Question

The following Spot exchange rates are available: ¥64.00/SF, SF60/$ and, ¥105.00/$. You have $100,000 available. Can you make money by triangular arbitrage, and if so, how much?US dollars are currently being quoted at a 60-day Spot rate of $6050/£.

US dollars are also being quoted at a Forward rate of $6015/£. Is the dollar at a Forward Premium or Forward Discount and by what annualized percentage?

The Spot Singapore dollar is quoted Bid S$1.7160/US$ and Ask S$1.7200/US$. What is the direct Bid and Ask quote in the United States to the nearest 4 decimal points?

please show and explain all work!

Answer 1

The following Spot exchange rates are available: ¥64.00/SF, SF60/$ and, ¥105.00/$. You have $100,000 available. Can you make money by triangular arbitrage, and if so, how much?

E₁ = ¥ 64.00 / SF, E₂ = SF 60 / $ and E₃ = ¥ 105.00 / $

Implied ¥/$ rate = E₁ x E₂ = ¥ 64.00 / SF x SF 60 / $ = ¥ 3840 / $ (Please check the values in your question for any typo error, this appears to be very high in comparison to the actual, if your question values are correct, please do proceed with this solution)

Actual ¥/$ rate = ¥ 105.00 / $

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

Amount available, A = $ 100,000

Convert it into SF = E₂ x A = 60 x 100,000 = SF 6,000,000

Convert it into ¥ = SF 6,000,000 x E₁ = 6,000,000 x 64 = ¥ 384,000,000

Convert ¥ into $ = ¥ 384,000,000 / E₃ = $ 384,000,000 / 60 =  $ 6,400,000

So, i started with $ 100,000 and ended up with $ 6,400,000 by completing one full cycle of conversion between the currencies.

Hence, arbitrage gain = $ 6,400,000 - 100,000 = $ 6,399,000

(This value is unbelievable, i still believe there is some typo error in the exchange rates given in the question, but the mechanics of calculation remains the same)

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US dollars are currently being quoted at a 60-day Spot rate of $6050/£. US dollars are also being quoted at a Forward rate of $6015/£. Is the dollar at a Forward Premium or Forward Discount and by what annualized percentage?

Spot, S = $ 6,050/£ > $ 6,015/£ = F, Forward

hence, the dollar is at forward discount

Annualized %age forward discount = (1- F / S) x 360 / 60 = (1 - 6,015 / 6,050) x 360 / 60 = 3.47%

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The Spot Singapore dollar is quoted Bid S$1.7160/US$ and Ask S$1.7200/US$. What is the direct Bid and Ask quote in the United States to the nearest 4 decimal points?

Direct bid quote in the United states =  1/ 1.7160 = 0.5828

Direct ask in the United States = 1 / 1.7200 =  0.5814