Question

Given the following prices and rates,

USD borrow and lend rates: 4% and 2.5%

SF borrow and lend rates: 3% and 1.5%

Spot $/SF bid and ask: $0.9705/SF and $0.9710/SF

Forward $/SF bid and ask: $1.025/SF and $1.030/SF

a. Is there an arbitrage opportunity available (show why or why not – provide a numerical justification for your answer and explain what that numerical justification means)?

b. If there is an arbitrage opportunity, how would you exploit it? The forward contract expires in one year and the interest rates are annual. If you engage in an arbitrage strategy, please provide a description of every transaction and cash flow. If you need to borrow, assume you borrow 100 units of the currency.

Answer 1

Solution;

(A) There exist a arbitrage oppurtinuity available as per intrest rate parity theorem (IRPT)

As per IRPT  Forward rate/ Spot Rate = 1+ R.H.S currency borrowing rate/ 1+ L.H.S currency barrowing Rate

It is given $ in R.H.S and SF in L.H.S  

Consider R.H.S currency borrowing rate as y

Substituting IRPT Formula =1.03$/0.9710 = 1+y%/1+3%

Solving above Equation we get y=9.2% ( theoritical interest Rate)

Actual intrest rate =4%

Theoritical interest rate is greater than actual interest rate there exist arbitrage opputunity

(B) Barrow 100 $ from usd @ 4% for one year

now convert $ to Sf at spot rate of $.9705 per SF(ask rate)

No of SFs =100$x.0.9705=97.05 invest for 1Year @ 1.5% intrest amount=4.8525

Total amount=97.05+4,8524=101.9025

now covert total amount to $ at forward rate =101.9025x 1.025=104.45$

Dollers Requred = 100$+4% =104$

Arbitrage Gain   =0.45$