currency as the quote so the sign is easy to read. This gives the whole change only if net assets stay constant through the year. If profit is earned, the OCI difference = Opening net assets × (Closing rate − Opening rate) + Profit × (Closing rate − Average rate).
Direct and indirect quote: Indirect quote = 1 ÷ Direct quote; For a two-way quote, invert and swap: indirect bid = 1 ÷ direct ask; indirect ask = 1 ÷ direct bid.
Spread: Spread = Ask − Bid; Spread % = (Ask − Bid) ÷ Ask × 100 is common; some questions use bid as the base. Follow the question's wording.
Cross rate (common currency in the quote position of both): For A/C from A/B and C/B (B is the common quote currency): A/C = (A/B) ÷ (C/B). Bid A/C = Bid A/B ÷ Ask C/B; Ask A/C = Ask A/B ÷ Bid C/B; Divide bid by ask and ask by bid to widen the spread correctly.
Cross rate (chained quotes): For A/C from A/B and B/C: A/C = (A/B) × (B/C). Bid = Bid × Bid; Ask = Ask × Ask; Use only when the common currency is the quote currency in the first quote and the base currency in the second, as in A/B and B/C. A/B means units of B per one unit of A. If a quote is given the other way round (for example USD/EUR when you need EUR/USD), invert it first and swap its bid and ask.
Forward premium or discount (annualised): Premium or (discount) % = (Forward − Spot) ÷ Spot × 12 ÷ n × 100; n is the forward period in months. Rate must be in the same quote as spot (e.g. both INR per USD). Positive means premium for the base currency.
Forward rate from premium or discount: Forward = Spot × [1 + (Premium % × n ÷ 12)]; Use a minus sign for a discount. Apply to bid and ask separately when points are given.
Forward points: Outright forward = Spot + Premium points (or − Discount points); First convert the points to the same unit as the spot rate (for example 40 paise = ₹0.40). If the first (bid) points are smaller than the second (ask) points, add both to spot: this is a premium. If the first points are larger than the second, subtract both: this is a discount. Check that the forward ask stays above the forward bid.
Interest Rate Parity (forward rate): F ÷ S = (1 + i_h × n) ÷ (1 + i_f × n) [simple, for periods up to one year]; S and F are home currency per one unit of foreign currency. i_h is the home rate and i_f the foreign rate, both for the same n years. For multi-year, use (1 + i_h)^n ÷ (1 + i_f)^n.
IRP with periodic rates: F = S × (1 + home rate for the period) ÷ (1 + foreign rate for the period); If annual rates are given for 6 months, use half the annual rate (simple method) unless the question says compound.
Purchasing Power Parity (expected spot): S₁ = S₀ × (1 + inflation_h) ÷ (1 + inflation_f); For n years use the ratio raised to the power n. Quote must be home currency per unit of foreign currency.
Relative PPP (approximate): Expected % change in spot ≈ inflation_h − inflation_f; Approximation only. Use the exact ratio form if the question asks for a precise rate.
Fisher effect: (1 + nominal rate) = (1 + real rate) × (1 + expected inflation); Approximately nominal rate ≈ real rate + inflation.
International Fisher Effect: S₁ ÷ S₀ = (1 + i_h) ÷ (1 + i_f); Gives the expected future spot from nominal interest rates. Same form as IRP but gives expected spot, not the forward rate.
Forward premium or discount (annualised): (F − S) ÷ S × (12 ÷ months) × 100; Positive means the foreign currency is at a premium. Negative means a discount.
Forward hedge: receivable: ₹ received = Foreign amount × Forward bid rate (₹ per unit); The bank buys foreign currency from you, so use the lower (bid) rate of the pair.
Forward hedge: payable: ₹ paid = Foreign amount × Forward offer rate (₹ per unit); The bank sells foreign currency to you, so use the higher (offer) rate.
Money market hedge: receivable: Foreign loan today = Receivable ÷ (1 + foreign borrowing rate for the period); ₹ today = Loan × Spot bid; ₹ at end = ₹ today × (1 + ₹ deposit rate for the period); Use the period rate, not the annual rate. For 3 months, take annual rate × 3/12 unless told otherwise.
Money market hedge: payable: Foreign deposit today = Payable ÷ (1 + foreign deposit rate for the period); ₹ needed today = Deposit × Spot offer; ₹ cost at end = ₹ today × (1 + ₹ borrowing rate for the period); If the firm has surplus cash, compare using the rupee opportunity (deposit) rate instead of the borrowing rate, as the question directs.
Forward premium or discount (annualised): (Forward − Spot) ÷ Spot × 12 ÷ months × 100; Positive means foreign currency at a premium. Use it to judge forward cost.
Leading and lagging decision: Compare: rupee outcome of paying or receiving at the changed date, adjusted for interest, against the outcome at the original date; Bring both outcomes to the same date before comparing.
Number of contracts: Contracts = Foreign currency exposure ÷ Contract size; For USD-INR, the contract size is USD 1,000. Round to a whole number and mention any unhedged balance.
Tick value: Tick value = Contract size × Tick size; USD-INR tick size is ₹0.0025, so one tick is USD 1,000 × ₹0.0025 = ₹2.50 per contract.
Profit or loss on a long position: (Exit price − Entry price) × Contract size × Number of contracts; Buyer of futures gains when the price rises.
