# FIN 3410 Lecture Notes - Lecture 2: Srf 1, Direct Market, U.S. Route 3

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Day 2 Notes

EX: 5-11

Triangular Arbitrage

DRB: S(X/$) = 0.7627 $1 = 0.7627 X

CS: S(SF/$) = 1.1806 $1 = SF 1.1806

UBS is making a direct market between SF and X

UBS: S(X/SF) = 0.6395 SF 1 = 0.6395 X

I = $5,000,000 (available for the arbitrage)

1. Show how to make a triangular arbitrage profit

2. Find the implied cross-rate

a. Si(X/SF) = S(X/$) / S(SF/$) = [0.7627 X / $] / [SF 1.1806 / $]

i. = 0.6460 X/SF

b. Si(X/SF) = 0.6460 X/SF =/= S(X/SF) = 0.6395 X/SF

i. Implied cross-rate does not equal UBS quote, so arbitrage is

possible

3. Directions of trade

a. Implied cross rate: 1 SF = 0.6460 X

b. UBS: 1 SF = 0.6395 X

i. SF is cheaper in the UBS (direct) trade buy SF from UBS (buy

low)

1. X SF

ii. Sell SF to CS (sell high)

1. SF $

4. Trades

a. Buy X with $ $5,000,000 at S = 0.7627 X/$

i. $5,000,000 * (0.7627 X/$) = 3,813,500 X

b. Buy SF with X at S(X/SF) = 0.6395 X/SF

i. 3,813,500 X / (0.6395 X/SF) = 5,963,253 SF

c. Sell SF to CS at S(SF/$) = 1.1806 SF/$

i. 5,963,253 SF / (1.1806 SF/$) = $5,051,036

d. Arbitrage profit

i. $5,051,036 - $5,000,000 = $51,036

5. What happens if you initially sell $ for SF?

a. Losses!

6. What X/SF price will eliminate a triangular arbitrage?

a. UBS cross rate S(X/SF) should equal the implied cross rate 0.6460 X/SF

Forward Contract: agreement to buy or sell an asset in the future at prices agreed

upon today

Markets expect value of L in $ terms

Markets expect that L will depreciate against $ ($ will appreciate against L)

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