Chapter Objective: This chapter examines several key international parity relationships, such as interest rate parity and purchasing power parity. 6 Chapter Six International Parity Relationships & Forecasting Foreign Exchange Rates INTERNATIONAL FINANCIAL MANAGEMENT Fourth Edition EUN / RESNICK

Chapter Outline Interest Rate Parity Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates Efficient Market Approach Fundamental Approach Technical Approach Performance of the Forecasters Interest Rate Parity 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 PPP Deviations and the Real Exchange Rate Evidence on 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 The Fisher Effects Forecasting Exchange Rates

Important concepts Arbitrage: actions that seek to take advantage of price discrepancies between different markets for the purpose of making guaranteed profits. Law of One Price (LOP): similar goods cost the same in different countries of the world LOP requires that there be no transportation costs, tariffs, monopolies, price restrictions In an absence of these costs, arbitragers will ensure that similar goods cost the same across countries by buying where the goods are cheap and selling where the goods are expensive.

Interest Rate Parity (IRP) Uncovered Interest Rate Parity (UIRP) Condition: Covered Interest Rate Parity (CIRP) Condition: E = expected spot rate on the future date F = forward rate i = domestic interest rate i* = foreign interest rate

Covered Interest Rate Parity (CIRP) Consider alternatives one year investments for $1,000: Option 1: Invest in the U.S. at i$. Future value1 = $1,000 × (1 + i$) Option 2: Trade your $ for £ at the spot rate, invest $1,000/S$/£ in Britain at i£ while eliminating any exchange rate risk by selling the future value of the British investment forward. S$/£ F$/£ Future value2 = $1,000(1 + i£)× Since these investments have the same risk, they must have the same future value (otherwise an arbitrage would exist) S$/£ F$/£ 1,000(1 + i£) × = $1,000(1 + i$)

IRP $1,000  (1+ i£) S$/£ $1,000×(1 + i$) $1,000  (1+ i£) × F$/£ = Alternative 2: Send your $ on a round trip to Britain Step 1: S$/£ $1,000 Step 2: Invest those pounds at i£ $1,000 Future Value = $1,000 S$/£  (1+ i£) Step 3: repatriate future value to the U.S.A. Alternative 1: invest $1,000 at i$ $1,000×(1 + i$) $1,000 S$/£  (1+ i£) × F$/£ = IRP Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would exist

Covered arbitrage and Equilibrium exchange rate If the CIRP does not hold. Suppose… Arbitrage strategy: 1. Borrow $x, pay back principal + interest = x(1+i$) dollars Exchange $X for x/S($/ £) pounds, and sell forward contract. Invest x/S($/ £) pounds. Receive x/S($/ £)(1+i£) pounds. Convert back to $: x/S($/ £)(1+i£) F($/ £) dollars Net profit = x/S($/ £)(1+i£) F($/ £) - x(1+i$) > 0 (1 + i$) F$/£ S$/£ × (1+ i£) < 2

Interest Rate Parity (IRP) F$/£ S$/£ × (1+ i£) = From above example, Formally, 1 + i$ 1 + i฿ S$/฿ F$/฿ = IRP is sometimes approximated as Forward premium/discount i$ – i฿ ≈ S F – S Interest rate differential

Forward Premium It’s just the interest rate differential implied by forward premium or discount. For example, suppose the ฿ is depreciating from S(฿/$) = 33.30 to F180(฿/$) = 34.50 The forward premium is given by: F180 (฿/$) – S (฿/$) S (฿/$) × 360 180 f180 = $34.5 – $33.3 $33.3 × 2 = 0.036

Interest Rate Parity Carefully Defined Depending upon how you quote the exchange rate ($ per ฿ or ฿ per $) we have: 1 + i$ 1 + i฿ S฿/$ F฿/$ = 1 + i$ 1 + i฿ S$/฿ F$/฿ = or …so be a bit careful about that

IRP and Covered Interest Arbitrage If IRP failed to hold, an arbitrage would exist. However, … Reasons for Deviations from IRP: Transactions Costs The interest rate available to an arbitrageur for borrowing, ib,may exceed the rate he can lend at, il. There may be bid-ask spreads to overcome, Fb/Sa < F/S Thus (Fb/Sa)(1 + i$l)  (1 + i¥ b)  0 Capital Controls Governments sometimes restrict import and export of money through taxes or outright bans.

Transactions Costs Example Will an arbitrageur facing the following prices be able to make money? 1 + i$ 1 + i€ S$/ € F$/ € =   Borrowing Lending $ 5% 4.50% € 6% 5.50%   Bid Ask Spot $1.00=€1.00 $1.01=€1,00 Forward $0.99=€1.00

Purchasing Power Parity (PPP) The exchange rate between two currencies should equal the ratio of the countries’ price levels: S($/£) = P£ P$ Law of One Price S($/£) = P£ P$ £150 $300 = = $2/£ For example, if an ounce of gold costs $300 in the U.S. and £150 in the U.K., then the price of one pound in terms of dollars should be:

Absolute and Relative PPP Absolute PPP: Relative PPP: Real ER: Absolute PPP states that the real exchange rate is always equal to 1. But, this will only hold under the most stringent conditions (no tariffs, transport costs or other distortions). Relative PPP states that the real exchange rate is constant but not necessarily equal to 1. PPP is a way of defining exchange rate in the long run. * = foreign S = DC/FC Price of foreign goods in DC Price of domestic goods in DC

Relative PPP According to relative PPP,  - * = Depreciation of domestic currency Depreciation of domestic currency Domestic inflation Foreign inflation An economy that has relatively high inflation rate, its currency tends to depreciate in value.

