Capital Flows and the FX Market: formula sheet

Key formulas

Spot settlement convention

Settlement date = trade date + 2 business days (T+2) for most pairs

Exceptions exist, such as USD/CAD at T+1. A forward has settlement later than spot.

Forward contract settlement

Forward = exchange at a rate fixed today for a date later than spot

The rate is the forward rate, set from the spot rate and interest rate differentials.

FX swap structure

FX swap = spot (or near-leg) exchange + opposite exchange on a later date

Net currency exposure is roughly zero. It is not the same as a currency swap.

NDF settlement amount (cash-settled)

For a USD/XXX quote (XXX per 1 USD) with the notional in USD, the party long USD receives: notional × (spot at maturity − NDF rate) ÷ spot at maturity, paid in USD

The gain is first found in the price currency (XXX) as notional × (spot − NDF rate), then converted to USD at the maturity spot rate, which is why you divide by spot. A negative value means the party long USD pays that amount to the other party. The party short USD receives the opposite amount. For any other quote, say which currency is the price currency, compute the gain in that currency, then convert it to the settlement currency at spot. Always check the quote direction first.

Market participants

Sell side = dealers/banks; Buy side = corporations, real money, leveraged accounts, governments, central banks, retail

Know which group each participant belongs to.

Quote convention

A/B = x means 1 A = x B

A is the base currency, B is the price currency. The quote tells you the price of one unit of the base.

Inverse quote

B/A = 1 ÷ (A/B)

Use this to flip a quote. With bid-ask: bid(B/A) = 1 ÷ ask(A/B) and ask(B/A) = 1 ÷ bid(A/B).

Bid-ask spread

Spread = ask − bid

Spread as a percentage is (ask − bid) ÷ ask or ÷ midpoint, depending on the question; follow the wording.

Cross rate, same base

A/B = (A/C) ÷ (B/C)

Both quotes share the same price currency C, so it cancels by division.

Cross rate, base meets price

A/B = (A/C) × (C/B)

C is the price currency of one quote and the base of the other, so it cancels by multiplication.

Cross-rate bid and ask (multiplication)

A/B bid = (A/C bid) × (C/B bid); A/B ask = (A/C ask) × (C/B ask)

Apply when both quotes are set up for multiplication. If you must divide, use the division rule below or invert the other quote first using the inverse bid-ask rule.

Cross-rate bid and ask (division)

For A/B = (A/C) ÷ (B/C): bid(A/B) = bid(A/C) ÷ ask(B/C); ask(A/B) = ask(A/C) ÷ bid(B/C)

Both quotes share the same price currency C. The lowest cross bid divides the lowest numerator by the highest denominator; the highest cross ask does the reverse.

Forward rate (annual rates, simple interest)

F = S × (1 + i_P × T) ÷ (1 + i_B × T)

S and F are P/B. i_P is the price-currency rate, i_B the base-currency rate. T is the year fraction, such as 90/360. Use the day-count the question gives for each currency.

Forward rate (compounded annual rates)

F = S × (1 + i_P)^T ÷ (1 + i_B)^T

Use when the question gives annual compounded rates for periods of a year or more.

Forward points

Points = (F − S) × scaling factor

Scaling factor is 10,000 for most pairs and 100 for yen pairs. Convert back by dividing by the factor.

Forward premium or discount

Premium (+) or discount (−) on base = (F − S) ÷ S

Positive means the base currency is worth more forward. This happens when i_P > i_B.

Value of a forward before expiry (long base currency)

V = [F_new − F_contract] ÷ [1 + i_P × T_remaining] per unit of base currency

F_new is the current forward rate for the remaining term. Multiply by notional. Value is in the price currency. The short position has the opposite sign.

BOP identity

Current account + Capital account + Financial account = 0

Holds apart from a statistical discrepancy. Reserve changes sit inside the financial account in the current IMF presentation.

Current account composition

CA = Net trade in goods and services + Net primary income + Net secondary income

Net means receipts minus payments.

Trade balance

Trade balance = Exports − Imports

A deficit is a negative value. It is only part of the current account.

Saving-investment identity

CA = S − I (S = total national saving, private + government; I = domestic investment)

Equivalent form: CA = (S_private − I) + (T − G), where S_private is private saving, T is government tax revenue and G is government spending. Government saving is T − G.

Financing link

CA deficit ⇒ net financial account inflow (a surplus in the financial account)

Direction matters: inflows from foreign purchases of domestic assets finance the deficit.

Covered interest rate parity (forward rate)

F(P/B) = S(P/B) × (1 + i_P × t) ÷ (1 + i_B × t)

t is the fraction of a year, using the day-count convention given (usually days ÷ 360). For one year, t = 1. Price currency P on top, base currency B on the bottom.

Forward premium or discount rule

If i_P > i_B, then F > S: the base currency B trades at a forward premium and the higher-rate price currency P trades at a forward discount

The base currency has the lower interest rate and the forward rate is higher. The higher-rate currency, here P, is at a forward discount: its value in B terms falls.

Uncovered interest rate parity

E(S1) ÷ S0 = (1 + i_P) ÷ (1 + i_B); approx. expected % change in the P/B rate ≈ i_P − i_B

If i_P is higher, the P/B rate is expected to rise, so the base currency B appreciates and the higher-yield price currency P depreciates. Uses the expected spot rate. No hedge, so it is an equilibrium idea, not a risk-free arbitrage.

