1. Five Parity Conditions 1. Interest Rate Parity aka Covered Interest Parity. 2. Unbiased Forward Rates. 3. Uncovered Interest Parity. 4. Real Interest Parity. 5. Purchasing Power Parity.

2. Unbiased Forward Rates On the average, forward rate = spot rate that will prevail at maturity. If = does not hold, the prospect of profits exists. Arbitrage? Not! Make money with no investment but with risk: Buy low, sell high! FX that exhibits a forward premium (discount) will appreciate (depreciate).

3. Uncovered Interest Parity Combine interest rate parity with unbiased forward rates. Transactions are identical to those of interest rate parity but with no forward hedging. There is FX risk. Seek profit by borrowing low and investing high but this is not arbitrage.

4. UIP: Intuition R F >R D implies S 1 <S 0. A high interest rate currency will depreciate (IRP: exhibit forward discount). Similarly, a low interest rate currency will appreciate (IRP: exhibit a forward premium).

5. UIP: Formulas

6. Ex-post application of uncovered interest parity. True ex-post by definition. Split up domestic currency rate of return on a foreign security into two components: rate of return of the foreign security and the appreciation of the foreign currency. Investment in a foreign security means investment in two different factors.

7. Application of ex-post uncovered interest parity CAC 40 rose by 53.64 %, euro depreciated by 14.94% (vis-à-vis C$)during a certain year. What rate of return did Canadian investor achieve? 30.69% = (1+53.64%)x(1- 14.94%) –1 30.69% measured in C$’s, 53.64% measured in euros.

8. Who ripped off Charlie Canuck? Focus: S&P500 for 2003. RU$, rate of return in U$’s, = 19%. RC$, rate of return in C$’s, = 1.7%. Jan’03:U$0.63/C$ vs. Dec’03:U$0.737/C$. Appreciation of C$: (.737/.63)-1=17%. (1+19%)=(1+1.7%)(1+17%)

9. Charlie Canuck continued What’s depreciation of U$? 17%? Not!! Jan’03:C$1.587 vs. Dec’03:C$1.357. U$appreciation=(1.357/1.587)-1= -14.5%

10. Real Interest Parity Real interest rates tend to be equalized across currencies. High inflation currency exhibits high interest rates. (1+foreign interest rate) / (1+foreign inflation rate)=(1+domestic interest rate) / (1+domestic inflation rate).

11. RIP: Formulas

12. Purchasing Power Parity Law of one price: a commodity must trade at same exchange rate adjusted price. Domestic price = S x Foreign price. If > holds: buy foreign, sell domestic. If < holds: buy domestic, sell foreign. Commodity arbitrage tends to make inequality disappear.

13. Big MacCurrencies Down Unda BM price in U.S. = U$2.32 BM price in Aus. = A$2.45 PPP implies: S(A$/U$) = A$2.45/U$2.32 = A$1.06/U$. Compare to actual S = A$1.35/U$. U$ overvalued, A$ undervalued. Overvaluation of U$ = 27.36% implies undervaluation of A$ = 22%.

14. More on Aussie Big Macs Price of BM in Aus. In U$=A$2.45/A$1.35 = U$1.82. Compare with US price = U$2.32. Overvaluation of BM in Aus. = -22%. The overvaluation of a commodity in a country reflects the overvaluation of that country’s currency.

15. PPP across time PPP holds at start of year PPP holds at end of year (S end /S start ) = (1+I d )/(1+I f ) (1+a f ) = (1+I d )/(1+I f ) Intuition: A high inflation currency will depreciate.

16. PPP across time: Formulas

17. Real Exchange Rate Inflation adjusted exchange rate Must account for two inflation rates: domestic and foreign Real FX Rate at t = (Nominal FX Rate at t) X (1+Foreign Inflation Rate/1+Domestic Inflation Rate) ^ t Important over long time horizons when inflation exerts its effect

18. PPP and Real FX Rates PPP implies that real FX rates don’t change All inflation rates cancel out Result: real FX rate at end of period = nominal (and real) FX rate at start of period Interpretation: If inflation is the sole cause of a change in FX rates, then the FX rates although changing in nominal terms are constant in real terms.

19. PPP and Real FX Rates

20. Thai T-Shirt Tale: application of real FX rate Gauge profitability at start vs. end of year Profitability = Baht profit margin per T-shirt Two different year end scenarios examined First scenario: Violation of PPP, nominal FX rate constant, real FX rate changes Second scenario: Consistent with PPP, nominal FX rate changes, real FX rate constant

21. Thai T-Shirt: First Scenario Real value of baht (currency of cost) rises Real value of C$ (currency of revenue) drops No nominal change in FX rate Profit margin is squeezed Conclusion: Profitability impaired if currency of cost appreciates or currency of revenue depreciates in real terms

22. Thai T-Shirt: Second Scenario Real FX rate does not change Nominal FX rate changes Profitability is unaffected, real value of profit margin remains intact Conclusion: Nominal exchange rate may change but if real exchange rate does not, profitability is not affected.

23. Thai T-Shirt: Addendum If currency of cost depreciates or the currency of revenue appreciates in real terms, profitability is enhanced No numerical example given for this case

24. To assess competitive advantage, get real!! (not nominal) Real Appreciation Real Depreciation Currency of Revenues GainLose (Thai T-shirt 1 st scenario) Currency of Costs Lose (Thai T-shirt 1 st scenario) Gain