CMA Final · Strategic Financial Management

Foreign Exchange Market: formula sheet

Full chapter guide

Key formulas

Spot settlement: Spot delivery = trade date + 2 business days (T+2); Standard for most major currency pairs. Say 'normally' in answers, as some pairs settle differently.
Bid-ask spread: Spread = Ask rate − Bid rate; The dealer buys at the bid and sells at the ask. The spread is the dealer's margin.
Spread percentage: Spread % = (Ask − Bid) ÷ Ask × 100; Use the base given in the question. Some use the bid or mid-rate, so state your base.
Market tiers: Interbank (wholesale) market + Merchant (retail) market; Banks deal among themselves in the first and with customers in the second.
Direct and indirect quote: Indirect quote = 1 ÷ Direct quote; Reciprocal of bid gives the ask of the reversed pair, and reciprocal of ask gives the bid. Bid and ask swap places.
Reversing a two-way quote: If A/B = Bid / Ask, then B/A = (1 ÷ Ask) / (1 ÷ Bid); The lower number of the new quote comes from the higher number of the old one.
Spread: Spread = Ask − Bid; Spread % = (Ask − Bid) ÷ Ask × 100; Some questions use bid as the denominator. Follow the question's instruction, otherwise use ask and state it.
Cross rate, common currency on the same side: A/C = (A/B) × (B/C); Bid A/C = Bid A/B × Bid B/C; Ask A/C = Ask A/B × Ask B/C.
Cross rate, common currency in the same position: A/C = (A/B) ÷ (C/B); Bid A/C = Bid A/B ÷ Ask C/B; Ask A/C = Ask A/B ÷ Bid C/B.
Appreciation or depreciation of a foreign currency (direct quote): % change = (New rate − Old rate) ÷ Old rate × 100; Positive means the foreign currency has appreciated against the rupee.
Rupee change from a rate move: Rupee depreciation % = (New − Old) ÷ New × 100 for a direct quote rise; The rupee's own value is the reciprocal, so its percentage change uses the new rate as the denominator.
Forward premium or discount (absolute): Forward rate − Spot rate; Positive means the base (foreign) currency is at a premium. Negative means a discount. Use the same quote direction for both rates.
Annualised forward premium or discount (%): [(Forward − Spot) ÷ Spot] × (12 ÷ n) × 100; n is the forward period in months. For days, use 365 ÷ days. This is the simple annualised rate, which is the usual exam approach.
Forward rate from points: Forward = Spot + premium points, or Spot − discount points; Apply points to bid and offer separately. Points are usually quoted in paise.
Reading the points: If the first point is smaller than the second, ADD. If the first is larger, SUBTRACT.; For example, 20/30 is added to spot. 30/20 is subtracted from spot. This keeps the offer above the bid.
Forward rate from interest rates: Forward = Spot × (1 + i_quote × n/12) ÷ (1 + i_base × n/12); Direct quote, rate for quote currency (₹) in numerator. Uses simple interest for periods up to a year. Covered in the parity topic.
Exporter and importer cover: Exporter sells at bank's bid. Importer buys at bank's offer.; Rupee amount = foreign amount × applicable forward rate.
Interest rate parity (forward rate): F ÷ S = (1 + i_quoted currency) ÷ (1 + i_base currency); For a quote such as ₹ per US$, F = S × (1 + i_₹) ÷ (1 + i_$). Adjust the rates to the forward period, for example 6-month rate = annual rate × 6/12 when simple interest is used.
Forward premium or discount (annualised): (F − S) ÷ S × 12 ÷ n × 100; n is the forward period in months. A positive result is a premium on the base currency; a negative result is a discount.
Relative PPP (expected spot rate): E(S1) = S0 × (1 + inflation_quoted currency) ÷ (1 + inflation_base currency); Use inflation for the same period as the forecast. For a quote such as ₹ per US$, the quoted currency is the rupee.
International Fisher Effect: E(S1) ÷ S0 = (1 + i_quoted currency) ÷ (1 + i_base currency); Uses nominal interest rates to forecast the future spot rate. It is the same form as IRP but gives an expected spot, not a forward.
Fisher Effect: (1 + nominal rate) = (1 + real rate) × (1 + expected inflation); Approximation: nominal rate ≈ real rate + inflation.
