Lecture 3 Foreign Exchange Rate Determination Some basic

Lecture 3 Foreign Exchange Rate Determination

Some basic questions • Why aren’t FX rates all equal to one? • Why do FX rates change over time? • Why don’t all FX rates change in the same direction? • What drives forward rates – the rates at which you can trade currencies at some future date? 2

Exchange Rate Determination • Exchange rate determination is complex. • Exhibit 3. 1 provides an overview of the many determinants of exchange rates. • This road map is first organized by the three major schools of thought (parity conditions, balance of payments approach, asset market approach), and secondly by the individual drivers within those approaches. • These are not competing theories but rather complementary theories.

Exhibit 3. 1 The Determinants of Foreign Exchange Rates

Exchange Rate Determination • Two other institutional dimensions are considered—whether the country possesses the capital markets and banking systems needed to drive and discover value. • Most determinants of the spot exchange rate are mutually determined by changes in the spot rate.

Exchange Rate Determination: Theoretical Thread • The theory of purchasing power parity is the most widely accepted theory of all exchange rate determination theories: – PPP is the oldest and most widely followed of the exchange rate theories. – Most exchange rate determination theories have PPP elements embedded within their frameworks. – PPP calculations and forecasts are however plagued with structural differences across countries and significant data challenges in estimation.

The Purchasing Power Parity Theory (PPP) • The PPP theory was developed by Swedish economists Gustav Cassel in 1920 to determine the exchange rate between countries on inconvertible paper currencies. • This theory states that, the rate of exchange between two countries is determined by purchasing power in two different countries. PPP have two versions: 1. The absolute purchasing power parity theory 2. The relative purchasing power parity theory

Purchasing power parity Law of One Price Versions of PURCHASING POWER PARITY Absolute PPP Relative PPP 8

The Law of One Price • A commodity will have the same price in terms of common currency in every country – In the absence of frictions (e. g. shipping costs, tariffs, . . ) – Example Price of wheat in France (per bushel): P€ Price of wheat in U. S. (per bushel): P$ S€/$ = spot exchange rate P€ = s€/$ P$ 9

The Law of One Price • Example: Price of wheat in France per bushel (p€) = 3. 45 € Price of wheat in U. S. per bushel (p$) = $4. 15 S€/$ = 0. 83215 (s$/€ = 1. 2017) Dollar equivalent price of wheat in France= s$/€ x p€ = 1. 2017 $/€ x 3. 45 € = $4. 15 When law of one price does not hold, supply and demand forces help restore the equality 10

Absolute PPP • Extension of law of one price to a basket of goods • Absolute PPP examines price levels – Apply the law of one price to a basket of goods with price P€ and PUS (use upper-case P for the price of the basket): S€/$ = P€ / PUS where P€ = i (w. FR, i p€, i ) PUS = i (w. US, i p. US, i ) 11

Absolute PPP • If the price of the basket in the U. S. rises relative to the price in Euros, the U. S. dollar depreciates: May 21 : s€/$ = P€ / PUS = 1235. 75 € / $1482. 07 = 0. 8338 €/$ May 24: s€/$ = 1235. 75 € / $1485. 01 = 0. 83215 €/$ 12

Relative PPP Absolute PPP: P€ = s€/$ P$ For PPP to hold in one year: P€ (1 + i€) = E(s€/$) P$ (1 + i$), or: P€ (1 + i€) = s€/$ [E(s€/$)/s€/$ )] P$ (1 + i$) Using absolute PPP to cancel terms and rearranging: Relative PPP: 1 + i€ = E(s€/$) 1 + i$ s€/$ 13

Relative PPP • Main idea – The difference between (expected) inflation rates equals the (expected) rate of change in exchange rates: 1 + i€ = E(s€/$) 1 + i$ s€/$ 14

Relative PPP • According to this version, the change in the exchange rate over a specific period of time should be proportional to the relative change in price level in the two nations over the same period of time • The formula used for determination of exchange rate is: R 1 =P 1 a/P 0. R 0 where R 1 shows exchange rate in period 1, and R 0 shows exchange rate in base period • For example if general price level does not change in foreign nation from the base period to period 1, Where as general price level in the home nation increase by 50% P 1 b/P 0

