International Parity Relationships

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Chapter Outline

• Interest Rate Parity
• Purchasing Power Parity
• The Fisher Effects
• Forecasting Exchange Rates

• Interest Rate Parity
• Covered Interest Arbitrage
• IRP and Exchange Rate Determination
• Reasons for Deviations from IRP
• Purchasing Power Parity
• The Fisher Effects
• Forecasting Exchange Rates

• Interest Rate Parity
• Purchasing Power Parity
• PPP Deviations and the Real Exchange Rate
• Evidence on Purchasing Power Parity
• The Fisher Effects
• Forecasting Exchange Rates

• Interest Rate Parity
• Purchasing Power Parity
• The Fisher Effects
• Forecasting Exchange Rates

• Interest Rate Parity
• Purchasing Power Parity
• The Fisher Effects
• Forecasting Exchange Rates
• Efficient Market Approach
• Fundamental Approach
• Technical Approach
• Performance of the Forecasters

• Covered Interest Rate Parity (CIRP)
• Purchasing Power Parity (PPP) absolute
  relative
• The Fisher Effects Domestic International
• Forward Parity
• Forecasting Exchange Rates

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CIRP Defined

• Idea 1 (or any amount in or in any FC)
  invested in anywhere should yield the same
  return (or FC return) If the world investment
  market is perfect, we expect competitive returns!
  Why?
• CIRP is an no arbitrage condition.
• If CIRP 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
  CIRP holds.

almost all of the time!
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A Simple Covered Interest Rate Arbitrage Example
when CIRP does not hold!

• BOA 4 vs Nations Bank 5
• Identify L and H, Borrow Low Invest (Deposit)
  High
• Borrow say 1 from BOA and Deposit at NB
• Cash Flow at 0 1 from BOA -1 to NB gt Net CF
  0
• Cash Flow at1 1.05 from NB -1.04 to BOA gt
  0.01 arbitrage gain.
• A few issues
• 1) Bid-Asked? How about 3.994.01 vs 4.995.01
• Use average rates (BidAsked)/2 to determine H
  L, then figure out!
• 2) Can it be sustained?
• What is the equilibrium situation, then?

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What about

• 4 in the US vs 5 in the UK?
• Well, we need more info to determine the
  arbitrage opportunity. Why? What needed?
• US interest rate, i, is a interest rate and
  the UK rate, i, is a interest rate. It is like
  comparing apples and oranges.
• What do you need? Exchange rates!

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.

• A Box Diagram to show (LHS RHS)
• 1 invested in the US gt 1.04, or 1i (more
  generally)
• 1 gt 0.5 BPs at So 2/, or (1/So) BPs
• PV0.5 BPs gtFV0.5(1.05) 0.525 BPs, or
  (1/So)(1i) BPs
• To convert BPs to s, we need a future exchange
  rate. To have no risks, we can use a forward
  contract with the forward rate, say F2.01/.
  Then amount is 1.055, or (1/So)(1i )F
• interest rate investing in the UK is 5.5 gt 4
• Why 5.5 gt 5.0? Investing in UK involves two
  investments (buying selling pounds and
  buying and selling the security)!
• Borrow from the US and Invest in UK!
• Arbitrage strategy Arbitrage profit 0.015
• In equilibrium with no arbitrage opportunity,
• gt 1i (1/So)(1i)F, LHSRHS, CIRP (why
  Covered?)

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CIRP Defined

• Consider alternative one-year investments for 1
  
• Invest in the U.S. at i. LHS Future value (1
  i)
• Trade your for at the spot rate, invest (1/So
  ) s in Britain at i while eliminating any
  exchange rate risk by selling the future value of
  the British investment forward.

Since these investments have the same risk, they
must have the same future value (otherwise an
arbitrage would exist)
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CIRP
Alternative 2 Send your on a round trip to
Britain
Step 2
Invest those pounds at i
1,000
Future Value
Step 3 repatriate future value to the U.S.A.
Alternative 1 invest 1,000 at i 1,000(1
i)

Since both of these investments have the same
risk, they must have the same future
valueotherwise an arbitrage would exist
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CIRP Defined

• Formally,

CIRP is sometimes approximated as
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CIRP and Covered Interest Arbitrage

• If CIRP failed to hold, an arbitrage would exist.
  
