PPP, IRP and IFEDr. Anurag Agnihotri

*Parity ConditionsUFR=Forward rates as unbiased predictors of future spot ratesPPP=Purchasing power parityIFE=International Fisher effectFE=Fisher effectIRP=Interest rate parity

*Arbitrage and Law of One PriceSo many relationships in international finance, including the parity conditions, depends on arbitrage activities.

Arbitrage is defined as simultaneous purchase and sale of the same assets or commodities on different markets to profit from price discrepancies.

Law of one price (LOP) stems from arbitrage and states that: In competitive markets free of transportation costs and official barriers to trade, identical goods sold in different countries must sell for the same price when their prices are expressed in terms of the same currency. Mathematically, for good i

*Arbitrage and Law of One PriceExample:

If a DVD sells for $30 in New York, and if the $/BP=1.50 (BP=British Pound), based on the law of one price, same DVD must sell for 20 BP in London. Suppose the price in US is $28 for the same DVD. In that case, US exporters and British importers will have an incentive to buy the DVD in New York and ship it to London for a profit (of course, in the absence of any transportation costs and barriers to trade). This will push the prices up in New York, and push the prices down in Londonuntil the price of same DVD equalized in both locations.

Hence, international arbitrage enforces the law of one price.

*Purchasing Power ParityIn its absolute version, PPP states that price levels should be equal worldwide when expressed in a common currency a unit of home currency should have the same purchasing power around the world. In other words, exchange rate between two currencies should be equal to the ratio of the countries price levels. When one countrys inflation rate rises relative to that of another country, decreased exports and increased imports depress the countrys currency.The theory of purchasing power parity (PPP) attempts to quantify this inflation - exchange rate relationship. where PUS and PGBR are the prices of the reference currency baskets. Hence, PPP theory predicts that a fall in a currency's domestic purchasing power (increase in the domestic price level) will be associated with a proportional currency depreciation in the foreign exchange market. If, for example, the reference basket costs $200 in US and 120 British pounds in UK, PPP predicts price of BP as 1.67 (200/120).

*Purchasing Power ParityIf law of one price holds (for all commodities), then absolute PPP must hold. Could we say that law of one price must hold if absolute PPP holds? Note that absolute PPP ignores

Transportation costsTariffs, quotas and other restrictionsProduct differentiationLaw of one price and absolute PPP (to a degree) are best illustrated by the Big Mac index (initially put together by The Economist).

*Rationale behind Purchasing Power ParityThe absolute form of PPP, or the law of one price, suggests that similar products in different countries should be equally priced when measured in the same currency.The relative form of PPP accounts for market imperfections like transportation costs, tariffs, and quotas. It states that the rate of price changes should be similar.Suppose U.S. inflation > U.K. inflation. U.S. imports from U.K. and U.S. exports to U.K., so appreciates.This shift in consumption and the appreciation of the will continue until in the U.S., priceU.K. goods priceU.S. goods, & in the U.K., priceU.S. goods priceU.K. goods.

*Purchasing Power ParityFor example, a Big Mac cost 1.99 BP in London, while its price is $2.71 in US. Implied PPP exchange rate for $/BP can be calculated by (2.71/1.99)=1.36 Implied PPP exchange rate for BP/$ can be calculated by (1.99/2.71)=0.73Actual price of dollar was 0.63 BP on that date, implying US dollar was undervalued and BP was overvalued. 0.73 - 0.63 =+16% (note we used Price of dollar) 0.63What are the problems with the Big Mac approach?

Ignores what is included in the price of a Big Mac:- cost of real estate; local taxes ;local servicesIn other words, it includes both traded and non-traded goods and services.So, absolute PPP doesnt make sense if the baskets are different.

*Purchasing Power Parity

Relative PPP, which is mostly used, states that the percentage change in the exchange rate over any period equals the difference between the percentage changes in national price levels. In other words, exchange rates should change to offset differences in inflation rates.

