Fundamental equilibrium relations: parity conditions

1. Fundamental equilibrium relations: parity conditions • What are Parity Conditions? • Parity Conditions are a set of equilibrium relationships that should apply to product prices, interest rates and spot and forward exchange rates if markets are not impeded. They are • Pricing relationships based on the law of one price • Hold if no arbitrage opportunities exist • Law of One Price • Identical products should sell for the same price everywhere • Otherwise, arbitrage opportunities will exist • Seldom holds for non traded assets • Can’t compare assets that vary in quality • May not hold precisely when there are market frictions • An example: The world price of gold Suppose P£ = £250/oz in London P€ = €400/oz in Berlin The law of one price requires: Pt£= Pt€ St£/€ Þ £250/oz = (€400/oz) (£0.6250/€) or 1/(£0.6250/€) = €1.6000/£ • If this relation does not hold, then there is an opportunity to lock in a riskless arbitrage profit.

2. Fundamental equilibrium relations: parity conditions • Arbitrage • Profit-guaranteeing strategy of “Buy low, sell high” • No investment and no risk • Why Study Parity Conditions? • They provide the foundation of international finance. • They are useful in: • Explaining the determinants of foreign exchange rates. • Forecasting the long-run trend in an exchange rate.

3. International Parity Conditions • Purchasing Power Parity (PPP) • Absolute PPP • Relative PPP • Fisher Effect (FE) • Generalized Fisher Effect (GFE) • International Fisher Effect (IFE) • Interest Rate Parity (IRP) • Unbiased Forward Rate (UFR) • Purchasing Power Parity • Absolute PPP • Asks what should be the current exchange rate • Is based on price levels • Relative PPP • Asks how the exchange rate should change • Is based on price changes

4. Absolute PPP • It states that exchange adjusted price levels should be identical world wide. • In other words a unit of home currency should have the same purchasing power around the world. • Application of the “law of one price” to national price levels rather than individual prices • Assumptions: • Free trade will equalize the price of any good in all countries • Otherwise there will be arbitrage opportunities • Criticisms • Ignores effects on free trade of transportation costs • Tarrifs • Quotas and other restrictions • Product differentiations • The Big Mac Hamburger Standard • The Economist developed the Big Mac Standard to track PPP: • Assuming that the Big Mac is identical in all countries, it serves as a comparison point as to whether or not currencies are trading at market prices • Big Mac in Switzerland costs Sfr6.30 while the same Big Mac in the US costs $2.54 • The implied PPP of this exchange rate is Sfr2.48/$ • However, on the date of the survey, the actual exchange rate was Sfr1.73/$

5. How Well Does the Absolute PPP Work? • Based on the assumption of free trade • It has limited usefulness due to: • Differentiated goods • Costly information • Transportation costs • Differential tariffs, quotas, and other restrictions on free trade • Thus, the Relative PPP is more commonly used today because it has more reasonable assumptions • Relative PPP • States the exchange rate between home currency and any foreign currency will adjust to reflect price levels in any two countries • For ex. If inflation is 5 % in Us and 1 % in Japan, then in order to equalize the dollar price of goods in the two countries, the dollar value of the Japanese Yen will have to rise by 4 % • et = (1 + ih)t eo (1 + if)t • Where ih and if price level increases for home currency and foreign currency • eo is the dollar value of one unit of home currency at the beginning of the period and et is the spot exchange rate in period t • For ex. If the US and Germany are running annual inflation rates of 5 % and 3 % respectively, and initial exchange rate was Euro 1 = $0.75, then according to the equation, the value of the euro in 3 years should be e3 = 0.75(1.05/1.03)3 = $0.7945 • PPP states that currencies with high rates of inflation should devalue relative to currencies with low rates of inflation

6. How Well Does Relative PPP Work? • Illustration Between June 1979 and June 1980 the US rate of inflation was 13.6% and the German rate of inflation was 7.7 %. In line with the higher rate of inflation in the US, the DM revalued from $0.54 in June 1979 to $0.57 in June 1980. thus the real rate of exchange in June 1980 equaled $0.57(1.077/1.136) = $0.54. In other words the inflation adjusted $ / DM exchange rate held constant at $0.54. During the same period, UK experienced a 17.6% rate of inflation and the Pound Sterling revalued from $2.09 to $2.17. Thus the real value of the pound in June 1980 (relative to June 1979) was 2.17(1.176/1.136) = $2.25 a real appreciation 7.6% • PPP does not hold over the short-run • Sticky goods prices (lagged changes) • Changes in exchange rates precede changes in prices. • PPP holds over the long-run • Clear relationship between relative inflation rates and changes in nominal exchange rates • PPP holds more closely when price indices cover tradable goods. • PPP holds better in high-inflation cases • Expected Inflation and Exchange Rate Changes • Changes in expected as well as actual inflation will cause exchange rate changes • An increase in a currency’s expected rate of inflation, all other things being equal, makes that currency more expensive to hold over time (as its value is being eroded at a faster rate) and less in demand at the same price • Consequently, the value of the higher inflation currencies will tend to be depressed relative to the lower inflation currencies, other things remaining same • To summarize, despite often lengthy departures from PPP, there is a clear correspondence between relative inflation rates and changes in the nominal exchange rate