• Consider the following set of foreign and
  domestic interest rates and spot and forward
  exchange rates.

Spot exchange rate So 2.0000/
360-day forward rate F360 2.0100/
U.S. discount rate i 3.00
British discount rate i 2.49
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CIRP and Covered Interest Arbitrage

• A trader with 1,000 could invest in the U.S. at
  3.00, in one year his investment will be worth
• LHS 1,000 ? (1 i) 1,000 ? (1.03) 1,030
• Alternatively, this trader could (RHS)
• Exchange 1,000 for 500 at the prevailing spot
  rate,
• Invest 500 for one year at i 2.49 earn
  512.45
• Translate 512.45 back into dollars at the
  forward rate F360(/) 2.01/, the 512.45
  will be worth 1,030.

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Arbitrage I
Alternative 2 buy pounds
Step 2
Invest 500 at i 2.49
In one year 500 will be worth 512.45
512.45
Step 3 repatriate to the U.S.A. at F360(/)
2.01/
500 ? (1 i)
Alternative 1 invest 1,000 at 3 FV 1,030
1,030
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CIRP Exchange Rate Determination

• There is only one 360-day forward rate which
  would satisfy CIRP,
• F360 2.01/
• Implied Forward Rate a theoretical forward
  rate which satisfies CIRP.
• If the actual F360 ? 2.01/, the implied forward
  rate, an astute trader could make money with one
  of the following strategies

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Arbitrage Strategy I

• If actual F360 gt 2.01/ implied gt then LHSltRHS
• gt Borrow Low from the US and Invest High in UK
• i. Borrow 1,000 at t 0 at i 3.
• ii. Exchange 1,000 for 500 at the prevailing
  spot rate, (note that 500 1,000 2/)
  invest 500 at 2.49 (i) for one year to achieve
  512.45
• iii. Translate 512.45 back into dollars, if the
  actual
• F360 gt 2.01/, then you can sell 512.45 for
  more than 1,030. If the actual F360 2.08 for
  example, your arbitrage profit 35.90 after
  repaying your debt of 1,030.

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Arbitrage Strategy II

• If actual F360 lt 2.01/ implied, then LHSgtRHS
• gt Borrow Low from UK and Invest High in the US
• i. Borrow 500 (1,000 equivalent amount at
  2/) at t 0 at i 2.49 . FV of 500 is
  512.45 (principal interest)
• ii. Exchange 500 for 1,000 at the prevailing
  spot rate, invest 1,000 at 3 for one year in
  the US to achieve 1,030.
• iii. Since the actual F360 lt 2.01/, then
  1,030 will be more than enough to repay your
  debt of 512.45. If the actual F360 1.95/,
  then you need to spend 999.28 to secure 512.45
  gt arbitrage profit of 30.72.

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Reasons for Deviations from CIRP

• Transactions Costs
• bid-ask spreads, fees, etc. Investing in or
  borrowing from a foreign country may incur
  additional costs.
• Capital Controls
• Governments sometimes restrict import and export
  of money through taxes or outright bans.
• Different risks
• So far, risks are not considered. However, CIRP
  is applicable with the same amount of risks in
  both countries.
• Investing in Libya or Afghanistan may look
  attractive in terms of higher (as well as LC)
  returns, but would you be interested?

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Transactions Costs Example

• Will an arbitrageur facing the following prices
  be able to make money one year later?

  Borrowing Lending
5.0 4.50
5.5 5.0
  Bid Ask
Spot 1.42 1.00 1.45 1,00
Forward 1.415 1.00 1.445 1.00
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.

• Averages of (BidAsked)/2 gt i 4.75,
  i 5.25, So 1.435, F 1.430
• LHS 1i 1.0475
• RHS (1/So)(1i)F
  (1/1.435)(1.0525)(1.430) 1.0488
• Since LHS lt RHS, an arbitrage opportunity, if
  exists, can be exploited by Borrowing Low from
  the US and Investing High in Europe
• Borrow say 1 from the US gt Buy euro at 1.45/,
  (1/1.45) euro gt Invest in Europe at 5, will
  have (1/1.45)(1.05) euro gt knowing today this
  amount will be available, forward contract today
  to sell the euro for s in the future,
  (1/1.45)(1.05)(1.415) 1.0247 USDs. On the
  other hand, to be able to pay off the 1 debt,
  you need 1.05 s. gt No Arbitrage Opportunity!

