Chapter 05 Currency Parity Conditions Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

Learning Objectives A. Discuss parity conditions and how they relate to arbitrage. B. Discuss and apply three kinds of currency arbitrage: locational, triangular and covered interest. C. Describe and apply interest rate parity (IRP). 5-2

Learning Objectives (cont.) D. Describe and apply purchasing power parity (PPP). E. Describe the Fisher effect and its link to other parities. F. Discuss and apply methods of deriving currency forecasts and methods of assessing forecasting accuracy. 5-3

A1. Overview of Parity Conditions  Parities relate currency values to fundamental variables such as interest rates and inflation  Two important parities are the Interest Rate Parity (currencies and interest rates) and the Purchasing Power Parity (currencies and inflation rates)  Parities help managers forecast future currency values  Parities arise because of money or products moving to locations offering greater value 5-4

A2. Overview of Arbitrage  When financial assets (or currencies) are mispriced in markets, arbitragers exploit discrepancies by buying (at low prices) and selling (at high prices)  Currency markets offer the following types of arbitrage opportunities:  Locational: when currencies trade at different values at different locations  Triangular: when the cross-rate of a currency pair is not in synch with the separate quotes for the two currencies  Covered Interest: when a foreign money market offers an attractive interest rate premium that is not entirely offset by projected decline in the foreign currency 5-5

B1. Locational Arbitrage 5-6

B2. Triangular Arbitrage 5-7

B3. Covered Interest Arbitrage 5-8

B4. Covered Interest Arbitrage: Another Example (using equation approach)  This example illustrates CIA where borrowing occurs in the high-interest currency. Assume S = 0.75, F = 0.70, r = 6%, r* = 10%. Calculate profit per unit of currency borrowed.  Arbitrage occurs because the rate of currency depreciation (s = 6.7%) exceeds the interest differential (4%). 5-9

C1. Interest Rate Parity  CIA will cease to be profitable in equilibrium because:  Interest rates will change (e.g., a heavy demand for a funding currency will raise interest rates)  Currency values (spot and forward) will change (e.g., heavy demand for a funding currency will increase the spot rate) 5-10

C2. IRP Application: Find the Forward Rate The 180-day LIBOR rates for USD and JPY are 4% and 1% respectively (actual/360 convention). The spot rate is as follows: USDJPY = 110. Estimate the 180-day forward rate for JPY. Adjust the IRP equation for LIBOR

C3. Impediments to IRP  When default risk varies, the interest levels in various countries may reflect not only the forward premium but also differential levels of default risk.  Transactions costs for conducting covered interest arbitrage may be high enough to prevent arbitrage from occurring even when there are deviations from parity.  Political risk or country risk would also cause deviations from IRP.  Taxations and other market imperfections that hinder the free movement of capital across borders. 5-12

C4. Empirical Evidence on IRP  Overall, IRP theory works quite well especially with major currencies.  Tests use two approaches:  Simulation Tests: The actual arbitrage strategy is simulated with available data to determine whether profits are available. Profits are typically calculated net of the costs of the following transactions: (a) selling a domestic security or borrowing money (b) purchase of spot foreign exchange (c) forward contract (d) buying a foreign security.  Regression Tests: The dependent variable (Y variable) is the ratio of forward-to-spot (or equivalently the natural log of forward minus the natural log of spot). The independent variable (X variable) is the interest differential (specification differs depending on whether logs are used for the Y variable). IRP requires an intercept of one. 5-13

D1. Law of One Price  The ability of goods to move freely across borders would mean that their prices in various locations should be similar.  Imagine that 5 lbs of sugar sells for USD 3.00 in the US and GBP 1.50 in the UK. The law of one price relies on the currency rate to makes these prices equal. This implies that the spot rate GBPUSD =  5-14

D2. Purchasing Power Parity  The law of one price, when applied to national price indexes, is known as purchasing power parity theory (PPP).  The relative version of PPP is a less restrictive and perhaps more useful version of the theory. While the absolute version of PPP requires equivalent prices, relative PPP only requires that price changes are harmonized with currency changes.  Absolute PPP focuses on price levels, relative PPP focuses on price changes or inflation. 5-15

D3. PPP Equation Ratio of Inflation Ratio of Expected Spot Rate Factor to Spot 5-16

D4. PPP Example  Starting values for CPI: US CPI = 300 and Canadian CPI = 250.  Spot CADUSD =  A year later CPI levels are expected to rise to 309 (US) and 255 (Canada).  What are inflation rates in the US and Canada? What is expected ending value of CADUSD? What is its change? 5-17

D4. PPP Example (CONT.) 5-18

D5. Impediments to PPP  Taxes differ between countries, and can cause major deviations in prices between countries. For example, value-added taxes often lead to higher prices in Europe compared to the US.  Transportation costs can be prohibitive and can discourage cross-border transactions. For example, durable goods like cars and washing machines can sometimes incur transportation costs of more than 5% of value.  National consumption preferences can differ. Because even similar products are no longer substitutes in the minds of consumers, they may trade at different prices. 5-19

D6. Empirical Evidence on PPP  Tests involve calculation of real exchange rates to see if they are constant.  There are numerous difficulties constructing tests including differences in national CPI indexes, non-traded goods and sticky prices.  Absolute PPP is rejected (e.g., Big Mac tests!)  Relative PPP is somewhat supported. In the long-term currency values converge toward PPP. Deviations from PPP appear to decrease at a rate of about 15% a year. 5-20

E1. Fisher Effect: National  Denoting the nominal rate, the real rate and the rate of inflation as r, rr and i respectively, the Fisher effect (FE) is given by: 5-21

E2. Fisher Effect: International Ratio of Interest Ratio of Expected Spot Rate Factor to Spot S SE r* r)( 1 1    5-22

E3. Overview of Parity Conditions 5-23

F1. Currency Forecasting  FX theories and parities are useful to MNC managers in deriving currency forecasts  The simplest forecast is today’s spot.  If a forward rate is available, it could be a better forecast than the spot rate. If unavailable, try to estimate the forward using parity conditions.  Fundamental methods may also be used to forecast currencies. 5-24

F2. Forecasting using Parities  A UK based MNC wishes to forecast the value of JPY in 7 years time. GBP and JPY denominated risk-free (government) debt instruments have yields of 6% and 3% respectively. If JPYGBP = now, what is the expected future spot? 5-25

F3. Assessing Forecast Accuracy: Methods 5-26

F4. Forecast Accuracy Example (Inputs) Pre-forecast spotPost-forecast spotForecast AForecast B

F5. Forecast Accuracy Example (Solution) AB AFE Succes sAFESuccess Y Y N Y N Y Y N MAF E RMS E SR50%75% 5-28