IAI Actuarial Core Principles · Business Economics

Balance of payments and exchange rates: formula sheet

Full chapter guide

Key formulas

Balance of payments identity: Current account + Capital account + Financial account + Errors and omissions = 0; The sum-to-zero form holds when the financial account is recorded as credits minus debits, so a net capital inflow is positive. Under the net-acquisition-of-assets convention (IMF BPM6), write CA + KA = FA + E&O, which is the same as CA + KA − FA − E&O = 0. State your sign convention in written answers.
Current account: CA = (X − M) + net primary income + net secondary income; X − M is the balance on trade in goods and services. Net means credits minus debits.
Trade balance: Trade balance = Exports of goods − Imports of goods; Positive is a surplus, negative is a deficit. This is only part of the current account.
Financing of a deficit: CA deficit = net capital inflow (capital + financial account, including reserve changes); Under the older presentation, the capital account and financial account together are shown as net capital inflow.
Saving-investment link: CA = S − I (national saving minus domestic investment); A current account deficit means the country invests more than it saves.
Exchange rate quote: Domestic price of foreign currency = units of domestic currency per 1 unit of foreign currency; Example: ₹85 per $1. A rise in this number means the rupee has depreciated. State which quote you use.
Equilibrium condition: Demand for currency = Supply of currency; The floating rate adjusts until the two are equal. Here the price of the currency means the foreign currency price of one unit of the domestic currency, for example $ per ₹1. It is not the ₹ per $ number. When the price of the currency is above equilibrium, there is excess supply of that currency. When it is below equilibrium, there is excess demand.
Percentage change in exchange rate: % change = (New rate − Old rate) ÷ Old rate × 100; Use the same quote for both rates. With rupees per dollar, a positive result means the rupee has depreciated.
Inverse of a quote: Foreign currency per ₹1 = 1 ÷ (₹ per 1 unit of foreign currency); Use this to switch quotes. The rupee appreciates when ₹ per $ falls, and when $ per ₹ rises.
Direction of shifts (rule): Higher demand for the currency → appreciation; higher supply of the currency → depreciation; Other things equal. Always say which curve shifts first.
Exchange rate quote: Domestic price of foreign currency = ₹ per 1 unit of foreign currency; A rise in ₹ per US$ means the rupee has depreciated. Always state which currency is the base.
Percentage change in a currency: % change in foreign currency's value = (new rate − old rate) ÷ old rate × 100; Rate is quoted as ₹ per unit of foreign currency. A positive result means the foreign currency has appreciated and the rupee has depreciated.
Defence of a peg: weak currency: Central bank sells foreign reserves, buys domestic currency, and may raise interest rates; Reserves fall. This cannot go on if reserves run out.
Defence of a peg: strong currency: Central bank sells domestic currency, buys foreign currency, and may cut interest rates; Reserves rise. Unsterilised sales can raise the money supply and inflation.
Reserves cover: Import cover (months) = foreign exchange reserves ÷ average monthly imports; A common reserve adequacy measure. Higher cover gives more room to defend the currency.
Law of one price: P(domestic) = S × P(foreign); S is the domestic price of one unit of foreign currency (for example ₹ per US$). Holds for a tradable good with no transport costs or barriers.
Absolute PPP: S = P(domestic basket) ÷ P(foreign basket); Same quote as above. Assumes identical baskets. Rarely holds exactly.
Relative PPP (approximate): % change in S ≈ inflation(domestic) − inflation(foreign); A higher domestic inflation rate means the domestic currency depreciates (S rises).
Relative PPP (exact): S1 = S0 × (1 + i_d) ÷ (1 + i_f); i_d and i_f are domestic and foreign inflation over the period. S0 is the starting rate.
Real exchange rate: R = S × P(foreign) ÷ P(domestic); S is domestic currency per unit of foreign currency. A rise in R means domestic goods are cheaper relative to foreign goods (more competitive). R is constant if PPP holds.
Covered interest parity: F = S × (1 + i_d) ÷ (1 + i_f); F is the forward rate, quoted as domestic currency per unit of foreign currency, for the same period as the interest rates. Higher domestic rate means forward premium for the foreign currency.
Uncovered interest parity: E(S1) = S0 × (1 + i_d) ÷ (1 + i_f); Uses the expected future spot rate. Approximately: expected % change in S ≈ i_d − i_f.
Marshall-Lerner condition: |PEDx| + |PEDm| > 1; PEDx is price elasticity of demand for exports, PEDm for imports. If the sum is above 1, depreciation improves the trade balance. If it equals 1, no change. If below 1, it worsens. Standard form assumes trade starts near balance and supply is elastic.
Exchange rate change: % change in rate = (new rate − old rate) ÷ old rate × 100; Be clear on quotation. If the rate is ₹ per $, a rise means rupee depreciation.
Elasticity: PED = % change in quantity demanded ÷ % change in price; Use absolute values when applying Marshall-Lerner.
Net exports: Net exports = X − M; Trade balance in value terms. Net exports is a component of aggregate demand: AD = C + I + G + (X − M).
Foreign-currency price of exports: Foreign price = rupee price ÷ exchange rate (₹ per unit of foreign currency); A higher ₹ per $ rate lowers the dollar price of an Indian export, if rupee price stays fixed.

