Ch.

International Parity
Conditions

Interest Rate Parity

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 Learning Objectives

• Examine how P and price level change (inflation) determine the ER

• Show how IRs are related with inflation and ER

• Explain how forward rate is determined

• Analyze how, in EQ’M, S & F are aligned with IR differentials and

differentials in expected inflation

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 International Parity Conditions

•The economic theories which link ER to P level & IR

in order to understand flows of finances & products are
called IPC.

• It seems fictional, but is central to realize how

international business is conducted

•Generally, the P parity and IR parity are taken for

study
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 ER & P parity
•The Law of one P states that all else being equal (& no
transaction cost) a good’s P should be the same in all MKTs

– But nations use different currencies

•Even if P for a particular good are in different currencies,

the law of one price states that…

P$  S = P¥

Where (P$ ) = US P; S = spot ER (¥ / $)

(P¥) = Japanese P

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 PPP & the Law of One Price

• PPP is the relative P of a set of goods b/w 2 countries. If the Law of one
P were true for all goods, the PPP is the ER, called the PPPER

• This is the Theory of absolute PPP

• Absolute PPP states that the spot ER is determined by the RPs of similar
basket of goods

Theory of absolute PPP says that ER should be the RP of a good in two

separate countries

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 Relative PPP

• RPPP is the linkage of Δ(inflation rate) b/w countries in a

period of time and Δ(S).
– Otherwise, any change in the differential rate of inflation b/w two

countries is offset by an equal relative change in the spot ER.

│ t – * t │ = (St / S t –1)− 1 = %ΔS

-(US, t – CN, t ) = (SCNY/$,t / SCNY/$, t –1)− 1

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Remark: opposite direction !
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 Relative PPP -(US, t – CN, t ) = (SCNY/$,t / SCNY/$, t –1)− 1

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Remark: opposite direction !
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 • The international Fisher effect, or Fisher-open, states that S
should change in an amount equal to but in the opposite direction of
the difference in IR b/w countries

S2 − S1
x 100 = i ¥ − i $ %ΔS = i – i*
S1

-- Due to IFE, ΔS makes investors gain or lose

-- IFE says that with unrestricted capital flows, investors should

be indifferent b/w investing in $ or in ¥ bonds, since they have
the same result.

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 1. The Theory of Interest Rate Parity

→ The logics behind IRP:

– suppose you buy a currency forward, there are two ways:
(1) Buy a forward contract;
(2) Buy FOREX, then invest for the required term.

-- State of nature: if no IRP there would be ……

-- Theoretically, (Forward rate/Spot rate) & IR-differential would be…

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 E.g. Kevin has $10M to invest;

iU.S.=8%; iU.K.= 10%; S=$1.60/£; F1-yr = $1.56/£

$10M * 1.08??

Calculation

1. Convert into FOREX using S: $10M/$1.60/£) = £6.25M

2. Invest at foreign IR: £6.25M * 1.10 = £6.875M

3. Convert back at forward rate: £6.875M * $1.56/£) = $10.725M

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.

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 Situational Analysis

$10M to invest; iU.S.=8%; iU.K.= 10%; S=$1.60/£; F1-yr = $1.56/£

$10M * 1.08

Another scenario:

1.Borrow pounds: £1M * 1.10 = £1.1M (what Kevin owes at end of

investment term)

2.Convert pounds to dollars: £1M * ($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 / $1.56/£) = £1,107,692

Kevin would make £7,692 profit for every £1M that is borrowed!

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 Diagram of Interest Arbitrage

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 • Deriving IRP
- When it occurs, investors are indifferent b/w investing at home

or abroad. General expression for IRP:

Subtracting 1 from each side and simplifying we obtain

Premium/discount = i – i*

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 Covered Interest Arbitrage is …..

Uncovered Interest Arbitrage is …..

Annualized rate * (number of days/360) = de-annualized rate

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 CIA

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 UIA

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 Interest Rates in the External Currency Market

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 Covered IR Parity with Bid-Ask Rates

ERs & IR associate with each arrow indicate

funds obtained in the currency at the arrow’s
point from selling 1 unit of the currency at the
arrow’s tail. E.g., at the $ today node, selling
$1 for $ in 1 year give (1+ i($)bid) in 1 year

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 An Example with Transaction Costs

$10M to invest Bid Ask

• Convert $10M to yen:
Spot (¥/$) 82.67 82.71
$10M * ¥82.67/$ = ¥826.7M
Forward (¥/$) 82.5895 82.6495
• Invest for 3 months:
Dollar int. rate 0.91 1.11
0.46 * (1/100) * (90/360) = 0.00115
Yen int. rate 0.46 0.58 ¥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 * 1.002275) = -$8,767

We lose M this way – no arbitrage this way, but borrowing ¥ results in

losses as well.
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 Does interest rate parity hold?

