3. Currently, the spot exchange rate is $1.5 O/E and the three-month forward exc

Question

3. Currently, the spot exchange rate is $1.5 O/E and the three-month forward exchange rate is S1.52/f. The three-month interest rate is 8.0 percent per annum in the U.s. and 5.8 percent per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000. a. Determine whether interest rate parity is currently holding. b. If IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit. c. Explain how IRP will be restored as a result of covered arbitrage activities.

Explanation / Answer

a) Interest Rate Parity Theory (IRPT) is given by

[(1+Rh) / (1+Rf)]^n= F1 / So

Where

Rh - Interest rate in home country =8% pa = 2%(8*3/12) for 3 months

Rf - Interest rate in foreign country = 5.8% = 1.45% (5.8*3/12)for 3 months

F1 - 3 months forward rate = ?

S0 - spot rate = 1.50

Here exchange rate is given in the format of $/£. That is US is the home country and UK is the foreign country.

(1.02)/(1.0145) = F1/1.5

F1 = (1.02*1.5)/1.0145

F1 = 1.51

Forward rate as per IRPT comes to $1.51/£. But the forwrd exchnge rate comes to $1.52/£. Hence IRPT is not holding currently.

b)

- Borrow $1,500,000

- Borrow £1,000,000

Since step 8 gives negative value, no arbitrage in this case.

c) Lets find out the Rh by putting F1=1.52

(1+Rh)/(1.0145) = 1.52/1.5

1+Rh = (1.52*1.0145)/1.50

= 1.0280

Rh = 1.0280-1

= .0280

Fair Rh = 2.80% pee 3 months = 11.20% per annuam

Fair Rh(11.20%) > Actual Rh(8%). Therefore money will flow from US to UK, even though the actual interest rate is higher in US. Hence IRPT is restored.

As you say above there will be arbitrage only when borrow in $. When borrow in £, there will be arbitrage loss.

1 Borrow at 8% pa $1,500,000 2 Convert to £ at spot exchange rate of 1.50 1,5000,000/1.50 £1,000,000 3 Invest in Uk at 5.8% per annum £1,000,000 4 Take forward cover for $1.52/£ 5 Realise the maturity value of investment £1,000,000+£1,000,000*5.8%*3/12 £1,014,500 6 Reconvert to $ at forward rete of $1.52/£ £1,014,500*1.52 $1,542,040 7 Repay the borrowings in step 1 $1500000+ $1500000*8%*3/12 $1,530,000 8 Arbitrage Gain (Step 6- Step7) 1542040-1530000 $12,040

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