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International Parity Relationships


International Parity Relationships Chapter 6 (134-149) – PowerPoint PPT presentation

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Title: International Parity Relationships

International Parity Relationships
  • Chapter 6 (134-149)

Lecture Objectives
  • Examine several key international parity
  • relationships, such as
  • interest rate parity
  • purchasing power parity

Interest Rate Parity
  • Interest Rate Parity Defined
  • Covered Interest Arbitrage
  • Interest Rate Parity Exchange Rate
  • Reasons for Deviations from Interest Rate Parity

Interest Rate Parity Defined
  • IRP is an arbitrage condition.
  • If IRP did not hold, then it would be possible
    for an astute trader to make unlimited amounts of
    money exploiting the arbitrage opportunity.
  • Since we dont typically observe persistent
    arbitrage conditions, we can safely assume that
    IRP holds.

Interest Rate Parity Defined
  • Suppose you have 100,000 to invest for one year.
  • You can either
  • invest in the U.S. at i. Future value
    100,000(1 i)
  • or
  • trade your dollars for yen at the spot rate,
    invest in Japan at i and hedge your exchange
    rate risk by selling the future value of the
    Japanese investment forward. The future value
    100,000(F/S)(1 i)
  • Since both of these investments have the same
    risk, they must have the same future
    valueotherwise an arbitrage would exist,
    therefore (F/S)(1 i) (1 i)

Interest Rate Parity
100,000(1 i)
  1. Trade 100,000 for at S

100,000(F/S)(1 i)
  1. One year later, trade for at F

Interest Rate Parity Defined
  • Formally,
  • (F/S)(1 i) (1 i)
  • or if you prefer,

IRP is sometimes approximated as
Interest Rate Parity Carefully Defined
  • Depending upon how you quote the exchange rate (
    per or per ) we have

IRP and Covered Interest Arbitrage
  • If IRP failed to hold, an arbitrage would exist.
    Its easiest to see this in the form of an
  • Consider the following set of foreign and
    domestic interest rates and spot and forward
    exchange rates.

Spot exchange rate S(/) 1.6000/
360-day forward rate F360(/) 1.5922/
U.S. discount rate i 2.0
British discount rate i 2.5
IRP and Covered Interest Arbitrage
  • A trader with 1,000 to invest could invest in
    the U.S., in one year his investment will be
    worth 1,020 1,000?(1 i) 1,000?(1.02)
  • Alternatively, this trader could exchange 1,000
    for 625 at the prevailing spot rate, (note that
    625 1,0001.6/) invest 625 at i 2.5
    for one year to achieve 640.625. Translate
    640.625 back into dollars at F360(/)
    1.5922/, the 640.625 will be exactly 1,020.

Interest Rate Parity
  1. Trade 1000 for 625

  1. One year later, trade 640.625 for at F360(/)
  1. Invest 625 at 2.5 i

Interest Rate Parity Exchange Rate
  • According to IRP only one 360-day forward rate,
  • F360(/), can exist. It must be the case that
  • F360(/) 1.5922/
  • Why?
  • If F360(/) ? 1.5922/, an astute trader could
    make money with one of the following strategies

Arbitrage Strategy I
  • If F360(/) gt 1.5922/
  • i. Borrow 1,000 at t 0 at i 2.0.
  • ii. Exchange 1,000 for 625 at the prevailing
    spot rate, (note that 625 1,0001.60/)
    invest 625 at 2.5 (i) for one year to achieve
  • iii. Translate 640.625 back into dollars, if
  • F360(/) gt 1.5922/ , 640.625 will be more
    than enough to repay your dollar obligation of

Arbitrage Strategy II
  • If F360(/) lt 1.5922/
  • i. Borrow 625 at t 0 at i2.50 .
  • ii. Exchange 625 for 1,000 at the prevailing
    spot rate, invest 1,000 at 2.0 for one year to
    achieve 1,020.
  • iii. Translate 1,020 back into pounds, if
  • F360(/) lt 1.5922/ , 1,020 will be more
    than enough to repay your obligation of

  • IRP provides a linkage between interest rates
    differential and forward premium
  • Interest rates are more stable the XRs. Thus, in
    IRP the F and S change to accommodate the demand
    and supply for currencies
  • If F360(/FC) gt S (1 ius)/ (1 iFC) borrow in
    and lend in FC
  • If F360(/FC) lt S (1 ius)/ (1 iFC) lend in
    and borrow in FC
  • If (1 ius) gt (F/ S )(1 iFC) lend in and
    borrow in FC
  • If (1 ius) lt (F/ S )(1 iFC) lend in FC and
    borrow in

Uncovered -IRP
Covered IRP arbitrage condition
Un-Covered IRP
IRP and Hedging Currency Risk
  • You are a U.S. importer of British woolens and
    have just ordered next years inventory. Payment
    of 100M is due in one year.

