* FORECASTING EXCHANGE RATESCHs. 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 BP interest rates). - Covered Interest Arbitrage: hedging against exchange rate risk – Example:ius = 4%, iuk = 5%, So = 2, F=2.01, then (1/So)(1+iuk)F=1.055 or 5.5% $ rateof return vs. 4% 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, Relationship between CIRP and forward premium. Showdifferent versions of CIRP. - Extra Example: US 4% vs UK 5%, So = $2/BP => Implied F = $1.981/BP,Actual NE (not equal to) Implied?Aside) Implied forward rate: a theoretical forward rate satisfying the CIRP. Ifthe actual 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?- If the actual F = $1.97/BP, then what happens? Show how you can makean arbitrage profits? -THREE ASSUMPTIONS: 1) THE SAME RISK 2) NO TRANSACTION COSTS 3) 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: euro 3 in France vs. $3.90 in Baltimore, inconsistent with this concept? With $/e = 1.2, the $ price of one Big Mac Meal in France is $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 $ (BP) prices should be the same.$CPI's IN TWO COUNTRIES SHOULD BE EQUAL.=> $ (BP) Living costs are the same! - ABSOLUTE VERSION: So = P$/PBP - RELATIVE VERSION: e = I$ – IBP- Real exchange rate: q = (1+I$)/[(1+e)*(1+IBP)] -THREE ASSUMPTIONS: 1) IDENTICAL CONSUMPTION PATTERNS ACROSS THE BORDER 2) NO TRANSPORTATION COSTS, 3) ALL GOODS ARE TRADABLE- EMPIRICAL EVIDENCE 3. THE FISHER EFFECT 1) THE FISHER EFFECT (CLOSED or DOMESTIC VERSION) THE NOMINAL INTEREST RATE IS EQUAL TO A REAL INTEREST RATE PLUS AN EXPECTED RATE OF INFLATION. I$ = p$ + E(I$) (simple one) - Example 2) THE FISHER OPEN (or THE INTERNATIONAL FISHER EFFECT)ASSUMING THAT THE REAL INTEREST RATES ARE EQUAL ACROSS COUNTRIES, THE NOMINAL INTEREST DIFFERENTIAL SHOULD BE EQUAL TO THE EXPECTED INFLATION DIFFERENTIAL, WHICH AGAIN SHOULD EQUAL THECHANGE IN THE EXCHANGE RATE (FROM THE RELATIVE PPP). e = i$ – 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) *EMPIRICAL EVIDENCE* Comparison of the (C)IRP, PPP, IFE, and Fwd Parity * FORECASTING EXCHANGE RATES* Why a firm needs to forecast exchange rates? – Exchange rate changes canaffect very substantially cashflows (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), statistical tools, and charts to extractpatterns/trends. - Moving Average?- Limitations 2) Fundamental Forecasting – based on fundamental relationships betweeneconomic variables and exchange rates. - Using key economic variables (e.g., yardeni.com) from economic theories,sensitivity analyses, and parity conditions. (traditional flow model, assetmarket model, and parity conditions) - Limitations 3) Efficient Market-Based Forecasting – Using the current spot rates (RandomWalk Hypothesis) or the forward rates. 4) Mixed Forecasting and Exchange Rate Forecasts (e.g., biz.yahoo.com/ifc) * Evaluation of Forecast Performance* Exchange Rate forecasting in a fixed-rate