INTRODUCTION (chapter 4 of Text – read in conjunction with notes and understand textbook examples). See Chapter 4 Problems and Solutions (Posted on Sakai)

A simple set of equilibrium relationships that should hold between product prices, interest rates, and forward exchange rates, in relatively efficient markets. Basically these five economic relationships exist due to the potential of arbitrage activities. Arbitrage activities refer to the flow of goods or capital to take advantage of riskless profit opportunities.

Note: in the formulas below e = $F/$D (foreign dollar / domestic dollar)

PURCHASING POWER PARITY (PPP)

e e E e

t F D F D

0

  [  ]  

F D

F D F D F D

e e

E e R R

t F D F D

0

f e

t F D F D

0

f e

E e e f E e

t t

t t

0 0

A simple set of equilibrium relationships that should hold between product prices, interest rates, and forward exchange rates, in relatively efficient markets. Basically these five economic relationships exist because of, or are due to, the potential for arbitrage.

Arbitrage activities refer to the flow of goods or capital to take advantage of riskless profit opportunities.

5 THEORETICAL ECONOMIC/FINANCIAL RELATIONSHIPS

RELATIONSHIP OF PARITY CONDITIONS TO THE BALANCE OF PAYMENTS MODEL

BOP model explains the exchange rate in terms of international transactions in goods, services and assets (real and financial).

These transactions are often the result of decisions by:

The international parity conditions represent the guiding principles or factors that dictate the international trade flows and capital movements of the above participants.

In reality trade from one good unlikely to move the x-rate. Equilibrium will most likely be partially achieved by movement in domestic prices. Due to imports downward pressure on price of wheat in Britain to $4/bushel x £/$1 = £2/bushel. The law of one price rests on the assumption that free trade will equalize the price of any good in all countries. (law of one price is based on one single good)

Assumes: - no transportation costs - no trade restrictions - no product differentials such as quality differences in the products of the two countries.

Economist Magazine: Big Mac Index (established in 1986). McDonald’s Big Mac is produced and sold in over 120 countries. Used as a “price index”.

Big Mac Currency Comparison Tool – might be useful for your paper assignment. economist/content/big-mac-index

Example: January 2019: prices and exchange rate Big Mac Price in the US: US$ 5. Big Mac Price in UK: £3. Implied x-rate: US$/£ = 5.58/3 = 1. Current x-rate: 1, implies £ undervalued by (1.2821-1)/1 = -. Important calculation ^

Even though the Big Mac itself can’t be shipped between countries, its components are internationally traded. Subsequently, under the law of one price, the composition of these traded goods should tend towards parity in the long run.

Absolute Version of Purchasing Power Parity

Basically the extension of the Law of One Price to all goods and services (applies to an index of goods). In its absolute version, purchasing power parity states that price levels should be equal worldwide when expressed in a common currency. Consequently:

The equilibrium exchange rate between two countries (foreign and domestic) equals the ratio of the foreign and domestic price levels.

e= $F/$D = PF/PD

Where PF and PD are price levels in the foreign and domestic country measured as a price index.

IMF has worldwide consumer price indices data:

data.imf/?sk=4FFB52B2-3653-409A-B471-D47B46D904B

Basically extends the absolute version over time.

If equilibrium exchange rates prevail over a period of time, changes in the ratio of foreign to domestic prices will indicate an offsetting change in equilibrium exchange rates.

Any change in the differential rate of inflation between two countries tends to be offset in the long run by a change in the exchange rate

Purchasing power parity is often used as a basis to forecast future exchange rates using expected inflation rates – particularly for the longer term.

In class example: Foreign country experiences 10% inflation while domestic country experiences inflation of 15%.

THE REAL EFFECTIVE EXCHANGE RATE

Nominal or actual exchange rate adjusted for changes in the relative purchasing power of the two counties since some base period.

If purchasing power parity holds then changes in the nominal exchange rate are fully offset by changes in the relative prices between two countries (Real value of goods should not change).

Deviations in purchasing power parity however will result in the real exchange rate changing over time. The real exchange rate is often calculated to determine whether PPP has held over the time period. Tests to see if PPP is holding The IMF produces data on the real exchange rate (versus a basket of currencies) over time:

datahelp.imf/knowledgebase/articles/537472-what-is-real-effective-exchange-rate-reer

Example: US dollar appreciates by 10% relative to the Swiss Franc during a year in which US inflation was 7% and Swiss inflation was 4%. What has happened to the real value of the SF relative to the US dollar? In notebook Common type of problem to see in exam etc

Frictions or transaction costs in the market place that do not allow for commodity arbitrage to freely take place.

Transportation costs between countries. You would expect US goods to be cheaper in terms of the transportation costs required to ship them up to Canada.