Covered arbitrage rule: If actual F > parity F, the base currency is expensive forward: borrow the quoted currency, buy the base currency at spot, invest it in the base currency and sell it forward. If actual F < parity F, the base currency is cheap forward: borrow the base currency, convert it to the quoted currency at spot, invest there and buy the base currency forward.; Check by comparing, in the quoted currency at the end of the period, the amount the invest-and-cover route gives with the amount you owe on the loan. The difference is the arbitrage profit.
Cross rate: A/C = A/B × B/C; Use it to find the rate implied by two quotes and compare it with the third quote on offer. If they match, there is no triangular arbitrage.
Bid-ask rule for a customer using a bank's quote: You buy at the ask rate; you sell at the bid rate; Bid is the rate at which the bank buys the base currency. Ask is the rate at which the bank sells it.
Locational arbitrage gain: Gain per unit = Bid in the dearer centre − Ask in the cheaper centre; Positive only if the two spreads do not overlap. Multiply by the amount of currency traded.
Interest rate parity (simple interest): Forward = Spot × (1 + i of quoted currency × n) ÷ (1 + i of base currency × n); Here the rate is quoted as units of the quoted currency per one unit of the base currency. Use n in years, for example 0.5 for six months. Use the rates given for the period.
Covered interest arbitrage test: Actual forward vs parity forward; If actual forward is above parity, the base currency is dear forward; if below, it is cheap forward. Choose borrowing and investing currencies to match.
Arbitrage profit: Profit = Amount received at end − Amount owed at end (in the same currency); Convert both to one currency using the forward rate before subtracting.
Percentage change in a currency: % change in foreign currency = (New rate − Old rate) ÷ Old rate × 100; Rate is in direct quote (₹ per unit of foreign currency). A positive value is the foreign currency's rise in rupee terms, which means the rupee has depreciated.
Real exchange rate (direct quote): Real rate = Nominal rate × (Foreign price level ÷ Domestic price level); Quote convention: direct quote, ₹ per unit of foreign currency. A rise in this real rate means Indian goods have become cheaper relative to foreign goods, so competitiveness has improved. Use consistent price indices. This is not the RBI's REER convention. The sign of a rise is opposite in the two.
NEER: NEER = weighted average of bilateral exchange rate indices, weights = trade shares; No inflation adjustment. Index form, base year = 100.
REER: REER = Π (e_i × P_domestic ÷ P_foreign,i)^wi; Quote convention: e_i is the indirect quote (foreign currency i per ₹), expressed as an index to the base year. Weights wi are trade shares and add up to 1. This is the form used in the RBI's published indices. A rise in REER means real appreciation of the rupee and reduced competitiveness. A fall means real depreciation and improved competitiveness. Keep this separate from the direct-quote real rate above: there a rise means improved competitiveness, here a rise means reduced competitiveness. Always check the quote convention first.
BoP identity: Current account + Capital and financial account + Change in reserves (with errors and omissions) = 0; Reserves fall when the first two together are in deficit.
Receivable hedge: forward: Rupees received = Foreign amount × Forward bid rate; The bank buys the foreign currency from you, so use the bank's buying (bid) rate.
Payable hedge: forward: Rupees paid = Foreign amount × Forward offer rate; The bank sells the currency to you, so use the bank's selling (offer) rate.
Money market hedge for a receivable: Borrow = Foreign amount ÷ (1 + foreign borrowing rate × t); convert at spot bid; invest rupees at (1 + rupee deposit rate × t); t is the period as a fraction of a year. Use simple interest unless the question says otherwise. Compare the final rupee amount with the forward.
Money market hedge for a payable: Deposit now = Foreign amount ÷ (1 + foreign deposit rate × t); buy at spot offer; rupee cost at maturity = rupees spent × (1 + rupee borrowing rate × t); If the firm has surplus rupees, use its rupee deposit rate as the opportunity cost instead.
Forward premium or discount (annualised): (Forward − Spot) ÷ Spot × 12 ÷ months × 100; A positive result is a premium, a negative result a discount, for the quoted currency.
Net exposure: Net exposure = Foreign currency receivables − Foreign currency payables (same currency, same date); Net first, then hedge only the open position.

