James Clark is a foreign exchange trader with Citibank. He notices the following
ID: 2765091 • Letter: J
Question
James Clark is a foreign exchange trader with Citibank. He notices the following quotes.
Spot exchange rate SFr1.2051/$
Six-month forward exchange rate SFr1.1922/$
Six-month $ interest rate 2.5% per year
Six-month SFr interest rate 2.0% per year
A)Is the interest rate parity holding? You may ignore transaction costs.
B)Is there an arbitrage opportunity? If yes, show what steps need to be taken to make arbitrage profit. Assuming that James Clark is authorized to work with $1,000,000, compute the arbitrage profit in dollars.
C)Repeat the spreadsheet analysis as above, but this time obtaining two NPV values (when parity conditions do not hold) in Euros rather than pesos.
Explanation / Answer
Interest rate parity: Forward rate = spot rate*(1+interest rate of other country)/(1+interest rate of home country interest rate)
Forward rate = .2051*(1+.02/2) / (1+.025/2)
Forward rate = .204594 Since given forward rate is different from calculated forward rate therefore interest rate parity is not holding.
As interest parity doesn't hold here, there is an opportunity for arbitrage
i. Borrow $1M in the U.S.
ii. Convert $1M to SFs at S0 = $(1/1.2051)/SF
$1M * SF(1.2051)/$ = SF 1,205,100
iii. Invest SF 1,205,100 in Switzerland at iCHF = 2% APR
SF 1,205,100 * (1 + interest rate) = SF 1,205,100 *{1 + (0.02/2)} = SF 1,217,151
iv. Convert SFs into $s to realize revenue at F6mo = $(1/1.1922)/SF
SF 1,217,151 * $(1/1.1922)/SF = $1,020,928.54
v. Calculate the debt
$1M * (1 + interest rate) = $1M * {1 + (0.025/2)} = $1,012,500
vi. Realize profit
$1,020,928.54 - $1,012,500 = $8,428.54
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