🌐 Economics

Exchange Rate Calculations — Forward Rates & Interest Rate Parity

Exchange rate formulas: spot rates, forward rates, cross rates, and covered interest rate parity. How to calculate forward exchange rates with examples.

Key Concepts

Exchange Rate Quotation

Direct: domestic per foreign (e.g., 1.25 USD/EUR). Indirect: foreign per domestic. Price/Base convention: P/B.

Bid-Ask Spread

Dealer buys at bid, sells at ask. Spread = ask - bid. Always buy high (ask) and sell low (bid) from YOUR perspective.

Cross Rates

Exchange rate between two currencies derived through a third. A/C = (A/B) × (B/C).

Forward Exchange Rate

Rate agreed today for exchange in the future. Forward premium: forward > spot. Forward discount: forward < spot.

Covered Interest Rate Parity

Forward premium/discount reflects interest rate differential. Eliminates arbitrage between money markets and FX forwards.

Triangular Arbitrage

Exploiting mispricing among three currency pairs. If cross rate differs from market rate, profit is possible.

Formulas

From this module

Cross Rate

A/C = (A/B) × (B/C)

Where: Multiply rates to find the cross rate

Forward Rate (CIP)

F/S = (1 + rprice) / (1 + rbase)

Where: F = forward, S = spot, r = interest rate for the period

Forward Premium/Discount

Forward Premium = (F - S) / S × (360/days)

Where: Annualized forward premium

Bid-Ask with Cross Rates

(A/C)bid = (A/B)bid × (B/C)bid

Where: Take bid of bid, ask of ask for cross

Master Formula Sheet -- Economics

GDP (Expenditure)

GDP = C + I + G + (X - M)

Consumption + Investment + Government + Net Exports

Fiscal Multiplier

Multiplier = 1 / (1 - MPC)

MPC = marginal propensity to consume

Quantity Theory of Money

M × V = P × Y

Money supply × Velocity = Price level × Real output

Fisher Equation

Nominal rate ≈ Real rate + Inflation

Exact: (1+nom) = (1+real)(1+inf)

Elasticity of Demand

E = %ΔQ / %ΔP

|E| > 1: elastic, |E| < 1: inelastic

No-Arbitrage Forward Rate

F = S × (1 + rₐ)/(1 + r_b)

Interest rate parity

Real Exchange Rate

Real FX = Nominal FX × (P_foreign / P_domestic)

Adjusting for price levels

Decision Frameworks

How to determine if arbitrage exists?

Use when:

  • Compare calculated cross rate to market cross rate
  • If different, buy low and sell high through the triangle
  • Forward rate vs spot × interest rate differential for covered interest arbitrage

Avoid when:

  • Ignoring transaction costs which may eliminate the arbitrage profit

Test Your Understanding

If the USD/EUR spot rate is 1.10 and the 1-year US interest rate exceeds the EUR rate, the forward USD/EUR rate will be:

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