Foreign Exchange Markets, Purchasing Power Parity, and Real Interest Parity ECO 473 - Money & Banking - Dr. D. Foster

Perspective! The U.S. We want to buy foreign exchange. We don’t really want the “money.” We want the goods/services/financial assets We pay $ to get foreign exchange. When the $ appreciates, we can buy more . . . i.e. the price is lower. When the $ appreciates, the £ depreciates. When $ depreciates … price is higher.

Perspective! The U.S. We demand foreign exchange - £, Ұ, € $ (per £) The market for pounds (£) E = $2 Demand shows: our demand for British goods and services (our imports) E = $1 D £ At higher prices… it takes more dollars to buy a pound, British goods are more expensive, the dollar is depreciating (and the £ is appreciating). At lower prices … Q£

Perspective! The U.S. $ (per £) What would shift the demand for British pounds? The market for pounds (£) The Fed may buy pounds! A change in our tastes and preferences for their goods. A change in our income. A change in trade restrictions. A change in monetary policy... D’£ D £ D”£ Q£

Perspective! The U.S. Foreigners supply foreign exchange - £, Ұ, € S £ Q£ E = $2 E = $1 Supply shows: British demand for dollars to buy our goods (our exports). To acquire $ they must supply £. The market for pounds (£) At higher prices… pounds buy more dollars, American goods are cheaper, the dollar is depreciating (and the £ is appreciating). At lower prices …

Perspective! The U.S. S £ $ (per £) Q£ S’£ What would shift the supply of British pounds? S’£ A change in their tastes and preferences for our goods. A change in their income. A change in trade restrictions. A change in monetary policy... The Fed may sell pounds! The market for pounds (£)

Perspective! The U.S. $ depreciates; the price rises; we buy less $ appreciates; the price falls; we buy more D £ S £ $ (per £) Q£ E Equilibrium in the market for pounds (£) Exchange rate changes as S & D change . . .

Perspective! The U.S. Q - What if we want less British goods? A - Increase Demand; E rises; $ depreciates E’ S’ A - Increase Supply; E falls; $ appreciates E’ D’ A - Decrease Demand; E falls; $ appreciates D £ S £ $ (per £) Q£ E Q - What if our incomes rise? Q - What if Brits want more US goods?

Perspective! Britain They want to buy foreign exchange ($). They don’t really want the “money.” They want our goods/services/financial assets They pay £ to get $ (foreign exchange). When the £ appreciates, they can buy more . . . i.e. the price is lower. When the £ appreciates, the $ depreciates. When £ depreciates … price is higher.

Exchange rate changes as S & D change . . . Perspective! Britain £ depreciates; the price rises; we buy less D $ S $ £ (per $) Q$ 1 E $ appreciates £ appreciates; the price falls; we buy more $ depreciates Exchange rate changes as S & D change . . .

Perspective! Britain Q - What if we want less British goods? A - Increase Demand; 1/E rises; $ appreciates 1/E’ D’ 1/E’ S’ A - Increase Supply; 1/E falls; $ depreciates 1/E’ S’ A - Decrease Supply; 1/E rises; $ appreciates Q - What if U.S. incomes rise? D $ S $ £ (per $) Q$ 1/E Q - What if Brits want more US goods?

Current Exchange Rates D $ S $ £ (per $) Q$ $ (per £) S £ .7994 1.251 D £ Q£

Real Exchange Rates Nominal: What we see reported. SFr/US $: 2015 – 1.229 2016 – 1.171 Nominal %Δ: – 4.72% (1.171−1.229) 1.229

Real Exchange Rates Nominal: What we see reported. Real: Adjusted for price level changes. Real = Nominal*(CPIUS/CPISFr) SFr/US $: 2015 – 1.229 2016 – 1.171 CPI (Swiss): 2015 - 100 2016 - 102 CPI (US): 2015 - 100 2016 - 103 1.1825 Nominal %Δ: – 4.72% Real %Δ: – 3.785% (1.171−1.229) 1.229 1.171∗ 103 102 (1.1825−1.229) 1.229

Real Exchange Rates Who’s perspective? Draw it out . . . SFr/$ S$ So, the $ is . . . 1.171 1.229 . . . depreciating in value.

Purchasing Power Parity Where . . . transportation costs are zero. tax differentials do not exist. there are no trade restrictions. goods are homogeneous. Law of One Price: A unit of goods in one country trades for the same price in another country.

Example - Apples in U.S. & Britain U.S. price = $.50; British = £.75 If exchange rate is .667 ($/£) then the apple sells for the same price in both. What if the exchange rate is .75? Sell apple in Britain for .75 (£) and convert to $: (£.75)*(.75) = $.562 for a 6.2 cent profit! What happens . . .?

Arbitrage results U.S. -  demand for apples -  apple prices Britain -  supply of apples -  apple prices .667 .75 S£ S£1 D£ S/£ Q£ In U.S. foreign exchange market,  S£ as arbitrageurs convert back to $. On your own - show this from the British perspective.

Different PPP models Absolute PPP: CPIUS = E(CPIBrit) if this can be applied to all goods, assumes goods mix the same in both. Solve for rate: E = (CPIUS)/(CPIBrit) Relative PPP: %ΔE = %Δ(CPIUS) - %Δ(CPIBrit) differences in inflation rates explain . . . appreciating/depreciating exchange rates. Long-run data tends to confirm this.

Hedging your bets - Futures Market Buying Future Dollars Hedging your bets - Futures Market You want to buy British bonds . . . earning iBrit but you face the risk of changing E . . . So, you buy $ futures contract. Locks in your financial outcome . . .

What if the risk premiums differed? Wait … Buying Future Dollars Let iUS=6% and iBrit=8% with E=1.2 E aka “spot rate.” Let the forward rate be Ef=1.18 With $1200, should you invest in US bonds or British bonds? British bonds . . . buy £1000 bond; in one year, worth £1080; converts back at (1.18)*(1080) = $1274; In US, would make $1272. What if the risk premiums differed? Wait …

(Ee - E)/E = (ius-reUS) - (iBrit-reBrit) Buying Future Dollars British bond earns: iBrit + [(Ef - E)/E] in equilibrium, this equals ius Noting relative PPP: %Ee = eUS - eBrit where e=expected and =inflation. Using r to represent real interest, rewrite as: (Ee - E)/E = (ius-reUS) - (iBrit-reBrit)

Real Interest Rate Parity Substituting for iUS (Ee - E)/E = (iBrit + [(Ef - E)/E] -reUS) - (iBrit-reBrit) Canceling for iBrit cancel out and if Ee=Ef, then: reUS = reBrit

Revisit Bond Problem What if the UK bond had a risk premium of +0.3% over the US bond? U.K. return = $74/1200 = 6.17% … but adjusted for risk = 5.87% U.S. return = 6%; take the U.S. bond!!!

Foreign Exchange & Monetary Policy Gold Standard Fixed X∆ rates, K flows, $ policy Bretton Woods System Fixed X∆ rates, K flows, $ policy Unmanaged free floating rates Volatile X∆ rates, K flows, $ policy Managed rates Semi-fixed X∆ rates, K flows, ???$ policy

Foreign Exchange Markets, Purchasing Power Parity, and Real Interest Parity ECO 473 - Money & Banking - Dr. D. Foster