• No, but approximately

• Prior to 2007 – no significant violation of IRP

• Crisis or MKT volatility creates apparent arbitrage opportunities

Why Deviation from IRP seems to Exist: Too good to be true?

–Default risks – one counterparties may fail to honor its contract

– Exchange controls: limitations & taxes

–Political risk
✓Political disorder cause foreign investors to perceive a higher default
risk on their investments.

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 4. Hedging Transaction Risk in the Money Market

• There are two ways to hedge a transaction (either a

liability or a receivable)

-- Forward MKT hedge (FMH)

-- Money market hedge (MMH) – if an underlying

transaction gives you a receivable/payable, you use a money
MKT to borrow/lend in order to hedge the position

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 Hedging a FOREX liability (cost/payment/payable)

Zachy is a wine company in NY which imports wine from France with

payable of €4M in 90 days.
S = $1.10/ € F = $1.08/ €
US 90-day IR = 6% p.a. EU 90-day IR = 8% p.a
Option 1: enter into forward contract

In 90 days deliver: 4,000,000  1.08 = $4,320,000

Option 2: Money MKT hedge
Invest x amount now to own €4M in 90-days (deposit, buy securities),
and how much should be X?

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 Discounting FV!
De-annualization the €-IR for 90-days:

Buy Pv-amount at S, we have PV in $:

Pv ($) = €3,921,569 * 1.10 = $ 4,313,725

To make decision we compare the PV-of-MMH and PV-of-FH

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 Your decision? Difference: 57,567$

Pv (€) = 4,000,000 / (1.02) = 3,921,568 €

➔ Pv($) = 3,921,568 € * 1.10 = 4, 313,725$

➔ Fv ($) = 4, 313,725$ * (1.015) = 4,378,431$

Vs. FH, Fv ($) = 4,320,000$, (FC fee = 10,000$)

Fv + fee = 4, 330,000,
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 Hedging a FOREX receivable (revenue/asset)

Shetland Sweaters is winter clothing company in UK which exports

sweaters to Japan with revenue to come of ¥500M in 30 days.
-- S=¥179.5/£ & 30-day F = ¥180/£
-- 30-day £IR = 3.0% p.a. & 30-day ¥IR = 6.0% p.a.
Option 1: By using the forward contract, Shetland sells ¥ forward and it
is going to receive:

In 30 days: ¥500,000,000/ ¥180/£ = £2,777,778

Option 2: Money MKT hedge
Shetland borrows ¥PV now for ¥500,000,000 (FV in 30 days) and buys
£ in current Spot MKT?
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 Discounting FV!
De-annualization the ¥-IR for 30-days:

Buy £ at S, we have PV in £:

To make decision we compare the FV-of-MMH and FV-of-FH

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 Compare and make decision?
Difference: £808

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 5. The Term Structure of Forward Premiums and Discounts

•The term structure of IRs is a variety of spot IRs for various

maturities into the future
On the vertical axis, yields p.a.

On the horiz. axis, years of maturity

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 • A review of bond pricing

1) Price of a 10-year pure discount bond with a face value of $1,000 is

$460. What is the spot IR for the 10-year maturity per annum?

$460(1+i) 10= $1,000 ; solving i=8.07%

* Yields to maturity = the discount rate

2) A 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])

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 A Small quiz
Yen: Spot and Forward (¥/$)
Mid Rates Bid Ask
Spot 129.87 129.82 129.92
Forward Rates
1 month
20 18
6 months 136 132

Swaps

12 months 117.65
Bp: 1232 Bp: 1212
15 months 115.50
Bp: 1452 Bp: 1422

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 Summary

1. F ≠ S by an amount equal to the interest differential (ih - if)

2. The forward premium or discount equals the IR differential.
(F - S)/S = (ih – if )
3. When the international financialMKT is in equilibrium, the interest
parity occurs which can be written…
(1+i)/(1+i*) = F/S
4. Covered Interest Arbitrage occurs because i – i* ≠ (F - S)/S. Finances
will move from a country to another seeking a more attractive rate.

END of
CHAPTER
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