Purchasing Power Parity (PPP) Suppose the spot exchange rate is $1.25 = €1.00 If the inflation rate in the U.S. is expected to be 3% in the next year and 5% in the euro zone, Then the expected exchange rate in one year should be $1.25×(1.03) / €1.00×(1.05) F($/€) = $1.25×(1.03) €1.00×(1.05) $1.23 €1.00 =

Purchasing Power Parity (PPP) and Exchange Rate Determination The euro will trade at a 1.90% discount in the forward market: $1.25×(1.03) €1.00×(1.05) = F($/€) S($/€) 1.03 1 + $ = = 1.05 1 + € $1.25 €1.00 Relative PPP states that the rate of change in the exchange rate is equal to differences in the rates of inflation—roughly 2%

PPP & IRP Notice that our two big equations today equal each other: = F($/€) S($/€) 1 + $ 1 + € 1 + i€ 1 + i$ = F($/€) S($/€) =

Expected Rate of Change in Exchange Rate as Inflation Differential We could also reformulate our equations as inflation or interest rate differentials: = F($/€) S($/€) 1 + $ 1 + € = F($/€) – S($/€) S($/€) 1 + $ 1 + € – 1 1 + $ 1 + € – = Expected ER = F($/€) – S($/€) S($/€) $ – € E(e) = ≈ $ – € 1 + €

Expected Rate of Change in Exchange Rate as Interest Rate Differential = F($/€) – S($/€) S($/€) i$ – i€ ≈ i$ – i€ E(e) = 1 + i€

Quick and Dirty Short Cut Given the difficulty in measuring expected inflation, managers often use ≈ i$ – i€ $ – €

Evidence on PPP PPP probably doesn’t hold precisely in the real world for a variety of reasons. Services are non-tradable: eg. Haircuts cost 10 times as much in the developed world as in the developing world. (Services are unlikely to be arbitraged across countries.) Different quality: eg. Tradable goods produced in China may be of lower quality than those produced in Europe. (Also, the basket of goods and services consumed can differ across countries.) Shipping costs, as well as tariffs and quotas can lead to deviations from PPP. PPP-determined exchange rates still provide a valuable benchmark.

The Fisher Effects An increase (decrease) in the expected rate of inflation will cause a proportionate increase (decrease) in the interest rate in the country. For the U.S., the Fisher effect is written as: 1 + i$ = (1 + $ ) × E(1 + $) Where $ is the equilibrium expected “real” U.S. interest rate E($) is the expected rate of U.S. inflation i$ is the equilibrium expected nominal U.S. interest rate

International Fisher Effect If the Fisher effect holds in the U.S. 1 + i$ = (1 + $ ) × E(1 + $) and the Fisher effect holds in Japan, 1 + i¥ = (1 + ¥ ) × E(1 + ¥) and if the real rates are the same in each country $ = ¥ then we get the International Fisher Effect: 1 + i$ 1 + i¥ E(1 + ¥) E(1 + $) =

International Fisher Effect If the International Fisher Effect holds, E(1 + ¥) E(1 + $) 1 + i$ 1 + i¥ = and if IRP also holds 1 + i$ 1 + i¥ S¥/$ F¥/$ = E(1 + ¥) E(1 + $) = S¥/$ F¥/$ then forward rate PPP holds:

Equilibrium Exchange Rate Relationships IFE FEP PPP 1 + i$ 1 + i¥ IRP FE FRPPP E(1 + ¥) E(1 + $)

Forecasting Exchange Rates Efficient Markets Approach Fundamental Approach Technical Approach Performance of the Forecasters

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 = E[St+1] and Ft = E[St+1| It] Predicting exchange rates using the efficient markets approach is affordable and is hard to beat.

Fundamental Approach Involves econometrics to develop models that use a variety of explanatory variables. This involves three steps: step 1: Estimate the structural model. step 2: Estimate future parameter values. step 3: Use the model to develop forecasts. The downside is that fundamental models do not work any better than the forward rate model or the random walk model.

Technical Approach Technical analysis looks for patterns in the past behavior of exchange rates. Clearly it is based upon the premise that history repeats itself. Thus it is at odds with the EMH

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 forward rate. The founder of Forbes Magazine once said: “You can make more money selling financial advice than following it.”

Homework/Make-up class Homework: on page 156-158 (Chapter 6): Problems # 3, 4, 6, 7, 9 to be handed in next class Make-up class: Option 1: Friday 2-5pm Option 2: Sunday 9am-12pm