Slide 0Chapter OutlineCovered Interest Rate Parity DefinedA Simple Covered Interest Rate Arbitrage ExampleWhat about.Slide 7CIRPCIRP DefinedCIRP and Covered Interest ArbitrageSlide 11Arbitrage ICIRP & Exchange Rate DeterminationArbitrage Strategy IArbitrage Strategy IIReasons for Deviations from CIRPTransactions Costs ExamplePurchasing Power ParityPurchasing Power Parity and Exchange Rate DeterminationRelative PPPFisher EquationsEvidence on PPPForward ParityApproximate Equilibrium Exchange Rate RelationshipsForecasting Exchange RatesEfficient Markets ApproachFundamental ApproachTechnical ApproachPerformance of the ForecastersChapter Objective:This chapter examines several key international parity relationships, such as interest rate parity and purchasing power parity.6Chapter SixInternational Parity Relationships and Forecasting Foreign Exchange Rates6-1Chapter 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 Rates6-2…almost all of the time!Covered Interest Rate Parity 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! Competitive returns! Otherwise?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 don’t typically observe persistent arbitrage conditions, we can safely assume that CIRP holds.6-3A Simple Covered Interest Rate Arbitrage Example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 => Net CF= $0Cash Flow at1: +$1.05 from NB -$1.04 to BOA => $0.01 arbitrage gain.A few issues:1) Bid-Asked? How about 3.99~3.01% vs 4.99~5.01%2) Can it be sustained?What is the equilibrium situation, then?What about4% in the US vs 5% in the UK?Well, we need more info to determine the arbitrage opportunity. Why?Why? US interest rate, i$, 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!.A Box Diagram to show$1 invested in the US => $1.04$1 => 0.5 £s at So = $2/ £, or (1/So) £ sThen 0.5 £ s => 0.5*(1.05) = 0.525 £ s, or (1/So)*(1+iBP) £ sTo convert £ s to $s, we need the future exchange rate. To have no risks, we use a forward contract with the forward rate, say F=$2.01/ £. Then $ amount is $1.055, or $(1/S0)*(1+i £)*F$ interest rate investing in the UK is 5.5% > 4%Why 5.5% > 5.0%? Investing in UK involves two transactions (or investments)!Borrow from the US and Invest in UK!Arbitrage strategy: Arbitrage profit = $0.015In equilibrium with no arbitrage opportunity, 1+i$ = (1/So)*(1+i£)*F. CIRP (why Covered?)S$/£ ×F$/£ =(1 + i£)(1 + i$)Covered Interest Rate Parity DefinedConsider alternative one-year investments for $1: 1. Invest in the U.S. at i$. Future value = $ (1 + i$) 2. 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. SoFFuture value = $(1 + i£) ×SoF(1 + i£) × = (1 + i$)Since these investments have the same risk, they must have the same future value (otherwise an arbitrage would exist)6-7CIRPInvest those pounds at i£$1,000 So$1,000Future Value = Step 3: repatriate future value to the U.S.A.Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would existAlternative 1: invest $1,000 at i$ $1,000×(1 + i$) Alternative 2:Send your $ on a round trip to BritainStep 2: $1,000So (1+ i£) × F $1,000So (1+ i£)=6-8CIRP DefinedFormally, CIRP is sometimes approximated as i$ – i¥ ≈SoF – So1 + i$1 + i¥SoF=6-9CIRP and Covered Interest ArbitrageIf CIRP failed to hold, an arbitrage would exist. It’s easiest to see this in the form of an example.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%6-10CIRP and Covered Interest ArbitrageA trader with $1,000 could invest in the U.S. at 3.00%, in one year his investment will be worth $1,030 = $1,000  (1+ i$) = $1,000  (1.03)Alternatively, this trader could 1. Exchange $1,000 for £500 at the prevailing spot rate, 2. Invest £500 for one year at i£ = 2.49%; earn £512.453. Translate £512.45 back into dollars at the forward rate F360($/£) = $2.01/£, the £512.45 will be worth $1,030.6-11Arbitrage IInvest £500 at i£ = 2.49% $1,000£500£500 = $1,000×$2.00£1In one year £500 will be worth £512.45 = £500  (1+ i£)$1,030 = £512.45 ×£1F£(360)Step 3: repatriate to the U.S.A. at F360($/£) = $2.01/£ Alternative 1: invest $1,000 at 3%FV = $1,030Alternative 2:buy poundsStep 2:£512.45$1,0306-12CIRP & Exchange Rate DeterminationAccording to CIRP only one 360-day forward rate, F360, can exist. It must be the case that F360 = $2.01/£Why? If F360  $2.01/£, an astute trader could make money with one of the following strategies:6-13Arbitrage Strategy IIf F360 > $2.01/£ => then LHS<RHSi. 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 £512.45iii. Translate £512.45 back into