Absolute PPP

S(P/B) = Price level in P ÷ Price level in B

Applies to a common basket. Rarely holds exactly.

Relative PPP

E(S1) = S0 × (1 + π_P) ÷ (1 + π_B); approx. % change in the P/B rate ≈ π_P − π_B

The currency with higher inflation depreciates. If π_P is higher, the P/B rate rises and P depreciates against B. Ex-ante version uses expected inflation.

Fisher relation

i ≈ r + E(π)

Nominal rate equals real rate plus expected inflation (approximation).

International Fisher effect

i_P − i_B ≈ E(π_P) − E(π_B), when real rates are equal

Combines Fisher with relative PPP. The nominal rate gap (i_P − i_B) approximately equals the expected percentage change in the P/B rate. If P has the higher nominal rate, the P/B rate is expected to rise, so P is expected to depreciate against B.

Mundell-Fleming summary (floating rates)

Monetary expansion: currency depreciates. Fiscal expansion: appreciates if capital mobility is high, depreciates if low

For mixed policy combinations, check the effect of each policy separately and see whether they agree.

Real exchange rate (d/f)

Real S(d/f) = S(d/f) × (CPI foreign ÷ CPI domestic)

Use the same quote direction as the nominal rate. Higher value = real depreciation of the domestic currency.

Change in real rate (approximate)

% change in real rate ≈ % change in nominal (d/f) + foreign inflation − domestic inflation

Approximation for small changes. Use the exact formula when options are close.

Marshall-Lerner condition

|ε exports| + |ε imports| > 1

ε = price elasticity of demand. Applies when trade is roughly balanced at the start. Sum above 1 means depreciation improves the trade balance.

J-curve pattern

Short run: trade balance worsens. Long run: it improves if Marshall-Lerner holds.

Reason: volumes are slow to adjust, but import prices rise at once.

Crisis warning signs

Falling reserves, large current account deficit, overvalued real rate, rapid credit growth, short-term foreign debt

Indicators, not guarantees. Know the list and the direction of each.

Quick revision

• Quote P/B means units of price currency per 1 unit of base currency; a rise in the quote means the base currency appreciates.
• Inverting a quote gives the quote in the opposite direction: B/P = 1 ÷ (P/B).
• Cross rate: combine two quotes so the common currency cancels; check that the result has the right base and price currency.
• Dealers buy the base currency at the bid and sell it at the offer; you buy at the offer and sell at the bid.
• Forward rate = spot × (1 + price currency rate × t) ÷ (1 + base currency rate × t), with the same time basis for rates and t.
• Forward points are the forward minus the spot, quoted in the unit set by the market convention; check the scale before you add them.
• The currency with the higher interest rate trades at a forward discount under covered interest parity.
• Fixed regimes need credibility and reserves; floating regimes let the market set the rate.
• Current account + capital account + financial account (including changes in official reserves) = 0 in principle; a current account deficit is financed by a net inflow in the financial account.
• Uncovered interest parity predicts the expected spot change from interest differentials; it often fails in the short run.
• Real exchange rate (d/f) = S(d/f) × CPI(f) ÷ CPI(d), where d is the domestic (price) currency and f the foreign (base) currency; a rise means the foreign currency has become more expensive in real terms.
• Currency crises often follow large deficits, falling reserves and loss of confidence in the peg.

Common mistakes

• Treating an FX swap as a currency swap. Fix: An FX swap is a spot plus an opposite forward. A currency swap exchanges periodic interest and principal over years.
• Classifying central banks or hedge funds as sell side. Fix: Sell side means dealer banks that quote prices. Central banks, hedge funds and corporations are buy side.
• Treating the first currency as the one you receive or pay in, instead of the base. Fix: Read A/B = x as 1 A costs x B. The price is always in the second currency.
• Using the bid when buying the base currency. Fix: Bid and ask are from the dealer's view. You buy the base at the ask and sell it at the bid.
• Putting the base-currency rate in the numerator. Fix: Always write P/B first. The rule is price-currency rate on top: the price currency (the numerator of the quote) has its rate in the numerator of the formula.
• Forgetting to scale points by 10,000 (or 100 for yen). Fix: Multiply by the scaling factor and say the answer in points. Check the options to see which form is expected.
• Treating the trade balance as the whole current account. Fix: Always add services, primary income and secondary income before judging the current account.
• Confusing the capital account with capital flows in general. Fix: Remember that the capital account is small (capital transfers and non-produced assets). Securities and loans are in the financial account.
• Inverting the ratio, putting the base currency's rate on top. Fix: Always write P/B first. The price currency's rate goes on top. Check direction: the higher-rate currency must end at a forward discount.
• Treating UIRP as a risk-free arbitrage like CIRP. Fix: CIRP uses the forward contract and is enforced by arbitrage. UIRP uses an expected spot rate and carries exchange rate risk. It often fails empirically.

Exam tips

• Expect conceptual items that ask you to classify a participant as sell side or buy side.
• Read carefully for FX swap versus currency swap wording.
• For date questions, count only business days and note the pair's convention.
• Know that NDFs settle in cash and are used for restricted currencies.
• With no penalty for wrong answers, never leave an item blank. Eliminate the clearly wrong options first.
• Write the quote as 1 base = x price on your scratch paper before anything else. It prevents most direction errors.
• Numerical options are listed from smallest to largest. Estimate the cross rate roughly first; often two options are on the wrong side of 1 and can be removed.
• Bid and ask are always the dealer's view and always for the base currency. Check this whenever a question asks what you pay or receive.