Relative PPP • So according to PPP theory the exchange rate (price of a unit of foreign currency in term of domestic currency) should be 50% higher in period 1 as compared to the base period (home currency depreciated by 50%) • This theory can be explain with the help of other example: Suppose India and England are on inconvertible paper standard and by spending Rs. 60, the bundle of goods can be purchased in India as can be bought by spending £ 1 in England. Thus, according to PPP, the rate of exchange will be Rs. 60= £ 1. Suppose domestic price index increase by 300 and foreign price index rises to 200 the new exchange rate will be Rs 60 =£ 1. 5 • The exchange rate would be a proper reflection of the purchasing power in each country if the relative values bought the same amount of goods in each country. 16

Deviations from PPP Simplistic model Why does PPP not hold? Imperfect Markets Statistical difficulties 17

Deviations from PPP Simplistic model Imperfect Markets Statistical difficulties ØTransportation costs ØTariffs and taxes ØConsumption patterns differ ØNon-traded goods & services ØSticky prices ØMarkets don’t work well ØConstruction of price indexes - Different goods - Goods of different qualities 18

What is the evidence? • The Law of One Price frequently does not hold. • Absolute PPP does not hold, at least in the short run. – See The Economist’s Big Mac Currencies • Homework: Use The Economist Big Mac Index: July 2018 and January 2019 1. Use January 2019 index and identify whether Euro, Japanese Yen, Great British Pound, Chinese Yuan, Swiss Frank and your own country’s currencies are overvalued or undervalued against US$. 2. Compare today's exchange rates with July rates and discuss whether the big mac index gives right directions or not. • The data largely are consistent with Relative PPP, at least over longer periods. 19

Interest rate parity • Main idea: There is no fundamental advantage to borrowing or lending in one currency over another • This establishes a relation between interest rates, spot exchange rates, and forward exchange rates – Forward market: Transaction occurs at some point in future – BUY: Agree to purchase the underlying currency at a predetermined exchange rate at a specific time in the future – SELL: Agree to deliver the underlying currency at a predetermined exchange rate at a specific time in the future 20

INTEREST RATE PARITY THEORY Theory states that: • the forward rate (F) differs from the spot rate (S) at equilibrium by an amount equal to the interest differential (rh - rf) between two countries. • The forward premium or discount equals the interest rate differential. (F - S)/S = (rh - rf) where rh = the home rate rf = the foreign rate 21

INTEREST RATE PARITY THEORY • In equilibrium, returns on currencies will be the same i. e. No profit will be realized and interest parity exists which can be written as: (1 + rh) = F (1 + rf) S 22

INTEREST RATE PARITY THEORY Covered Interest Arbitrage • If interest rate differential does not equal the forward premium or discount. • Funds will move to a country with a more attractive rate. • Market pressures develop: – As one currency is more demanded spot and sold forward – Inflow of fund depresses interest rates. – Parity eventually reached. 23

INTEREST RATE PARITY THEORY In summary: Interest Rate Parity states: 1. Higher interest rates on a currency offset by forward discounts. 2. Lower interest rates are offset by forward premiums. 24

Example of a forward market transaction • Suppose you will need 100, 000€ in one year • Through a forward contract, you can commit to lock in the exchange rate • f$/€ : forward rate of exchange Currently, f$/€ = 1. 19854 1 € buys $1. 19854 1 $ buys 0. 83435 € • At this forward rate, you need to provide $119, 854 in 12 months. 25

Interest Rate Parity START (today) $117, 228 END (in one year) r$=2. 24% (Invest in $) s€/$=0. 83215 $117, 228 0. 83215 = 97, 551€ One year (Invest in €) $117, 228 1. 0224 = $119, 854 f€/$=0. 83435 97, 551€ 1. 0251 = 100, 000€ r€=2. 51% 26

Interest rate parity • Main idea: Either strategy gets you the 100, 000€ when you need it. • This implies that the difference in interest rates must reflect the difference between forward and spot exchange rates Interest Rate Parity: 1 + r€ = f€/$ 1 + r$ s€/$ 27

Interest rate parity example • Suppose the following were true: 12 month interest rate U. S Dollar Euro 2. 24% 2. 70% Spot rate 1. 2017 € / $ Forward rate 1. 19854 € / $ – Does interest rate parity hold? – Which way will funds flow? – How will this affect exchange rates? 28

Evidence on interest rate parity • Generally, it holds • Why would interest rate parity hold better than PPP? – Lower transactions costs in moving currencies than real goods – Financial markets are more efficient that real goods markets 29