* FORECASTING EXCHANGE RATESCH. 6 PARITY CONDITIONS & CURRENCY FORECASTING- ARE TO DESCRIBE THE RELATIONSHIPS AMONG KEY MACROECONOMICVARIABLES OF OUR INTEREST. MOST PARITIES ARE DERIVED FROM THE NOARBITRAGE CONDITION (THE LAW OF ONE PRICE).* ARBITRAGE - Examples (with and without bid-asked spreads) - Triangular Arbitrage, Cross Exchange Rates - Interest Arbitrage: BOA 4% vs Nations 5% => Borrow Low and Invest(=Deposit) High. Determine the cash flows today and the future cash flows toshow that there is $0.01 arbitrage profit with $1.00 amount to start out with.What if there are bid-asked interest rates? - International Interest Arbitrage: US 4% vs UK 5%? : US interest rates are $interest rates and the UK interest rates are BP interest rates. Comparing thoseis like comparing apples and oranges. What shall we do? Get both $ interestrates (or £ interest rates). - Covered Interest Arbitrage: hedging against exchange rate risk – Example: i$= 4%, i£ = 5%, So = 2, F=2.01, then (1/So)(1+i£)F=1.055 or 5.5% $ rate ofreturn in the UK vs. 4% $ return in the US. 1. CIRP: FROM THE NO ARBITRAGE CONDITIONIDEA: ONE $ INVESTED ANYWHERE IN THE WORLD SHOULD YIELD THE SAME $ RATE OF RETURN => ONE $ INVESTED IN THE US T-BILLS SHOULD YIELD THE SAME RETURN AS AN INVESTMENT MADE IN UK T-BILLS IN $ TERMS BY THE TIME THE INVESTMENTS MATURE.- Parity Equation: Formalize based on the example in Covered InterestArbitrage above. Show the international interest rate arbitrage and determinethe arbitrage profits using the cashlows (Co and C1)- Implied forward rate: a theoretical forward rate satisfying the CIRP. If theactual forward rate is the same as the implied, the CIRP hold. If not, thenCIRP does not hold. More specifically, if the actual > implied, then? If theactual < implied, then?Example #1: US 4% vs UK 5%, So = $2/£ => Implied F = $1.981/£.Example #2: If the actual F = $1.97/£, then what happens? Show how youcan make an arbitrage profits? - Show different versions of CIRP and the relationship between CIRP andforward premium.1+i$ = (1/So)*(1+i£)*F or 1+i$ = (F/So)*(1+i£) or (1+i$)/(1+i£) = (F/So) orsubtracting “1” from both sides, (F – So)/So = i$ - i£Aside) With the implied forward rate, show that we have -1% on both sides. -THREE ASSUMPTIONS: 1) THE SAME RISK 2) NO TRANSACTIONS COSTS3) NO RESTRICTIONS ON FOREIGN INVESTMENTS INCLUDING NO ORIDENTICAL TAXES - EMPIRICAL EVIDENCE2. PPP IDEA:ONE $ (BP) SHOULD HAVE THE SAME PURCHASING POWER AROUND THEWORLD. =>PRICES OF CONSUMPTION BASKETS (or THE PRICE LEVELS) BEINGTHE SAME BETWEEN THE US AND UK WHEN PRICES ARE MEASURED IN ACOMMON CURRENCY ($ or BP). - Example: Big Mac Meal: €3 in France vs. $3.90 in Baltimore, inconsistent with this concept? With $/€ = 1.2, the $ price of one Big Mac Meal in Franceis $3.60. The exchange rate which would satisfy the law of one price should be = 3.9/3=$1.30/€=> Prices of twinkies/bagels/cars/--- in the US and UK should be the same aftermaking an adjustment for the different currency values i.e., exchange rates. Or $ (£) prices should be the same.$CPI's IN TWO COUNTRIES SHOULD BE EQUAL.=> $ (£) Living costs are the same!- ABSOLUTE VERSION: P$ = So* P£ or So = P$/P£ Ex1: If P$ =$225/basket, P£ =£150, then the equilibrium exchange rate shouldbe So = $1.50/£- RELATIVE VERSION: e = I$ – I£ (Approximately), e = (1+I$)/(1+I£) – 1 (exact)Does this make sense? Inflation => an erosion of the value (purchasing powerof money) and the currency of the country with a higher inflation is expectedto depreciate against the other currency.Ex2: If I$ =5%, I£ =3.5%, the equilibrium £ appreciation rate = e= 1.5% - Real exchange rate: q = P$ /(So* P£ ) or q = (1+I$)/[(1+e)*(1+I£)]. If theabsolute PPP or the relative PPP holds, q should be equal to “1” To the extentthat the real exchange rate deviates from 1, we can argue that the exchangerate is mispriced and the competitiveness the domestic country is eitherstronger (improves with q<1) or weaker (deteriorates q>1)Ex3: Ex1 and the actual exchange rate So=$1.6/£, then q=225/(1.6*150)=0.9375 => cost of living in the US is less than that of the UK => USis more competitive. Ex2 and the actual pound appreciation rate against thedollar is 4.5% => q=1.05/(1.045*1.035) =0.97 => £ has appreciated muchmore than what the relative PPP indicates, $ depreciated by more than iswarranted by PPP, strengthening the competitiveness of US industries. -THREE ASSUMPTIONS: 1) IDENTICAL CONSUMPTION PATTERNS ACROSS THE BORDER2) NO TRANSPORTATION COSTS3) ALL GOODS ARE TRADABLE - EMPIRICAL EVIDENCE 3. THE FISHER EFFECT 1) THE FISHER EFFECT (CLOSED or DOMESTIC VERSION) THE NOMINAL INTEREST RATE IS EQUAL TO A REAL INTEREST RATE PLUS AN EXPECTED RATE OF INFLATION. i$ = ρ$ + E(I$) (approximation) - Example: If ρ$ = 2% and E(I$) =3.4%, what should be i$ according to theFisher Effect? 2) THE FISHER OPEN (or THE INTERNATIONAL FISHER EFFECT): ASSUMINGTHAT THE REAL INTEREST RATES ARE EQUAL ACROSS COUNTRIES, THENOMINAL INTEREST DIFFERENTIAL SHOULD BE EQUAL TO THE EXPECTEDINFLATION DIFFERENTIAL. That is, i$ - i£ = E(I$) - E(I£). The significance of thisrelationship is that the difference in the expected inflation rates, which maynot be observable, can be captured by the interest rate differential, the datawhich can be easily obtained.Now, combining the International Fisher and the relative PPP ( E(e)= E(I$)-E(I£) ) , the change in the exchange rate should be then equal to the interestrate differential. That is, E(e) = i$ – i£ 4. FORWARD PARITY: THE FWD DIFFERENTIAL EQUALS THE EXPECTED CHANGEIN THE EXCH RATE. OR, THE FWD RATE IS AN UNBIASED PREDICTOR OF THEFUTURE SPOT EXCH RATE. F = E(S1) or (F-So)/So = E(e) *EMPIRICAL EVIDENCE* Comparison of the (C)IRP, PPP, IFE, and Fwd Parity. See Exh 6.9 on p.152* FORECASTING EXCHANGE RATES* Why a firm needs to forecast exchange rates? – Exchange rate changes canaffect very substantially cash flows (directly like contractual amount orindirectly via changes in firm’s competitive position), discount rates, andeventually the value of the firm.*Forecasting Techniques: 1) Technical Forecasting (“history repeats itself”)–using historical data (e.g., pacific),