Profit or loss on a short position: (Entry price − Exit price) × Contract size × Number of contracts; Seller of futures gains when the price falls.
Daily MTM: MTM = (Today's settlement price − Previous settlement price) × Contract size × Contracts, with the sign flipped for a short position; On day one, use the entry price as the previous price. The sum of all daily MTMs equals the total gain or loss.
Theoretical futures price: F = S × (1 + i₍INR₎ × t) ÷ (1 + i₍USD₎ × t); Interest rate parity form with simple interest. Here t is in years. Use the compounding form only if the question gives it.
Effective rate with a hedge: Effective rate = Spot rate at expiry ± Futures loss or gain per unit; For a perfect hedge this equals the futures entry price.
Margin account balance: Closing balance = Opening balance + MTM gain − MTM loss + Top-up − Withdrawal; A top-up is needed when the balance falls below the maintenance margin.
Call buyer's payoff (per unit): Max(S − X, 0) − Premium; S = spot rate at expiry, X = strike. Exercise only if S > X.
Put buyer's payoff (per unit): Max(X − S, 0) − Premium; Exercise only if S < X.
Writer's payoff: Writer's payoff = − Buyer's payoff (before any other positions); The writer's maximum gain is the premium received.
Break-even rate: Call: X + Premium. Put: X − Premium; Below the call break-even or above the put break-even, the buyer's payoff is a net loss.
Importer's effective rate with a call: If S > X: X + Premium. If S ≤ X: S + Premium; The effective rate is capped at X + Premium. Rupee outflow = effective rate × foreign currency amount.
Exporter's effective rate with a put: If S < X: X − Premium. If S ≥ X: S − Premium; The effective rate is floored at X − Premium.
Importer's collar: Buy call at higher strike Xc, sell put at lower strike Xp. Effective rate lies between Xp + net premium and Xc + net premium; Net premium = call premium paid − put premium received. Use the correct sign if the net is a receipt.
Exporter's collar: Buy put at lower strike Xp, sell call at higher strike Xc. Effective rate lies between Xp − net premium and Xc − net premium; Net premium = put premium paid − call premium received.
Long straddle: Payoff = Max(S − X, 0) + Max(X − S, 0) − (Call premium + Put premium); Break-evens: X + total premium and X − total premium.
Option vs forward cut-off (importer, call): Option beats forward when S + Premium < Forward rate, for S ≤ X; If S > X, compare X + Premium with the forward rate directly.
Net payment in an interest rate swap: Net payment = Notional × (Fixed rate − Floating rate) × days ÷ 360; Use the day count or period fraction given in the question. For annual settlement, use 1. A positive figure is paid by the fixed payer.
Total gain from swap (comparative advantage): Total gain = |Fixed-rate spread difference − Floating-rate spread difference|; Spread difference is the higher borrower's rate minus the lower borrower's rate, in each market. Share the gain equally unless told otherwise.
Post-swap cost of a party: Cost = Rate paid to lender + Rate paid to counterparty − Rate received from counterparty; Do this for each party and check that the total saving equals the total gain.
Principal exchange in a currency swap: Foreign principal = Domestic principal ÷ Spot rate (₹ per unit of foreign currency); Use the same rate for the re-exchange at maturity. The contract fixes it. Later spot rates do not matter for the swapped flows.
Interest on each leg of a currency swap: Interest = Principal in that currency × Rate of that leg × period fraction; Compute each leg in its own currency. Convert to rupees only when comparing, and use the rate that applies to that date.
Rupee cost of unhedged foreign loan: Rupee outflow = Foreign currency outflow × Spot rate on payment date; Compare this with the swapped rupee outflow to measure the benefit of the swap.
Implied cross rate: A/C implied = (A/B) × (B/C); Chain the quotes so the common currency cancels. Compare the result with the actual A/C quote.
Triangular arbitrage test: Start amount × rate 1 × rate 2 × rate 3 > Start amount ⇒ arbitrage; Convert every step in the correct direction (divide by a quote when buying the base currency with the quote currency, multiply when selling it). If the result is below the start, run the loop in reverse.
Interest rate parity forward: F = S × (1 + i quote × n) ÷ (1 + i base × n); Quote currency is the one in which the rate is expressed (INR in USD/INR). n is the period in years. Use the same compounding basis for both rates.
Covered interest arbitrage test: Market forward ≠ parity forward ⇒ arbitrage; If market forward is below parity, the base currency is cheap forward: borrow base currency, invest in quote currency, buy base currency forward. If it is above parity, reverse it.
Net exposure: Net exposure = Σ receivables − Σ payables (in the same currency and date); Netting offsets inflows against outflows. Only the net amount needs hedging.
Internal techniques list: Invoicing in home currency, netting, matching, leading and lagging, price variation, asset-liability management; Internal techniques come before external hedges such as forwards, futures, options and swaps.

