II.1. Interest Rate Parity Lecture note II1,

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II.1. Interest Rate ParityLecture note II-1, 3
MSE Ch. 4 (1st ed. pp 76-80 2nd ed. pp.
102-4)

• 6F130 International Finance
• Prof. David S. Bates
• Lecture 10

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FX and Eurocurrency markets
Now
Future

FC
3
FX and Eurocurrency markets
Now
Future

spot exchange market (S /FC)
FC
4
FX and Eurocurrency markets
Now
Future

forward exchange market (F /FC)
FC
5
FX and Eurocurrency markets
Now
Future
NY
U.S. money mkt (i )

London
Eurodollar mkt (i )
FC
6
FX and Eurocurrency markets
Now
Future

i (or i )

FC
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FX and Eurocurrency markets
Now
Future

FC
foreign money mkt (i )
natl
FC
FC
Euro-FC market (i )
London
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FX and Eurocurrency markets
Now
Future

i
FC
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FX and Eurocurrency markets
Now
Future
i

S
F
i
FC
10

• FX and money markets create multiple ways of
  moving money around
• Across currencies
• Across time
• This mobility constrains relative prices in the
  spot market, the forward market, and the
  Eurocurrency markets in any two currencies
• (interest rate parity)
• E.g., Why do forward and spot rates differ?
• Spot 1.3679 /euro
• forward 1.3759 /euro

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Example Two riskfree dollar investments
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Investment 1 Eurodollar deposit
Now
Future
i

Final Amount Initial Amount
- 1 i
Return
FC
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Investment 1 Eurodollar deposit
Now
Future
i
R i

1
FC
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Investment 2 Covered investment in foreign
currency

• Buy pounds (or other FC) spot
• Deposit in an interest-bearing Euro-FC account
• Contract now to convert principal interest (in
  FC) back to dollars _at_ forward rate F

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Investment 2 Covered investment in foreign
currency
1) Buy FC spot _at_ S /FC
Now
Future

S /FC
FC
1/S units of FC per invested
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Investment 2 Covered investment in foreign
currency
2) Invest _at_ Euro-rate i
Now
Future

S /FC
i
FC
(1/S) (1i) units of FC
1/S units of FC
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Investment 2 Covered investment in foreign
currency
3) Sell principalinterest at (precontracted)
forward rate F
Now
Future
(1/S) (1i)F dollars

S /FC
F /FC
i
FC
(1/S) (1i) units of FC
1/S units of FC
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Investment 2 Covered investment in foreign
currency
Now
Future
(1/S) (1i)F dollars

R
2
S
F
i
FC
R (F/S)(1i) - 1
2
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Investment 2 Covered investment in foreign
currency
Now
Future

R
2
S
F
i
FC
R (F/S)(1i) - 1
2
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Alternate computation of R2

• Each pound purchased has an initial cost of S
  /pound
• Each pound purchased has a (known) future dollar
  value of (1 i) x F
• Return on a covered pound investment

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Alternate computation of R2

• Each pound purchased has an initial cost of S
  /pound
• Each pound purchased has a (known) future dollar
  value of (1 i) x F
• Return on a covered pound investment

F(1 i) S
R - 1
2
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Investment 2 Covered investment in foreign
currencyInvestment 1 Eurodollar investment
Now
Future
i
R i
1

R
2
S
F
i
FC
R (F/S)(1i) - 1
2
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Interest rate parity

• Since both investments have known (riskfree)
  returns, those returns must be identical R1
  R2
• Reason all markets are two-way can invest or
  borrow at R1 R2
• A divergence between R1 R2 creates a money
  pump borrow low, invest high

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Example R 5, R 6
1
2
Now
Future

FC
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Example R 5, R 6
1
2
Now
Future
R 5
1

FC
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Example R 5, R 6
1
2
Now
Future
R 5
1

R 6
2
FC
R (F/S)(1i) - 1
2
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Example R 5, R 6Borrow _at_ R , invest
_at_ R
1
2
1
2
Now
Future
R 5
1

R 6
2
FC
R (F/S)(1i) - 1 6
2
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Example 2 R 6, R 5
1
2
Now
Future
R 6
1

R 5
2
FC
R (F/S)(1i) - 1 6
2
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Example 2 R 6, R 5Borrow FC with
forward cover _at_ 5, invest Euro- _at_6
1
2
Now
Future
R 6
1

R 5
2
FC
R (F/S)(1i) - 1
2
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Arbitrageurs eliminate divergences between R1 and
R2
R1 R2
i (F/S)(1 i) - 1
1 i (F/S)(1 i)
F 1 i S 1 i
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Interest Rate Parity
F 1 i S 1 i
(for S and F in /FC)
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Example 3-month /euro August 12, 2008(rates
from lecture notes II-1, 1 II-1, 2)

• spot rate S 1.4910 /euro
• forward rate F 1.4838 /euro
• 93 days between spot settlement date (Aug. 14)
  forward settlement date (Monday, Dec. 15)
• i() 3.005 x (93/360)
• .78 / 93 days
• i(euro) 5.30 x (93/360)
• 1.27 / 93 days

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Caution the formula depends on how exchange
rates are quoted

• Rule of thumb the interest rate ordering mimics
  the exchange rate quotations
• If exchange rates are quoted SF/ (European
  convention), its a SF interest rate in the
  numerator and a interest rate in the denominator

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Interest Rate Parity
F 1 i S 1 i
(for S and F in /FC)
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Interest Rate Parity
F 1 i S 1 i
(for S and F in /FC)
SF/
F 1 i S 1 i
SF
SF/

(for S and F in SF/)
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Implications for swap rates
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Interest rate parity must and does hold for
interbank rates from unconstrained markets

• Relevance
• Important constraint on forward rates
• Important constraint on returns from hedged
  foreign investing

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Interest rate parity will not necessarily hold
when

• one uses retail interest rates that corporations
  face (e.g., borrowing rates)
• one uses interest rates from segmented national
  money markets

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Implications

• There can be firm-specific opportunities when
  converting money internationally

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Example U.S. firm must pay 1 mln pounds in 3
months
Approach 1 deposit _at_ i, buy pounds forward
Now
Future
i

F
pounds
Liability 1 mln pounds
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Example U.S. firm must pay 1 mln pounds in 3
months
Approach 2 buy pounds spot, deposit _at_ i
Now
Future

S
i
pounds
Liability 1 mln pounds
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At interbank rates, both cost the same initially
(IRP).
Now
Future
i

F
S
i
pounds
Liability 1 mln pounds
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At interbank rates, both cost the same initially
(IRP).At retail (firm-specific) rates, one is
better than the other.
Now
Future
i

F
S
i
pounds
Liability 1 mln pounds
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Exception 2 IRP wont necessarily hold for
interest rates from segmented national money
markets

• Example France, 1980s

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Summary

• Interest rate parity is a no-arbitrage based
  parity condition constraining spot, forward, and
  Eurocurrency rates.
• Always holds for unconstrained interbank rates
• May not hold for retail interest/exchange rates,
  and rates from segmented national money markets