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Real life examples

• My sister-in-law in New Zealand
• Yen carry trade
• HW Assignment
• Covered Interest Rates Parity (CIRP) - the
  investment horizon is 3 months
• (1) Collect S0, F, i, iFC for your country
  selected (choose one from the two countries
  assigned.
• (2) Determine the implied forward rate
• (3) Check if CIRP holds
• (4) If the CIRP does not hold, show how you can
  make an arbitrage profit using 1M or 1M
  equivalent amount in FC (show your steps)

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Purchasing Power Parity

• Purchasing Power Parity and Exchange Rate
  Determination
• PPP Deviations and the Real Exchange Rate
• Evidence on PPP

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PPP and Exchange Rate Determination

• The exchange rate between two currencies should
  equal the ratio of the countries price levels
  (Absolute PPP)
• So P/P
• Alternatively, P SoP, Price level in each
  country determined in the same currency ()
  should be the same in both countries. What you
  can buy with 100 should be the same anywhere in
  the world. gt Living costs are the same!

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Relative PPP

• If Absolute PPP holds at each point in time, say
  at t0 and t1, then
• We can show that chg in the exchange rate (e
  (S1-So)/So, FC appreciation rate relative to )
  is equal to the difference between the chg in
  the US price level (US inflation rate) and the
  chg in the UK price level (UK inflation rate),
  E(e) E(p) E(p)
• If the inflation rate in the U.S. is expected to
  be 5 in the next year and 3 in the euro zone,
• Then the expected change in the exchange rate in
  one year should be 5 - 32, euro is expected to
  be 2 stronger against
• Make sense?

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Evidence on PPP

• PPP probably doesnt hold precisely in the real
  world for a variety of reasons.
• Non-tradable goods like services, perishable
  products
• Transactions Transportation costs including
  trucking costs, tariffs, etc.
• Different consumption baskets
• However, PPP-determined exchange rates can still
  provide a valuable benchmark. So P/P

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Fisher Equations

• Domestic (Closed)
• i ? E(p), 1i (1?)(1E(?)) to be
  exact
• International (Open)
• Assuming that ? ? ,
• Then, i - i E(p) E(p)
• Relative PPP International Fisher
• E(e) E(p) E(p) i - i
• HW
• Based on the collected information for CIRP, find
  out expected percentage change of the exchange
  rate
• Hint use E(e) i - iFC

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Forward Parity

• F E(S1)
• (F So)/So (E(S1) So)/So E(e)

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Approximate Equilibrium Exchange Rate
Relationships
E(e)
Fwd Parity
Rel PPP
(i i)
CIRP
Int Fisher
E(? ?)
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Forecasting Exchange Rates

• Efficient Markets Approach
• Fundamental Approach
• Technical Approach
• Performance of the Forecasters

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1) Efficient Markets Approach

• Financial Markets are efficient if prices reflect
  all available and relevant information.
• If this is so, exchange rates will only change
  when new information arrives, thus
• St ESt1 It
• and/or
• Ft ESt1 It
• Predicting exchange rates using the efficient
  markets approach is affordable and is hard to
  beat if financial markets are efficient.

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2) Fundamental (Theoretical )Approach

• Develop models that use a variety of
  macro-economic variables.
• Logical explanations!
• The downside is that fundamental models do not
  work any better than the forward rate model or
  the random walk model.

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3) Technical Approach

• Technical/statistical analysis looks for
  patterns/trend in the past behavior of exchange
  rates.
• Clearly it is based upon the premise that history
  repeats itself.
• Pretty good forecasting performance, but little
  logical explanations.
• At odds with the EMH

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Performance of the Forecasters

• Forecasting is difficult, especially with regard
  to the future.
• As a whole, forecasters cannot do a better job of
  forecasting future exchange rates than the
  current spot rate or the forward rate.
• The founder of Forbes Magazine once said
• You can make more money selling financial
  advice than following it.

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