7. Nominal versus Real Exchange Rates • Nominal exchange rate • Price of one currency in terms of another • Real exchange rate • Real purchasing power of one currency relative to another • The difference between real exchange rate and nominal exchange rate has important implications for foreign exchange risk measurement and management. If the real exchange rate remains constant, i.e. if PPP holds, currency gains or losses from nominal exchange rate changes will generally be offset over time by effects of differences in relative rates of inflation thereby reducing the impact of nominal devaluation and revaluation. Deviations from PPP will lead to real exchange gains and losses • PPP and real exchange rates • If an exchange rate adjusts fully to the inflation differential according with PPP, the real exchange rate remains constant. • PPP holds if real exchange rates are stable over time. • Real Exchange Rate • Quoted exchange rate adjusted for the country’s inflation rate. • The real exchange rate is equal to: et’ = et (1 + if)t (1 + ih)t If Purchasing power holds exactly, that is et eo (1 + ih)t (1 + if)t then et’ equals eo. In other words, if changes in the nominal exchange rateare fully offset by changes in the relative price levels between two countries, then the real exchange rate remains unchanged. Alternatively, a change in the real exchange rate is equivalent to a deviation from PPP.

8. Fisher Effect • Describes the relationship between the nominal interest rate, real interest rate, and the inflation rate. • The Fisher effect states that nominal interest rate r is made of two components • (1) real required rate of a and • (2) an inflation premium equal to the expected amount of inflation i • Fisher equation states that • 1 + Nominal rate = (1 + Real Rate)(1 + Expected inflation rate) = 1 + r = (1+a)(1+r) Or r = a + i + ai Often approximated by the equation r = a + i • The Fishers equation states that if the required real return is 3 % and the expected inflation rate is 10%, then the nominal interest rate will be about 13 % (13.3% to be exact) • The logic behind this result is that $1 will have the purchasing power of $0.90 in terms of today’s dollar. Thus the borrower must pay the lender $ 0.103 to compensate for the erosion in the purchasing power of the $1.03 in principal and interest payments, in addition to the $0.03 necessary to provide a 3 % return • The Brazilian govt. in 1980 spent $10 million on an advertisement campaign to boost savings. However the savings dropped because the interest rates on saving deposits and treasury bills in 1980 were far below the inflation rate of 110%

9. Generalized Fisher effect • GFE says that real rates are equal among countries through arbitrage • i.e ah = af where hand f refer to home currency and foreign currency • If expected real returns in one currency is higher than another, capital would flow from the second to the first currency. This will continue in the absence of govt. intervention till the real returns are equalized • In equilibrium, it should follow that nominal interest rate differential will approximately the anticipated inflation rate differential • Or 1 + rh= 1+ ih 1 + rf 1 +if Where rh and rf are the nominal home and foreign currency interest rates • For ex. If inflation rates in US and UK are 4 % and 7% respectively, then Fisher effect says the nominal interest rates should be 3 % higher in UK than in US • GFE states that currencies with high rates of inflation should bear higher interest rates than countries with lower rates of inflation.

10. How Well Does the FE (GFE) Work? • The FE (GFE) generally holds. • However, real interest rate differentials exist due to: • Currency risk • Inflation risk • Political risk • Differing tax policies • Regulatory barriers to free flow of capital • For ex. If political risk in Argentina causes foreign investors to demand a 7 % higher interest rate than they demand elsewhere, then foreign investors will consider a 10 % expected real return in Argentina to be equivalent to 3 % return elsewhere. • Hence real interest rates in developing countries can exceed those in developed countries without presenting attractive arbitrage opportunities to foreign investors • As the rate on bank deposits will not be the same as rate on treasury bonds, while computing interest differentials identical risk characteristics must be borne in mind save currency risk, otherwise one will be comparing apples and oranges