For example, if inflation is 5% in US and 1% in Japan, then the dollar value of Japanese Yen must rise by about 4% to equalize the dollar price of goods in the two countries (dollar depreciates). In mathematical terms,

where e1 = future spot rate e0 = spot rate ih= home inflation if = foreign inflation t = time periodand e is the price of foreign currency ($/BP)

*Purchasing Power ParityAssumehome countrys price index (Ph) =foreign countrys price index (Pf)When inflation occurs, the exchange rate will adjust to maintain PPP: Pf (1 + If ) (1 + ef ) = Ph (1 + Ih )whereIh=inflation rate in the home countryIf=inflation rate in the foreign countryef=% change in the value of the foreign currencyIf purchasing power parity is expected to hold, then the best prediction for the one-period spot rate should beA more simplified but less precise relationship is PPP says the currency with the higher inflation rate is expected to depreciate relative to the currency with the lower rate of inflation.

*Purchasing Power ParityExample: Projected inflation rates for the U.S. and Germany for the next twelve months are 10% and 4%, respectively. If the current exchange rate is $.50/dm, what should the future spot rate be at the end of next twelve months?

$0.529 is the best prediction for the future $/DM exchange rate.

*Purchasing Power ParityAs it is clear now, exchange rate changes may indicate nothing more than the reality that countries have different inflation rates (outcome of PPP). Hence, changes in nominal exchange rates may not be significant to evaluate the true effects of currency changes on a firm.

Real exchange rate is the nominal exchange rate adjusted for changes in relative purchasing power of each currency since some base period (so home price of the foreign basket relative to home basket). Where Pf is the foreign price level and Ph is the home price level at time 1, both indexed to 100 at time 0. Note that increases in the foreign price level and foreign currency depreciation have offsetting effects on real exchange rates.An alternative way is using the inflation rates. Note if PPP holds than er=e0.

*Purchasing Power ParityExample1: Assume Canadian reference commodity basket costs Can100, and US basket costs $50 and the nominal exchange rate is E$/Can=0.5 per Canadian dollar. Er$/Can=0.5*(100/50)=($50 per Canadian basket)/($50 per US basket)=1 US basket per Canadian basket Assume the Canadian baskets cost increases to Can110. Real exchange rate becomes 1.1 so we need to give 1.1 US basket for one Canadian basket real depreciation of dollar against Canadian dollar (Fall in the purchasing power of a US dollar within Canadian borders relative to its purchasing power within US).

*Purchasing Power ParityExample2: Assume Yen/$ exchange rate moved from Yen226.63/$ to Yen93.96/$ between 1980 and 1995. CPI in Japan rose from 91.0 to 119.2, and US CPI rose from 82.4 to 152.4.

(a) If PPP hold, what would be the exchange rate in 1995 (according to PPP real rates do not change)?Inflation in Japan was 31%, and in US was 85% over that time periodYen/$ PPP rate=226.63*(1.31/1.85)=Yen160.51/$ > Yen93.96/$ , so Yen appreciated more than PPP would suggest. (b) What happened to real value of Yen?Real rate=93.96*(1.85/1.31)=Yen132.69/$ n 1995Real rate n 1980 is just equal to nominal rate, Yen226.63/$. Yen appreciated in real terms by 71%.

*Purchasing Power ParityThe distinction between nominal and real exchange rate has important implications for foreign exchange risk management. If real exchange rate remains constant, changes in nominal exchange rate will be less important. Empirical Evidence: Law of one price doesnt hold (no surprise here)

There is a clear relationship between relative inflation rates and changes in exchange rates. In general, it appears that PPP holds well in the long-run, but doesnt perform well in the short-run we observe substantial deviations from PPP predicted rates in the short-run, but there is a tendency to move back to PPP predicted rates in the long-run. This is called mean reversion and it is important for currency risk management.

*Purchasing Power ParityWhy do we see deviations in the short-run?

sticky prices in the short-run transportation costs and restrictions departures from free competition differently constructed price indices relative price changesNon-traded goods and services

*Fisher EffectInvestors care about real interest rates and not about the nominal interest rates. However, almost all financial contracts are stated in nominal terms.

The Fisher effect states that nominal interest rate, r, is a function of

Real required rate of return, a, andAn inflation premium equal to the expected amount of inflation, iFormally, 1+Nominal rate=(1+Real rate)*(1+Expected inflation rate)1+r=(1+a)*(1+i) r=a+i+a*iThis equation can be approximated by r=a+i (under what conditions?)

*Fisher EffectExample: if a=3% and i=10%, Fisher equation tells us that nominal interest rate, r, should be 13%.

