# five parity conditions 1. interest rate parity aka covered interest parity. 2. unbiased forward...

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Five Parity Conditions1. Interest Rate Parity aka Covered Interest Parity.2. Unbiased Forward Rates.3. Uncovered Interest Parity.4. Real Interest Parity.5. Purchasing Power Parity.

Unbiased Forward RatesOn 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).

Uncovered Interest ParityCombine 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.

- UIP: IntuitionRF>RD implies S1
UIP: Formulas

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.

Application of ex-post uncovered interest parityCAC 40 rose by 53.64 %, euro depreciated by 14.94% (vis--vis C$)during a certain year.What rate of return did Canadian investor achieve?30.69% = (1+53.64%)x(1- 14.94%) 130.69% measured in C$s, 53.64% measured in euros.

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%.Jan03:U$0.63/C$ vs. Dec03:U$0.737/C$.Appreciation of C$: (.737/.63)-1=17%.(1+19%)=(1+1.7%)(1+17%)

Charlie Canuck continuedWhats depreciation of U$? 17%? Not!!Jan03:C$1.587 vs. Dec03:C$1.357.U$appreciation=(1.357/1.587)-1= -14.5%

Real Interest ParityReal 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).

RIP: Formulas

Purchasing Power ParityLaw 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.

Big MacCurrencies Down UndaBM price in U.S. = U$2.32BM price in Aus. = A$2.45PPP implies: S(A$/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%.

More on Aussie Big MacsPrice 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 countrys currency.

PPP across timePPP holds at start of yearPPP holds at end of year(Send/Sstart) = (1+Id)/(1+If)(1+af) = (1+Id)/(1+If)Intuition: A high inflation currency will depreciate.

PPP across time: Formulas

Real Exchange RateInflation adjusted exchange rateMust account for two inflation rates: domestic and foreignReal FX Rate at t = (Nominal FX Rate at t) X (1+Foreign Inflation Rate/1+Domestic Inflation Rate) ^ tImportant over long time horizons when inflation exerts its effect

PPP and Real FX RatesPPP implies that real FX rates dont changeAll inflation rates cancel outResult: 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.

PPP and Real FX Rates

Thai T-Shirt Tale: application of real FX rateGauge profitability at start vs. end of yearProfitability = Baht profit margin per T-shirtTwo different year end scenarios examinedFirst scenario: Violation of PPP, nominal FX rate constant, real FX rate changesSecond scenario: Consistent with PPP, nominal FX rate changes, real FX rate constant

Thai T-Shirt: First ScenarioReal value of baht (currency of cost) risesReal value of C$ (currency of revenue) dropsNo nominal change in FX rateProfit margin is squeezedConclusion: Profitability impaired if currency of cost appreciates or currency of revenue depreciates in real terms

Thai T-Shirt: Second ScenarioReal FX rate does not changeNominal FX rate changesProfitability is unaffected, real value of profit margin remains intactConclusion: Nominal exchange rate may change but if real exchange rate does not, profitability is not affected.

Thai T-Shirt: AddendumIf currency of cost depreciates or the currency of revenue appreciates in real terms, profitability is enhancedNo numerical example given for this case

To assess competitive advantage, get real!! (not nominal)