11. International Fisher Effect • Similar to Relative PPP except it uses interest rate rather than inflation rate differentials to explain exchange rate changes. • For ex. A rise in US inflation rate relative to those in other countries will be associated with a fall in the $ value. It will be also associated with a rise in the interest rate in the US relative to foreign interest rates. Combine these two we get the IFE • IFE states that • (1 + rh)t= et (1 + rf)t eo Where etis the expected exchange rate in period t • IFE states that currencies with low interest rates should appreciate relative to currencies with high interest rates • How Well Does IFE Work? • Nominal interest rate equals real interest rate plus expected inflation. • If real interest rate increases, the nation’s currency appreciates. • If expected inflation increases, the nation’s currency depreciates. • Considerable short-run deviations do occur. • Uncovered interest arbitrage • Arbitrage between financial markets in the form of capital flows, should ensure that interest differential between any two countries is an unbiased predictor in future change of spot rate of exchange • If real rates of interest are equal across countries (d =f ), then interest rate differentials merely reflect inflation differentials • This relation is unlikely to hold at any point in time, but should hold in the long run

12. Interest Rate Parity • Spot and forward rates are related by IRP • IRP states that Ftd/f/S0d/f = [(1+id)/(1+if)]t Where S0d/f = today’s spot exchange rate E[Std/f] = expected future spot rate Ftd/f = forward rate for time t exchange i = a country’s nominal interest rate p = a country’s inflation rate • Forward premiums and discounts are entirely determined by interest rate differentials. • This is a parity condition that you can trust. • Interest rate parity:Which way do you go? If Ftd/f/S0d/f > [(1+id)/(1+if)]t then so... Ftd/f must fall Sell f at Ftd/f S0d/f must rise Buy f at S0d/f id must rise Borrow at id if must fall Lend at if

13. Interest rate parity:Which way do you go? If Ftd/f/S0d/f < [(1+id)/(1+if)]t then so... Ftd/f must rise Buy f at Ftd/f S0d/f must fall Sell f at S0d/f id must fall Lend at id if must rise Borrow at if • Interest rate parity is enforced through “covered interest arbitrage An Example: Given: i$ = 7% S0$/£ = $1.20/£ i£ = 3% F1$/£ = $1.25/£ F1$/£ / S0$/£> (1+i$) / (1+i£) 1.041667 > 1.038835 The fx and Eurocurrency markets are not in equilibrium.

14. Interest Rate Parity (IRP): Example • Suppose you have $1 million to invest for 90 days and the following choices: • Invest in dollar-denominated securities for 90 days earning 8.00% per annum, or • Invest in Swiss franc-denominated securities of similar risk and maturity earning 4.00% per annum • Suppose you have the following quotes: • Spot rate of SF1.4800/$ • 90-day forward rate of SF1.4655/$ • Would you invest in the U.S. or Switzerland? • Covered Interest Arbitrage • Spot and forward market are not in equilibrium. • Relative forward differential does not equal relative interest differential • How Well Does IRP Work? • Small deviations from IRP do occur. • Covered interest arbitrage opportunities • Lack of arbitrage profit opportunities due to: • Transactions costs • Differential tax rates • Government controls • Political risk • Time lag

15. Forward rates as predictors of future spot rates • Ftd/f = E[Std/f]or Ftd/f / S0d/f = E[Std/f] / S0d/f • Forward rates are unbiased estimates of future spot rates. • Speculators will force this relation to hold on average • For daily exchange rate changes, the best estimate of tomorrow's spot rate is the current spot rate • As the sampling interval is lengthened, the performance of forward rates as predictors of future spot rates improves • Are Forward Prices Unbiased? • Evidence that forward rates are biased predictors of future spot rates. • Risk premium • Appears to change signs • Averages near zero • Market efficiency • It appears that it does pay to use resources to forecast exchange rates

16. Currency Forecasting • Successful currency forecasting is difficult. • Currency forecasting can lead to consistent profits only if forecaster has: • Superior forecasting model • Access to information before other investors • Exploit small, temporary deviations from equilibrium • Ability to predict government intervention in foreign exchange market • Forecasting Fixed Exchange Rates • Forecasters must focus on predicting government action, since devaluations and revaluations are political decisions. • Basic forecasting methodology involves: • Determine pressure on a currency to devalue or revalue • Determine political will of leaders to persist with current level of disequilibrium • Forecasting Floating Exchange Rates • Market-Based Forecasts • Forward rate • Interest rate • Model-Based Forecasts • Fundamental analysis • Technical analysis

17. FE Interest Rate Differential Expected Inflation Rate Differential IFE Forward Differential Expected Change in Spot Rate International Parity Conditions PPP IRP UFR