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Parity Conditions and Currency Forecasting the Law of One Price

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Parity Conditions and Currency Forecasting the Law of One Price Chap. 4 (b) Parity Conditions and The Law of One Price Currency Forecasting • This is the assumption that identical goods sell for the same price worldwide. • Forecasts based on the Law of One Price. • Suppose gold trades in NYC at $300/oz. and in London • The Big Mac Index at $310/oz. • Forecasts based on Relative Purchasing Power Parity. • Where will people trade their gold? • Inflation and the Real Rate of Interest • The New York market would mostly attract buyers, • The original Fisher Effect. while the London market would mostly attract sellers. • The International Fisher Effect. • Also, arbitrage would occur: trades could “short-sell” gold in London, and simultaneously buy gold in NYC. • Sept. 19, 2002 by William Pugh • Gold prices in the two markets should soon equalize The Law of One Price and The Law of One Price Purchasing Power Parity • Purchasing power parity is often interpreted as, • What would cause a violation of the law of one starting with a set amount of dollars, converting price? those dollars into another currency buys the • If goods are not easily tradable, they are are same “market basket of goods” in the foreign difficult to arbitrage. country that it would in the U.S.A. • This is the really just the law one price. • Examples of nontradable goods?: • However we will find that this “law” is true only in a very limited sense. Violations of the Law of One Price Violations of the Law of One Price • Haircuts • Law of one price does not hold for nontradable • Taxi rides goods even within the United States! • Restaurant Meals (Big Macs) • Rents in New York City vs Lochapoka, AL • Apartments • Big Macs in Alaska vs. Auburn • Cement Blocks? • Big factors: shipping considerations, • Agricultural Products (most countries have perishability. protectionist policies). 1 Purchasing Power Parity Purchasing Power Parity • (1) Absolute PPP: Prices should be about the • In this text and this course we will assume that same in different countries (at current exchange the strict PPP only holds for tradable goods and rates) not for nontradable goods that, say, a tourist pays for: rents, meals, transportation, personal • or a “market basket” of goods should cost the services, etc. same everywhere in, say, dollar terms. • The strict PPP is sometimes called absolute PPP • (2) Relative PPP:Differences between countries’ price levels should be constant over time • or any differences in the cost of a “market basket”, between countries, should persist over time in, say, dollar terms. Relative Purchasing Power Parity Forecasting with Absolute PPP • The text refers to RPPP as just PPP • The law of one price extended to a market • Based on converting Swiss francs & Pesos to basket of goods (including a Big Mac for lunch after shopping). Absolute PPP says the currency some common currency (e.g. the $): if the cost of with the cheaper goods should appreciate or the living in Switzerland is twice as expensive as the currency with the more expensive goods and Mexico today, then RPPP says Switzerland will services should depreciate. be twice as expensive next year. • The Economist’s Big Mac Index is attempting • Relative PPP does not predict any convergence to forecast future exchange rates based on the in the cost of living between two countries. cost of the Big Mac. • In fact it assumes there will be no convergence! • The magazine appears to assuming that Absolute PPP is valid for nontradable goods. Forecasting with Absolute PPP Forecasting with (Relative) PPP • The Law of One Price, using the the Big Mac • RPPP says the currency with the higher inflation rate Index, predicts that the CHF will fall and the is expected to depreciate relative to the currency with Argentine Peso will rise. the lower rate of inflation. • We will find that Relative PPP predicts the • Domestic inflation: Remember, high inflation means a opposite. currency is losing local purchasing power. • Switzerland, like NYC, has been expensive for a • It is not unreasonable to assume that the same currency long time and will probably remain so. will also lose purchasing power on overseas goods and • The Economist is ignoring Argentina’s inflation services. and political turmoil. • With PPP, this loss of overseas purchasing power is • The Argentine Peso may fall further as the weak through a drop in the currency’s exchange rate. government prints too many pesos. 