Quick revision

The BoP records all transactions between residents and the rest of the world over a period.
The current account covers trade in goods and services, income and transfers.
The capital and financial accounts record asset transfers and cross-border investment and lending.
In principle the BoP balances overall, so a current account deficit is matched by net inflows elsewhere.
A currency appreciates when demand for it rises relative to supply, and depreciates in the opposite case.
Higher domestic interest rates tend to attract capital and raise the currency, other things equal.
In a fixed regime the central bank must buy or sell currency and hold reserves to defend the rate.
Floating rates adjust freely, but can be volatile and pass shocks into inflation and trade.
Absolute PPP says the exchange rate equals the ratio of price levels; relative PPP links rate changes to inflation differences.
Covered IRP says the forward premium or discount offsets the interest rate difference, so there is no risk-free arbitrage.
PPP and IRP depend on assumptions such as free trade, no transport costs and free capital movement.
A weaker currency can help exports but raises import prices and may raise inflation.

Common mistakes

Saying the balance of payments can be in deficit overall. Fix: Say the BoP always balances by construction. Deficits and surpluses refer to specific accounts, such as the current account.
Confusing the trade balance with the current account. Fix: Remember the current account also includes services, primary income and secondary income such as remittances.
Using devaluation or revaluation for a floating rate Fix: Floating rates depreciate or appreciate. Devaluation and revaluation are deliberate official changes in a fixed or pegged system.
Reading the quote the wrong way round Fix: Write the quote in words first. If ₹ per $ rises, the rupee buys fewer dollars, so it has depreciated.
Confusing devaluation with depreciation. Fix: Devaluation is an official decision under a fixed regime. Depreciation is a market-driven fall under a floating regime.
Reading the quote the wrong way round. Fix: If the quote is ₹ per US$, a higher number means the rupee has weakened. Write the quote down before you reason.
Inverting the exchange rate quote, so the answer moves the wrong way. Fix: Write the quote at the start. If S is foreign per home currency, the ratio in the formula flips to (1 + i_f) ÷ (1 + i_d).
Saying a higher interest rate means the currency strengthens in the forward market. Fix: Under covered parity the high interest rate currency trades at a forward discount, which removes the gain from the extra interest.
Saying depreciation always improves the trade balance. Fix: Always test the Marshall-Lerner condition. Improvement needs the elasticity sum to exceed 1, and it is often delayed.
Using only one elasticity, such as export elasticity alone. Fix: Add the export and import elasticities (absolute values) and compare the sum with 1.

Exam tips

Always name the account when you say deficit or surplus. Writing "the BoP is in deficit" can lose marks.
State your sign convention in numerical questions, because the textbook and the IMF presentations treat the financial account differently.
Learn two or three items per account so you can classify quickly in MCQs. Remittances are secondary income, FDI is financial account.
For written questions, link the current account to the exchange rate, demand and competitiveness. Then discuss financing and sustainability.
Practise a short explanation of why the BoP always balances. It is a common 3-4 mark question.
Draw a small demand and supply diagram for the currency, with the exchange rate on the vertical axis. Label the axes and the quote.
In written answers, name the curve that shifts first and then the direction of the change in rate. Marks usually go to that chain.
Use the words appreciation and depreciation for floating rates, and state "other things equal".