Question

1)Citibank quotes USD1.8500/GBP, Barclays quotes EUR1.5000/GBP, and Dresdner quotes USD1.2000/EUR. If you have USD 1,000,000 to invest, find the triangular arbitrage profit.

2)Amanda Smyth is a foreign exchange dealer for a bank in Texas. She has USD 1,000,000 for a short-term money market investment and wonders if she should invest in U.S. dollars for six months or make a covered interest arbitrage (CIA) investment in the Japanese yen. If she makes the CIA investment, what is the total amount that Amanda will earn at maturity? Assume the following rates.

Spot Rate		6-mo Forward Rate		USD 6-mo Interest Rate			JPY 6-mo Interest Rate
JPY120/USD		JPY118.25/USD		6% per annum			4% per annum

Answer 1

1.)

Citibank quotes GBP 1 = USD 1.8500

Bardays quotes GBP 1 = EUR 1.5000

Dresdner quotes EUR 1 = USD 1.2000

Steps for triangular arbitrage are as follows :
STEP 1 - Convert USD 1,000,000 To EUR Using Dresdner Quote

EUR Received = USD 1,000,000 * EUR (1/1.20) / USD

= EUR 833,333.33

STEP 2 - Convert EUR to GBP using Bardays quote

GBP Received = EUR 833,300 * GBP (1/1.50) / EUR

= GBP 555,555.55

STEP 3 - Now, convert GBP receipt to USD using Citibank quote

USD Received = GBP 555,555.55 * USD 1.85 / GBP

= USD 1,027,777.77

Triangular Arbitrage Profir = USD 1,027,777.77 - USD 1,000,000

= USD 27,777.77

2.

Amount available for investment = USD 1,000,000

AT T₀

Step 1 - Sell USD 1,000,000 at SPOT

JPY Received = USD 1,000,000 * JPY 120 / USD

= JPY 120,000,000

Step 2 - Invest JPY 120,000,000 for 6 months @ 4% per annum

Step 3 - Enter into 6 month forward USD buy contract .

AT T_{6 MONTHS}

Receipt of maturity amount of investment = JPY 120,000,000 ( 1 + 0.04 * 6/12 )

= JPY 120,000,000 * 1.02

= JPY 122,400,000

Execute the forward contract and buy USD = JPY 122,400,000 * USD (1/118.25) /JPY

= USD 1,035,095.14

Hence, Amanda will earn USD 1,035,095.14 at maturity.