2 Forecasting with (Relative) PPP Forecasting with (Relative) PPP • Suppose Mexico has 10% inflation next year. It now • Suppose the peso is currently worth $0.10 ( e = $.10) costs ten percent more pesos to buy Mexican cars, food, 0 vacations, etc. • In Mexican terms, the USD ‘costs’ ten pesos. • Also, suppose the U.S. has no inflation, so cars, etc. still • If Mexico’s 10% inflation extends to foreign currency, cost the same in the U.S. (in terms of the USD). then the USD should rise in cost to 11 pesos. • If the exchange remains fixed, American consumers • The new spot rate (in American terms) will fall to will now want to wants U.S. goods and services over Mexican goods and services (which are now more 1USD/Peso11 = $.909 expensive). • e1 = e0 (1 + ih)/(1 + if) = $0.10 (1 + 0)/(1 + .10) = $.909 • Mexicans will want more American products and these • where e = expected future spot rate, e = spot rate, still sell at the old peso price. 1 0 i = expected home (USA) inflation (and is zero), and • Thus more demand for the USD, less demand for the h peso. The price of the peso should fall until?.... if = expected foreign inflation. Values only known in the future (uncertainties) are represented by italics. Forecasting with (Relative) PPP Forecasting with Relative PPP • e1 = e0 (1 + ih)/(1 + if) Note, this very important • The general version for “t” periods is equation uses direct quotes. e = e (1 + i )t/(1 + i )t or • If the U.S. also has inflation - assume two percent - • t 0 h f then we would expect the peso depreciation to be less • In the previous example, if the Peso is worth ten severe. cents today, we would estimate that the peso • e1 = e0 (1 + ih)/(1 + if) would be worth • = $0.10 (1 + .02)/(1 + .10) • $0.10(1.02)/(1.10) = $0.0927 in one year • = $.927 $0.10(1.02)2/(1.10)2 = $0.0856 in two years • Exhibit 4.5 shows a relationship between changes in $0.10(1.02)3/(1.10)3 = $0.0797 in three years exchange rates and relative inflation rates. Yen: lowest inflation, held value best. PPP: Real Exchange Rates PPP: Real Exchange Rates • Suppose Mexico has 10% inflation, we have none. From • PPP is based on the assumption that real the previous example, we found that we could expect the ’) exchange rates ( et stay the same. Peso to fall from $0.10 to $0.0909. ’ • That is, the barter exchange rate of goods stays • e1 = e1(1 + if)/(1 + 0) the same between countries, so exchange rates • = .09107 (1 + .10) = .10 adjust to differences in inflation. • (1) If the peso falls to $.0909, we say the peso’s real exchange rate is unchanged. ’ t t • et = et(1 + ih) /(1 + if) is constant. • (2) If the peso falls more than 0.0909, it has fallen in • This property is usually violated in the short run real terms. but appears to hold up in the long run. • (3) If it stays at 10 cents we say it has risen in real terms. 3 PPP: Real Exchange Rates Inflation and “Real” Interest Rates • It is important that you understand, at least intuitively, the logic of the these three outcomes. • We often make a distinction between the normal everyday contract rate of interest, and the • Again, real exchange rates are rarely constant in the short run but appears to be steady in the long run. interest rate that is adjusted for any loss of purchasing power caused by inflation. • Look at the 9 graphs in Exhibit 4.6: the dark steady lines represent a constant real (inflation-adjusted) exchange • The everyday contract rate is called the nominal rate. interest rate, denoted in the text as “r”. • The blue, wiggly lines are the actual rates. • The rate adjusted to any reflect loss of • The real rate acts like a ‘magnet’ for the actual exchange purchasing power is the real rate, denoted in rate. textbook as “a”. • Irving Fisher popularized the use of the real rate and thus the relationship was named after him. Inflation and “Real” Rates Inflation and “Real” Rates • A simple version of this “Fisher Effect” is a • The T-bill rate is more like 1.7%, so the real T- = r- i, where a is the expected real rate, r is the bill rate is expected to be 0.2%. nominal rate, and i is expected inflation. • Note that each nominal rate has its own • Under current conditions this would be: the T- corresponding real rate. bond YTM is 3.9%, inflation is expected to be 1.5%, therefore the expected real rate on the • There is, however, an interaction effect that is T-bond is 2.4% . reflected in the full, more correct formula: • Note: the real rate is usually the residual of the • (1+a) = (1 + r)/(1 + i) nominal rate and inflation. That is, you start • or (1+r) = (1 + a)(1 + i) = 1 + a + i + a*i with some nominal rate and inflation and compute the real rate. • r = a + r + a*r where a*i is similar to compounding between i and a. Inflation and “Real” Rates Inflation and “Real” Rates • Example: Suppose we expect Russia to have • Not just 105% 100% inflation next year and we want an • (1+r) = (1 + a)(1 + i) investment that will increase our purchasing • r = (1 + a)(1 + i) -1 power by 5% (the real return).
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