© 2012 pearson education, inc. all rights reserved.6-1 6.1the theory of covered interest rate...

© 2012 Pearson Education, Inc. All rights reserved. 6-1

6.1 The 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

• Fh/f / Sh/f = (1 + ih) / (1 + if).



$10M to invest; iU.S.=8%; iU.K.= 12%; S=$1.60/£;

F1-yr = $1.53/£

1. Convert into forex using spot rate: $10M/$1.60/£ = £6.25M2. Invest at foreign interest rate: £6.25M * 1.12 = £7M3. Convert back at forward rate: £7M * $1.53/£ = $10.71M4. Compare to what you could have earned by just investing in

your home nation: $10M * 1.08 = $10.8MInvesting at home (U.S.) is more profitable for Kevin.

But what if he could borrow/lend? Is the answer still the same?



$10M to invest; iU.S.=8%; iU.K.= 12%; S=$1.60/£;

F1-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/£) = $1.6M3. Invest at U.S. interest rate: $1.6M * 1.08 = $1.728M4. 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!



• 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/SSubtracting 1 from each side and simplifying we obtain(F-S)/SIf the result of this equation is (+), the forward is selling at a premium, if it is (-), the forward is selling at a discount


Exhibit 6.1 Diagram of Covered Interest Arbitrage


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


6.2 Covered 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


Exhibit 6.3 Covered Interest Rate Parity with Bid-Ask Rates


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 months0.46 * (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 invest Bid Ask

Spot (¥/$) 82.67 82.71

Forward (¥/$) 82.5895 82.6495

Dollar int. rate 0.91 1.11

Yen int. rate 0.46 0.58


6.2 Covered 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


6.3 Why 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.


Exhibit 6.4 Covered Interest Parity Deviations During the Financial Crisis


6.4 Hedging 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



Hedging a foreign currency liabilityZachy's Wine and Spirits is importing some winefrom France for €4 million. It is payable in 90 days.

Spot exchange rate: $1.10/€90-day forward: $1.08/€90-day dollar interest rate: 6.00% p.a.90-day euro interest rate: 13.519% p.a.

Choice #1: Enter into a forward contractCost in 90 days is: €4,000,000 * ($1.08/€) = $4,320,000Choice #2: Money market hedgeInvest X amount now to become what you owe in 90 daysbut how much?€4,000,000/[1 + (13.519/100)(90/360)] = €3,869,229.71We buy this @ Spot rate: €3,869,229.71 * $1.10/€ = $4,256,152.68To compare the two, we need to take the PV of the forward hedge$4,320,000/[1 + (6/100)(90/360)] = $4,256,157.64Forward contract is more expensive ($4.96)



Hedging a foreign currency receivableShetlant Sweaters is selling sweaters to Japanese customers.They will receive ¥500,000,000 in 30 days.

Spot exchange rate: ¥179.5/£30-day forward: ¥180/£30-day dollar interest rate: 2.70% p.a.30-day euro interest rate: 6.01% p.a.

Choice #1: Sell yen forward(¥500,000,000)/(¥180/£) = £2,777,778Choice #2: Money market hedgeBorrow present value of ¥500,000,000¥500,000,000 / (1 + (6.01/100)(30/360)) = ¥497,508,313The pound revenue is found by selling yen @ spot:¥497,508,313/(¥179.5/£) = £2,771,634To compare the two, we need to take the FV of the mm hedge£2,771,634 * (1 + (2.7/100)(30/360)) = £2,777,785The money market hedge is more expensive ($7)

© 2012 pearson education, inc. all rights reserved.6-1 6.1the theory of covered interest rate...

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