Generalized version of Fisher effect:

Real returns tend towards equality across countries (ah=af)If ah>af then capital will flow from foreign to home currency.In the absence of government intervention, nominal interest rate differential should be equal to expected inflation differential between two currencies. rh-rf= ih-if How did we obtain this condition (remember ah=af)?Currencies with high rates of inflation should bear higher nominal interest rates than currencies with lower inflation rates.

*Fisher EffectExample: if inflation rates are 4% and 7% in US and UK, respectively, nominal interest rates should be higher by about 3% in UK.

Is D an equilibrium point?Do we expect capital to flow from home country to foreign country to take advantage of the real difference?

*Fisher EffectEmpirical Evidence:- Evidence is consistent with the hypothesis that most of the variation in nominal interest rates across countries can be attributed to differences in inflationary expectations.It is much harder to test the hypothesis that real returns are equal between countries. However, arbitrage will force pre-tax real interest rates to converge across all the major nations, if arbitrage is permitted to operate unhindered and capital markets are integrated worldwide.

Capital market integration means that real interest rates are determined by the global supply and demand for funds.Capital market segmentation means that real interest rates are determined by local credit conditions.

*Fisher EffectEmpirical evidence shows that capital markets are becoming increasingly integrated worldwide. However, we still observe real interest rate differential across countries (not arbitraged away). - Political risk and currency risk (higher inflation risk Canada example)- Different tax policies- Regulatory barriers to free flow of capital

Hence, real interest rates tend to be higher in developing countries.

Furthermore, integration of capital markets (and resulting flow of funds) impose some discipline on mismanagement of economies in developing nations.

*International Fisher EffectCombine PPP and FE to find IFE. Remember PPP is denoted as: And FE as rh-rf= ih-if. Is this familiar?Currencies with low interest rates are expected to appreciate relative to currencies with high interest rates. Is this consistent with our earlier discussions?

*International Fisher EffectFisher postulated:1. The nominal interest rate differential should reflect the inflation rate differential.2. Expected rates of return are equal in the absence of government intervention.Remember, changes in the nominal interest differential can have two sources: 1. Changes in real interest differential2. Changes in inflationary expectationsThese two have opposite effects on currency values. If the change is due to a higher real interest rate in the home country, value of home countrys currency will rise. If the change is because of an increase in inflationary expectations in home country, value of home countrys currency will fall.

*International Fisher EffectIf the /$ spot rate is 108/$ and the interest rates in Tokyo and New York are 6% and 12%, respectively, what is the future spot rate two years from now?

*Interest Rate Parity TheoryThe Theory states: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

THE UNBIASED FORWARD RATEStates that if the forward rate is unbiased, then it should reflect the expected future spot rate.ft = et

*Currency ForecastingImportant for financial executives of multinational corporations

Currency forecasting can lead to consistent profits only if the forecaster

Has superior forecasting modelHas access to private information consistently, or has access to public information with a time leadCan exploit small, temporary deviations from equilibriumCan predict the nature of government intervention in the foreign exchange market (more applicable for countries who manage their currencies to some extent)

*Currency ForecastingMarket-Based Forecasts

Extract the predictions already included in interest and forward ratesForward rate is an unbiased estimate of the future spot rate limited to forecast horizon of one yearInterest rate differential can be used to predict future interest rates exist for longer time periods

Model-Based ForecastsFundamental analysis involves the examination of macroeconomic variables and policies. Simplest is to use PPP. Technical analysis focuses on the past price and volume movements try to discover price patterns.

*Currency ForecastingThe possibility of consistent profit-making through currency forecasting is inconsistent with the efficient market hypothesis. According to efficient market hypothesis current exchange rates reflect all publicly available information.

Note the forecast doesnt have to be accurate. It needs to be profitable. Example: Yen/$ spot rate is Yen110 per $. A 90-day forward rate is Yen109/$. If our forecast for 90-day is Yen102/$, we should buy the Yen forward.

Buy $1million worth of Yen forward = 109,000,000 Yen. If the spot exchange rate 90-day from now turns out to be Yen108/$, sell Yen spot for a profit of $9259. Our forecast was off by 6%, but we made a profit.

Assume our forecast was Yen111/$. We would sell Yen forward and we would lose $9259. Our forecast was more accurate, it was off by 3% only.

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