Currency & Forex

Exchange-rate conversion, cross rates, spreads, pips and purchasing-power measures used in foreign exchange

Foreign = Domestic \times Rate

Convert an amount from one currency to another using the quoted exchange rate.

Rate_{B/A} = \dfrac{1}{Rate_{A/B}}

Flip a quoted rate to express it from the other currency’s point of view.

\%\Delta = \dfrac{Rate_1 - Rate_0}{Rate_0}\times 100\%

The percentage move in an exchange rate between two points in time.

Rate_{A/C} = Rate_{A/B} \times Rate_{B/C}

Derive the exchange rate between two currencies via a common third currency.

Spread = Ask - Bid

The gap between the price to buy and to sell a currency — the dealer’s markup.

Spread\% = \dfrac{Ask - Bid}{Ask}\times 100\%

The bid-ask spread expressed as a percentage of the ask price.

Pip\ Value = \dfrac{Pip\ Size}{Rate}\times Lot

The monetary value of a one-pip move for a given trade size.

App\% = \dfrac{Rate_1 - Rate_0}{Rate_0}\times 100\%

The percentage by which a currency strengthens (positive) or weakens (negative).

S = \dfrac{P_{domestic}}{P_{foreign}}

The exchange rate that would equalize the price of an identical basket of goods across countries.

RER = S \times \dfrac{P_{foreign}}{P_{domestic}}

The nominal rate adjusted for price levels, measuring relative purchasing power.

F = S \times \dfrac{1 + i_d}{1 + i_f}

The agreed future exchange rate implied by interest-rate differentials (covered interest parity).

Profit = \left(\dfrac{1}{R_{AB}} \times R_{AC} \times R_{CB}\right) - 1

A riskless profit captured when three currencies’ cross rates are momentarily inconsistent.