A London listed share trades at 850 pence and its American depositary receipt represents 5 ordinary shares. GBPUSD is 1.2650 and the receipt trades at $53.50. What is the receipt's fair price and the gross arbitrage per receipt?

A London listed share trades at 850 pence and its American depositary receipt represents 5 ordinary shares. GBPUSD is 1.2650 and the receipt trades at $53.50. What is the receipt's fair price and the gross arbitrage per receipt?

Approach: Convert the ordinary share price into pounds, multiply by the number of shares in the receipt, convert at spot, then compare with the traded price and net off the frictions.

$53.7625. The ordinary share is 850 pence, so 8.50 pounds, and the conversion ratio of five shares per receipt makes 42.50 pounds; at 1.2650 that is 42.50 * 1.2650 = $53.7625. The receipt at $53.50 is cheap by 26.25 cents, which is 0.49% of fair. Capturing that arbitrage means buying the receipt, cancelling it into ordinary shares through the depositary, selling the ordinaries in London and selling the pounds for dollars. The cancellation fee is typically 2 to 5 cents a receipt, the London leg pays a half spread, and cross-currency pricing has to use the exchange rate you can deal on rather than the mid, so the tradable part of a 26 cent gap is a fraction of the headline.

Follow-up: The London market closes five hours before the US close. How do you price the receipt in those five hours and what risk are you running?

Key concepts: depositary receipt, conversion ratio, cross-currency pricing, arbitrage.