1. © 2012 Pearson Education, Inc. All rights reserved.6-1 6.1The Theory of Covered Interest Rate Parity The intuition behind interest rate parity Two ways to buy a currency forward Enter into a forward contract Borrow domestic currency, buy foreign currency on spot market and invest for term Why there must be interest rate parity If not, arbitrage possibilities would exist Forces relationship between forward/spot rates and the interest rate differential between two countries F h/f / S h/f = (1 + i h ) / (1 + i f ).

2. © 2012 Pearson Education, Inc. All rights reserved.6-2 6.1The Theory of Covered Interest Rate Parity $10M to invest; i U.S. =8%; i U.K. = 12%; S=$1.60/£; F 1-yr = $1.53/£ 1.Convert into forex using spot rate: $10M/$1.60/£ = £6.25M 2.Invest at foreign interest rate: £6.25M * 1.12 = £7M 3.Convert back at forward rate: £7M * $1.53/£ = $10.71M 4.Compare to what you could have earned by just investing in your home nation: $10M * 1.08 = $10.8M Investing at home (U.S.) is more profitable for Kevin. But what if he could borrow/lend? Is the answer still the same?

3. © 2012 Pearson Education, Inc. All rights reserved.6-3 6.1The Theory of Covered Interest Rate Parity $10M to invest; i U.S. =8%; i U.K. = 12%; S=$1.60/£; F 1-yr = $1.53/£ 1.Borrow pounds: £1M at 12%. £1.12M is what Kevin owes at time of repayment 2.Convert pounds to dollars: £1.00M * ($1.60/£) = $1.6M 3.Invest at U.S. interest rate: $1.6M * 1.08 = $1.728M 4.Convert back at forward rate: $1.728M/$1.53/£ = £1,129,411.76 Kevin would make £9,411.76 (Step 4 – Step 1) profit for every £1M that is borrowed!

4. © 2012 Pearson Education, Inc. All rights reserved.6-4 6.1The Theory of Covered Interest Rate Parity Deriving interest rate parity –Stating that when the forward rate is priced correctly, an investor is indifferent between investing at home or abroad –General expression for interest rate parity [1+i] = [1/S] * [1+i*] * F –Interest rate parity and forward premiums and discounts (1+i)/(1+i*) = F/S Subtracting 1 from each side and simplifying we obtain (F-S)/S If the result of this equation is (+), the forward is selling at a premium, if it is (-), the forward is selling at a discount

5. © 2012 Pearson Education, Inc. All rights reserved.6-5 Exhibit 6.1 Diagram of Covered Interest Arbitrage

6. © 2012 Pearson Education, Inc. All rights reserved.6-6 Exhibit 6.2 Interest Rates in the External Currency Market Lower than they would be due to the skirted regulations and increased Competition, i.e., supply of said currency Annualized rate * (1/100) * (number of days/360) = de-annualized rate

7. © 2012 Pearson Education, Inc. All rights reserved.6-7 6.2Covered Interest Rate Parity in Practice External currency market influences rates elsewhere –Loans to investors/corporations are based on these interbank rates –Most important of rates is LIBOR Covered interest arbitrage with transaction costs

8. © 2012 Pearson Education, Inc. All rights reserved.6-8 Exhibit 6.3 Covered Interest Rate Parity with Bid-Ask Rates

9. © 2012 Pearson Education, Inc. All rights reserved.6-9 An Example with Transaction Costs Borrow $10M at 1.11 % per annum, for 3 months (0.2775 %) Convert $10M to yen: $10M * ¥82.67/$ = ¥826.7M Invest for 3 months 0.46 * (1/100) * (90/360) = 0.00115 ¥826.7M * 1.00115 = ¥827,650,705 Sell forward (enter into forward contract) (¥827,650,705)/ (¥82.6495/$) = $10,013,983 Compare to what we would make in U.S. $10,013,983 - ($10M * 1.002775) = - $13,767 We lose money this way – no arbitrage this way, but borrowing yen results in losses as well $10M to investBidAsk Spot (¥/$)82.6782.71 Forward (¥/$)82.589582.6495 Dollar int. rate0.911.11 Yen int. rate0.460.58

10. © 2012 Pearson Education, Inc. All rights reserved.6-10 6.2Covered Interest Rate Parity in Practice Does covered interest rate parity hold? –Prior to 2007, documented violations of interest rate parity were very rare –Frequency, size and duration of apparent arbitrage opportunities do increase with market volatility

11. © 2012 Pearson Education, Inc. All rights reserved.6-11 6.3Why Deviations from Interest Rate Parity May Seem to Exist Too good to be true? –Default risks – risk that one of the counterparties may fail to honor its contract –Exchange controls Limitations Taxes –Political risk A crisis in a country could cause its government to restrict any exchange of the local currency for other currencies. Investors may also perceive a higher default risk on foreign investments.

12. © 2012 Pearson Education, Inc. All rights reserved.6-12 Exhibit 6.4 Covered Interest Parity Deviations During the Financial Crisis

13. © 2012 Pearson Education, Inc. All rights reserved.6-13 6.4Hedging Transaction Risk in the Money Market When Interest Rate Parity holds, there are two ways to hedge a transaction (either a liability or a receivable) Forward hedge Money market hedge

14. © 2012 Pearson Education, Inc. All rights reserved.6-14 6.4Hedging Transaction Risk in the Money Market Hedging a foreign currency liability

15. © 2012 Pearson Education, Inc. All rights reserved.6-15 6.4Hedging Transaction Risk in the Money Market Hedging a foreign currency receivable