Question

1. The following Spot exchange rates are available: ¥64.00/SF, SF1.60/$ and, ¥105.00/$. You have $100,000 available. Can you make money by triangular arbitrage, and if so, how much?

please show and explain all work!

Answer 1

The exchange rates now appear to be in order.

E₁ = ¥ 64.00 / SF, E₂ = SF 1.60 / $ and E₃ = ¥ 105.00 / $

Implied ¥/$ rate = E₁ x E₂ = ¥ 64.00 / SF x SF 1.60 / $ = ¥ 102.40 / $

Actual ¥/$ rate = ¥ 105.00 / $

Since Implied ¥/$ rate < Actual ¥/$ rate , there exists an arbitrage opportunity.

Amount available, A = $ 100,000

Convert it into ¥ = E₃ x A = 105 x 100,000 = ¥ 10,500,000

Convert it into SF = ¥ 10,500,000 / E₁ = 10,500,000 / 64 = SF 164,062.50

Convert SF into $ = SF 164,062.50 / E₂ = 164,062.50 / 1.60 = $ 102,539.06

So, i started with $ 100,000 and ended up with $ 102,539.06 by completing one full cycle of conversion between the currencies.

Hence, arbitrage gain = $ 102,539.06 - 100,000 = $ 2,539.06