Rarely have we had extended periods in time when government intervention or activities did not exist that restrict the free flow of goods between countries: Tariffs Quotas

Statistical Problems

a) Tests should involve the identical basket of goods (index) in the two countries. This unfortunately is rarely the case.

b) Even if the two baskets contain the same goods, the weights (importance to consumers) attached to the goods may be different due to differences in tastes and preferences of the two societies. You can see the different weights in the IMF data:

data.imf/?sk=4FFB52B2-3653-409A-B471-D47B46D904B

For example, beef has twice the weighting in the US consumer price index than it does in the British consumer price index due to the relatively high consumption of beef in the US.

c) Price indices consist of both traded and non-traded goods. It is only traded goods for which PPP holds. Haircuts for example are a non-traded good. Pretty hard to earn riskless arbitrage profits on haircuts.

CONCLUSION

Aside from the statistical problems associated with testing PPP it would appear that it holds in the long run (greater than 2 years). Hence it can possibly be used as a long run estimator of exchange rate changes.

Chapter 4 problems to look at: 1, 2, 7, 8

Equilibrium relationship that describes the impact of relative changes in nominal interest rates between countries, on the currency.

Results from combining Purchasing Power Parity and the Fisher Effect.

FISHER EFFECT (FE)

Within a country, the nominal interest rate is comprised of both of the required real rate of interest plus the expected rate of inflation.

What is of importance to investors is the real rate of interest they earn. The real rate of interest describes the rate at which current real goods are converted into future real goods. As a result borrowers must compensate lenders for the real rate of interest plus any erosion in the purchasing power of the currency due to inflation (expected).

GENERALIZED VERSION OF THE FISHER EFFECT

As investors are concerned with real rates of return, then in efficient markets, real returns are equalized across countries through arbitrage. If not capital flows from one currency to another would take place until the real rates are equalized.

Assumptions:

Capital markets can be freely entered and exited without government restriction.

The capital markets possess investment opportunities that are acceptable substitutes (similar in risk). Not all T-bills from different countries are “risk free” as exhibited by Greece and others.

Market agents have complete and equal information regarding these possibilities.

As a result of equalized real rates of interest nominal interest rate differential between two countries should approximately equal the expected inflation differential.

Interest Rate parity is the condition that relates interest rates to spot and forward exchange rates, and is a major determinant in the movement of short term funds in the foreign exchange market.

FORWARD CONTRACTS FOR CURRENCY EXCHANGE

Spot Rate: The current rate of exchange between the two currencies.

Forward Rate: An agreed upon rate that is contracted today for the delivery of a currency at a specified date in the future.

Forward Contract: An agreement between two parties to exchange currencies at some fixed future date, at an exchange rate that is specified today (the forward rate).

Forward contracts are used to ensure the exchange rate for some future transaction of exchange of currencies. Forward contracts are usually drawn up between banks and their clients and frequently between banks. Forward contracts can be drawn up for any maturity, but banks offer forward exchange rates on some standard maturity contracts of 30, 90 and 180 days maturities.

COVERED INTEREST ARBITRAGE

In order for interest rate parity to hold there must be no potential for covered interest arbitrage.

Example: Swiss Franc (foreign currency), Canadian dollar (domestic currency). Current exchange rate (SF/C$) = 1. 3 month forward rate = 1. Three month CDN T-bill rate = 2%, Three month Swiss rate = 1%. What would happen if the Swiss three month rate increased to 1%?

EMPIRICAL EVIDENCE

The empirical evidence in support of interest rate parity is in general very strong. This is particularly the case in terms of the short run.

Deviation do occur but are not necessarily due to irrationality but rather market inefficiencies such as: - transaction costs. - imposition of taxes on interest payments to foreigners. - government controls or limitations on capital held by foreigners.

Du, W., Tepper, A., & Verdelhan, A. (2018). Deviations from covered interest rate parity. The Journal of Finance, 73(3), 915-957.

“We show that the CIP (covered interest parity) condition is systematically and persistently violated among G10 currencies, leading to significant arbitrage opportunities in currency and fixed income markets since the 2008 global financial crisis. Our findings are a puzzle for all no- arbitrage models in macroeconomics and finance.”

Chapter 4: problems 6, 10 (see also note on Sakai), 11, 13, 14

Also known as Uncovered Interest Rate Parity

The forward rate should reflect the expected spot rate at the date of settlement or maturity of the forward contract.

If expectations are unbiased, as they must be in an efficient market, then forward rates should be unbiased predictors of future spot rates.

EMPIRICAL EVIDENCE

The empirical evidence on the unbiasedness of forward rates is mixed and continues to be an area of empirical research.

Some evidence indicates that forward rates include a risk premium which is not inconsistent with market efficiency.