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

Perspective! The U.S. E $ 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 . . .

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 . . .

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 Purchasing Power Parity 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!

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

Purchasing Power Parity 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? US bonds earn $1200*1.06 = $1272. For British bonds: $1200/1.2 = £1000; in one year, bond earns £1080; converts back at (1.18)*(1080) = $1274.40  What if the risk premiums differed? Wait …

Buying Future Dollars iBrit + [(Ef - E)/E] In US terms, the British bond earns: iBrit + iBrit*[(Ef - E)/E] + [(Ef - E)/E] iBrit + [(Ef - E)/E] .08 + (.08)*[(1.18-1.2)/1.2] + (-.02/1.2) = 6.2% With well functioning markets 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) We can cancel out both iBrit If Ee=Ef, we can cancel them out reUS = reBrit

Revisit Bond Problem What if the UK bond had a risk premium of +0.3% over the US bond? U.K. return = $74.4/1200 = 6.2% … but adjusted for risk = 5.9% 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