Spot exchange rate S(/) 1.60/
360-day forward rate F360(/) 1.5922/
U.S. discount rate i 2.00
British discount rate i 2.50
IRP implies that there are two ways that you fix
the cash outflow to a certain U.S. dollar
amount a) Put yourself in a position that
delivers 100M in one yeara long forward
contract on the pound. You will pay
(100M)(1.5922/) 159.22M b) Form a forward
market hedge as shown below.
IRP and a Forward Market Hedge
To form a forward market hedge Borrow 156.098m
in the U.S. at 2 p.a. (in one year you will owe
159.22m). Translate 156.098m into pounds at the
spot rate S(/) 1.60/ to receive
97.561m. Invest 97.561m in the UK at i 2.5
for one year. In one year your investment will
have grown to 100 millionexactly enough to pay
your supplier.
Forward Market Hedge
Where do the numbers come from? We owe our
supplier 100 million in one yearso we know that
we need to have an investment with a future value
of 100 million. Since i 2.5 we need to
invest 97.561 million at the start of the year.
How many dollars will it take to acquire 97.561
million at the start of the year if S(/)
Reasons for Deviations from IRP
  • Transactions Costs
  • The interest rate available to an arbitrageur for
    borrowing, ib, may exceed the rate he can lend
    at, il.
  • There may be bid-ask spreads to overcome, Fb/Sa lt
  • Ex If (1 i) lt (F/ S )(1 i) exists, the
    arbitrage strategy involves lending in and
    borrowing in .
  • With transaction costs, it is possible that
  • (Fb/Sa)(1 i l) ? (1 i b) ? 0
  • Capital Controls
  • Governments sometimes restrict import and export
    of money through taxes or outright bans.

Purchasing Power Parity
  • Purchasing Power Parity (PPP)
  • A concept regarding the equilibrium value of a
    currency based upon its purchasing power in
    different countries
  • General idea is that prices in different
    countries once converted to a common currency
    should be equal

Purchasing Power Parity
  • Three concepts of PPP are used
  • The Law of One Price for individual goods
  • Absolute PPP for general price levels
  • Relative PPP for changes in the general price
    level (inflation rates)


The law of one price
  • Equivalent assets sell for the same price
  • Ptd price of an asset in domestic currency
  • Ptf price of the same asset in foreign
  • Ptd /Ptf std/f Û Ptd Ptf std/f
  • seldom holds for nontraded assets
  • may not hold when there are market frictions
  • cant be used to compare assets that vary in

An example of the law of one priceThe world
price of gold
  • Suppose P 500/oz in New York
  • P 550/oz in Berlin
  • The law of one price requires
  • Pt /Pt st/
  • Þ (500/oz)/(550/oz) .91/
  • If this relation does not hold, then there is an
    opportunity to lock in a riskless arbitrage

The Big Mac index (The Economist, 6 Jan 2010)
  • According to Burgernomics, the Chinese yuan is
    still undervalued!
  • Based on the theory of PPP exchange rates should
    equalize the price of a basket of goods in
    different countries.
  • The exchange rate that leaves a Big Mac costing
    the same in dollars everywhere is its fair-value
  • Most overvalued currency against the dollar is
    the Norwegian kroner, which is 96 above its PPP
    rate. In Oslo you can expect to pay around 7 for
    a Big Mac.
  • Most undervalued currency against the dollar is
    the Chinese yuan, which is undervalued by 49.

(No Transcript)
Absolute Purchasing Power Parity
  • Absolute PPP
  • Identical baskets of consumer goods in two
    countries will have exactly the same price (in a
    given currency)
  • Generally economists consider the basket of goods
    that comprise the CPI
  • The exchange rate is the ratio of the price
  • S(/ ) P/ P

Absolute Purchasing Power Parity
  • Example
  • PUS S(/) x PUK S(/)
  • The same number of dollars that buys the basket
    of goods in the U.S. also buys the basket of
    goods in Britain
  • Both currencies have the same purchasing power in
    terms of a basket of goods

Relative Purchasing Power Parity
  • Relative PPP states that the rate of change in
    the exchange rate is equal to the differences in
    the rates of inflation

If U.S. inflation is 5 and U.K. inflation is 8,
the pound should depreciate by about 3.
Important Points
  • If U.S. inflation gt U.K. inflation, the should
    appreciate against the , i.e. the should
  • If U.K. inflation gt U.S. inflation, the should
    depreciate against the , i.e. the should
  • If U.K. inflation U.S. inflation, there should
    be no change in the exchange rate.

PPP Deviations and the Real Exchange Rate
  • The real exchange rate is

If q lt 1 competitiveness of domestic country
improves with currency depreciations. If q gt 1
competitiveness of domestic country deteriorates
with currency depreciations.
Evidence on PPP
  • PPP probably doesnt hold precisely in the real
    world for a variety of reasons.
  • Haircuts cost 10 times as much in the developed
    world as in the developing world.
  • Film, on the other hand, is a highly standardized
    commodity that is actively traded across borders.
  • Shipping costs as well as tariffs and quotas can
    lead to deviations from PPP.

Problems with PPP
  • Transaction costs and restrictions on trade
  • high transportation costs, nontradables, import
  • Departures from free competition
  • product differentiation and market segmentation
    can produce large price differences
  • International differences in the measurement of
    price levels
  • different preferences and consumption baskets
    across countries

Learning outcomes
  • Explain how IRP (covered) is derived
  • Calculate a forward rate under the assumptions
    of IRP
  • Determine whether an arbitrageur can profit from
    given interest rates, and spot and forward
    rates. If yes, explain in detail the arbitrage
    strategy and calculate the profits.
  • Define uncovered IRP. Explain the differences
    between covered and uncovered IRP
  • Discuss the reasons for deviations from IRP
  • Define and discuss the law of one price, and the
    absolute and relative PPP
  • Define and discuss the real exchange rate
  • Discuss the implications of the deviations from
    PPP for countries competitive position
  • Discuss the evidence on and problems with PPP
  • Discuss the three approached to forecast
    exchange rates