# Indirect Quote

Indirect quote is the reporting of foreign exchange rate in terms of units of foreign currency per unit of domestic currency. For a resident of the United States intending to buy/sell British pounds, it means exchange rates expressed in British pounds per unit of US dollar.

## Formula

An indirect quote is the inverse of the direct quote.

When the foreign exchange rate is expressed as a mid-quote, the following formula can be used to calculate the indirect quote:

Indirect Quote = | 1 |

Direct Quote |

Where the foreign exchange rate is expressed in terms of bid and ask spread, indirect quote can be calculated by finding the inverse of both prices and switching their positions. It means that the direct bid becomes the indirect ask and the direct ask becomes the indirect bid. Direct quote of (x − y) would become indirect quote of (1/y − 1/x).

## Examples

**Example 1:** An Australian resident converted 500,000 AUD to 45,139,200 JPY. Find the indirect quote for the Australian resident.

__Solution__

For an Australian resident, Australian Dollar (AUD) is the domestic currency while Japanese Yen (JPY) is the foreign currency. Indirect quote expresses foreign currency in terms of one unit of domestic currency. Indirect quote in this situation would be 90.2784 JPY/AUD (45,139,200 JPY per 500,000 AUD).

Relevant direct quote would be 0.011077 JPY/AUD (=1/(90.2784 JPY/AUD)).

**Example 2:** EUR/USD exchange rate is 1.3391 − 1.3392. This is the direct quote for a resident of the European Union.

Since the exchange is quoted as bid-ask, we find reciprocals of both prices and switch their positions to get the relevant indirect quote.

Indirect exchange rate between Euro and US dollar for the European resident would be (0.7467 − 0.7468). The new bid is 0.7467 calculated as the inverse of the direct ask (1.3392), while 0.7468 is the new ask and is calculated as the inverse of the direct bid (1.3391).

Written by Obaidullah Jan, ACA, CFA