Exchange Rate Calculations

How to build a cross-rate from two quotes against a common currency, why cross-rates must agree with their components (triangular arbitrage), how to read currency moves in percentage terms, and how forward rates follow from spot rates, interest rates and maturity through a no-arbitrage relationship, quoted as forward points or percentages.

1. 1. Building a cross-rate from two quotesTreat every quote as a fraction, price currency over base currency, and chain two quotes so the common currency cancels; sometimes one quote must be inverted first.Video · 6 minFree12 min
2. 2. Triangular arbitrage and reading currency movesA quoted cross-rate must match the rate implied by the two underlying quotes, or traders earn a riskless profit by trading around the triangle; and a change in a quote tells you which currency strengthened and by how much.13 min
3. 3. Forward points, premiums and discountsForward rates are quoted as points added to the spot rate, scaled to the spot quote's last decimal; positive points mean the base currency trades at a forward premium.12 min
4. 4. The no-arbitrage link between spot, forward and interest ratesInvesting at home and investing abroad with the currency risk hedged forward are both riskless, so they must earn the same; that one condition fixes the forward rate.Video · 6 min14 min
5. 5. Forward points, maturity and the rate differentialFor horizons shorter than the rate period, forward points equal spot times the interest rate differential scaled by the fraction of the year, so they are proportional to the differential and almost proportional to maturity.13 min
6. 6. Integrated cases: hedging a receivable and comparing dealersA hedging case chains a cross-rate, a forward calculated from rates or points, a conversion of the receivable (divide when it is in the price currency) and a dealer comparison that may mix points with percentages.16 min