Slides prepared by April Knill, Ph.D., Florida State University Chapter 6 Exchange Rate Systems

Slides prepared by

April Knill, Ph.D., Florida State University

Chapter 6

Exchange Rate Systems

© 2012 Pearson Education, Inc. All rights reserved. 6-2

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 (borrowing

any government controls)

• 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/£

$10M * 1.08

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/£

$10M * 1.08

1. Borrow pounds: £1M * 1.12 = £1.12M (what Kevin owes at end of investment term)

2. Convert pounds to dollars: £1.12M * ($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– Expressing 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


6.2 Covered Interest Rate Parity in Practice

• The External currency market

• Bank market for deposits and loans that are denominated in foreign currencies (from the perspective of the bank)

• Example: pound-denominated deposits and loans made by banks in Frankfurt

• Market prospers because it is a way to get around reserve requirements, which are usually lower in this market


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



• Influence over other markets– 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

• 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



• 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 Exist0

• 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)

• Synthetic forward – borrowing/lending foreign currency and making a transaction in the spot market

• Money market hedge – if an underlying transaction gives you a liability, you use a money market asset to hedge the position (and vice versa)



Hedging a foreign currency liabilityZ ach y's W ine an d Spir its is im po rting som e w inef rom France for €4 m illion. It is p aya ble in 9 0 days.

S pot e xcha nge rate: $ 1.10/€9 0-da y forw ard: $ 1.08/€9 0-da y do llar in teres t ra te : 6 .00% p.a.9 0-da y eu ro in teres t ra te : 1 3.519 % p.a .

C hoic e #1: Enter in to a forw a rd c ontra ctC ost in 90 d ays is: € 4,000 ,000 * ($1.0 8/€) = $4 ,320,000C hoic e #2: M one y m ark et h edgeInvest X am ou nt now to bec om e w ha t yo u ow e in 90 daysb ut ho w m u ch?€ 4,000 ,000/[1 + (13.5 19/10 0)(90 /360) ] = €3,86 9,229 .71W e bu y th is @ Spo t ra te : €3,86 9,229 .71 * $ 1.10/€ = $4,25 6,152 .68T o c om pare the tw o , w e ne ed to tak e the P V of the forw ard hed ge$ 4,320 ,000/[1 + (6 /10 0)(90 /360) ] = $4,25 6,157 .64F orw a rd co ntrac t is m ore exp ensive ($4.9 6)



Hedging a foreign currency receivableS hetlan t Sw ea ters is se llin g sw e aters to J apane se c ustom ers.T hey w ill r ece ive ¥500 ,000,0 00 in 30 days.

S pot e xcha nge rate: ¥1 79.5/£3 0-da y forw ard: ¥1 80/£3 0-da y do llar in teres t ra te : 2.7 0% p .a.3 0-da y eu ro in teres t ra te : 6.0 1% p .a.

C hoic e #1: Sell yen forw ard(¥500 ,000,0 00)/(¥180/£) = £2,7 77,77 8C hoic e #2: M one y m ark et h edgeB orro w pres ent va lue of ¥500 ,000,000¥ 500,0 00,00 0 / (1 + (6 .01/1 00)(30/36 0)) = ¥49 7,508 ,313T he pound reven ue is foun d by se llin g yen @ spo t:¥ 497,5 08,31 3/(¥1 79.5/£ ) = £2,77 1,634T o c om pare the tw o , w e ne ed to tak e the F V of the m m hed ge£ 2,771 ,634 * (1 + (2 .7/100) (30/3 60)) = £ 2,777 ,785T he m on ey m a rke t hedg e is m ore ex pensiv e ($7 )


6.5 The Term Structure of Forward Premiums and Discounts

• The term structure of interest rates – description of different spot interest rates for various maturities into the future


Exhibit 6.5 Yield Curves for Four Currencies



• A review of bond pricing– Price of a 10-year pure discount bond with a face value of

$1,000 is $463.19. What is the spot interest rate for the 10-year maturity expressed in percentage per annum?$463.19[1+i(10)] 10= $1,000 ; solving i=8%

– Yields to maturity – the discount rate that equates the present value of the n coupon payments plus the final principal payment to the current market priceA 2-year bond with face value equal to $1,000, an annual coupon of $60 and a market price of $980. If the 1-year spot rate is 5.5%, the 2-year spot rate is found by solving:$980 = ($60/1.055) + ($1060/1+i(2)2)



• Long-term forward rates and premiums– Let i(2,¥) and i(2,$) denote the spot interest rates for yen

and dollar investments with 2-year maturities– If no arbitrage opportunities exist, then the rate of yen

per dollar for the 2-year maturity must beF(2) = S * [1+i(2, ¥)]2 /[1+i(2,$)]2 Spot: ¥110/$; i(2,$) = 5% p.a.; i(2, ¥) = 4% p.a.; ¥10M to investInvesting in Japan: ¥10M * (1.04)2 =¥10.816M, or $90,909.09 at current spotInvesting at home: $90,909.09 * (1.05)2 =$100,227.27

You are indifferent between the two if the forward rate is realized

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Slides prepared by April Knill, Ph.D., Florida State University Chapter 6 Exchange Rate Systems