Quick revision

A direct quote gives the home currency per unit of foreign currency; an indirect quote is the reverse.
The bid is the dealer's buying rate and the ask is the dealer's selling rate; the ask is higher.
The spread is ask minus bid and is the dealer's margin.
For cross rates, multiply or divide so that the common currency cancels, using bid with bid logic carefully.
Forward premium means the forward rate is above spot in a direct quote; discount means below.
Annualised premium = (Forward − Spot) ÷ Spot × (12 ÷ months) × 100.
Interest rate parity: Forward ÷ Spot = (1 + home rate) ÷ (1 + foreign rate), for the same period.
Purchasing power parity links the expected spot rate to the inflation difference between two countries.
The currency with the higher interest rate trades at a forward discount under interest rate parity.
Arbitrage means a riskless gain from a mispricing; start with a fixed amount and compare end value.
Transaction exposure affects actual cash flows; translation exposure affects reported statements; economic exposure affects long-term value.
Fixed, floating and managed regimes differ in who sets the rate and how adjustments happen.

Common mistakes

Saying FEDAI is a regulator like the RBI Fix: RBI is the regulator under FEMA. FEDAI is an association of authorised dealers that frames rules for members.
Calling the whole forex market exchange-traded Fix: Most dealing is OTC. Only currency futures and options trade on exchanges.
Taking the reciprocal without swapping bid and ask Fix: New bid = 1 ÷ old ask and new ask = 1 ÷ old bid. Check that the new ask is higher.
Using the wrong side when dividing in a cross rate Fix: When dividing, use bid ÷ ask for the bid and ask ÷ bid for the ask, so the spread widens correctly.
Using the offer rate for an exporter, or the bid rate for an importer. Fix: Remember the bank buys at bid and sells at offer. An exporter sells to the bank, so use the bid. An importer buys from the bank, so use the offer.
Adding forward points when they should be subtracted. Fix: Check that the forward offer stays above the forward bid. If the first number is larger, subtract both from spot.
Putting the rates in the wrong way up in the formula. Fix: Always write the quote first. The quoted currency's rate goes on top. For ₹/US$ the rupee factor is the numerator.
Using the full annual rate for a 3-month or 6-month forward. Fix: Multiply the annual rate by n/12 before adding 1. Do this as the first calculation step.
Using the wrong side of the bid-ask quote Fix: Remember: you buy at the ask and sell at the bid. Write 'buy at ask' or 'sell at bid' next to each leg.
Inverting a cross rate the wrong way Fix: Write the unit of each quote, such as ₹ per USD or USD per EUR, and cancel units like fractions. The units that remain must match the target quote.

Exam tips

Expect 2-mark MCQs that test classification: spot vs forward, OTC vs exchange-traded, RBI vs FEDAI.
In descriptive answers, use headings for functions, segments and participants, then one example each.
When a quote is given, label bid and ask from the dealer's side before computing anything.
Write 'normally T+2' for spot settlement rather than an absolute claim.
Link the topic to hedging: a closing line that forwards and derivatives manage exchange risk earns easy marks.
In MCQs, the most common traps are bid-ask reversal and wrong viewpoint. Read who is buying and who is selling before calculating.
Show the cancellation of the common currency in one line. It earns method marks even if arithmetic slips.
Keep four decimal places in intermediate rate work and round only the final answer.