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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