Quick revision

Transaction exposure arises on contracts already entered into whose foreign currency cash flows will be settled in future at uncertain exchange rates; translation exposure arises on consolidation; economic exposure affects long-term cash flows.
A bank buys foreign currency at the bid rate and sells at the ask rate. When the customer buys foreign currency, the bank sells at the ask rate. When the customer sells foreign currency, the bank buys at the bid rate.
For cross rates, line up the currencies so the common currency cancels, and use bid and ask carefully.
Interest rate parity: Forward (₹/US$) = Spot (₹/US$) × (1 + i₹ × n) ÷ (1 + i$ × n), where n is the period in years.
Purchasing power parity links expected spot rate to inflation differentials.
Forward hedge fixes the rupee amount; compare it with money market hedge in rupees at the same date.
Money market hedge for a receivable: borrow PV = receivable ÷ (1 + foreign borrowing rate × n), so that the loan plus interest equals the receipt. Convert the PV at the spot bid rate, as the bank buys the foreign currency, and invest the rupees to the due date at the rupee rate (or use them to reduce rupee borrowing). The rupees are received today, so compare the rupee maturity value on the due date with the forward proceeds on the due date, so both outcomes are at the same date.
Money market hedge for a payable: buy PV = payable ÷ (1 + foreign deposit rate × n) of the foreign currency at the spot ask rate, funding it with rupees (borrowed or existing funds). Deposit it abroad until the due date, when it grows to the payable. Carry the rupee cost forward at the rupee borrowing or opportunity rate before comparing with the forward cost.
Futures gains and losses are settled daily and lot size must be respected.
An option buyer's loss is limited to the premium; compute the premium in rupees and bring it to the same date if asked.
Swaps exploit comparative advantage; check that total savings are shared as the question states.
In arbitrage, start where you can sell high and buy low, and confirm the profit by tracking cash flows.

Common mistakes

Calling translation exposure a cash loss. Fix: Translation changes reported figures only. Cash is affected only when funds are actually remitted or converted.
Saying economic exposure arises only for firms with foreign contracts. Fix: A purely domestic firm facing imported competition has economic exposure. It works through prices, volumes and costs.
Using the same side (bid with bid) when dividing rates. Fix: For division, use bid ÷ ask for the lowest result and ask ÷ bid for the highest. Bid × bid and ask × ask apply only when both quotes are in chained base/quote form (A/B and B/C). Check the spread is positive.
Inverting a two-way quote without swapping bid and ask. Fix: Indirect bid = 1 ÷ direct ask and indirect ask = 1 ÷ direct bid. The higher direct rate gives the lower indirect rate.
Putting the foreign rate on top of the ratio when the quote is home per foreign unit. Fix: Always write the quote first. For ₹ per USD, the rupee rate goes on top. Check the direction: higher home rate means a higher forward rate.
Using the full annual rate for a 3 or 6 month forward. Fix: Multiply each annual rate by n (months ÷ 12) before adding 1, unless the question asks for compounding.
Using the wrong side of the quote, for example the offer rate for an export receivable. Fix: Say it aloud: the bank buys what I sell. Exporter sells foreign currency, so use bid. Importer buys, so use offer.
Using the annual interest rate for a 3 or 6 month period. Fix: Convert to the period rate first and write it beside the formula before computing.
Taking the wrong side of the hedge, such as buying futures for an export receivable. Fix: Ask which way the rupee move hurts you. An exporter loses if the foreign currency falls, so the exporter sells futures. An importer loses if it rises, so the importer buys.
Forgetting the contract size and computing the gain on one unit only. Fix: Always write gain per unit × contract size × number of contracts. Check that this equals gain per unit × total exposure.

Exam tips

Write a one-line definition of each exposure type first. Many written questions award marks for the distinction itself.
In case MCQs, the keywords in the scenario decide the type. Underline them before reading the options.
In numericals, always state the position as long or short before computing. It protects you from sign errors.
When asked how to manage each exposure, pair it correctly: forwards, options and money market for transaction; matching assets with liabilities for translation; diversifying markets and sourcing for economic.
For translation, quote Ind AS 21 treatment briefly: closing rate for assets and liabilities, difference to OCI.
Write BASE/QUOTE above every rate before you start. Most lost marks come from direction errors.
State whose side you are on, for example 'bank buys USD at bid', in one line. It earns method marks even if a number slips.
Show the spread check at the end. Bid must be less than ask.