five parity conditions

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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. Unbiased Forward Rates. On the average , forward rate = spot rate that will prevail at maturity. - PowerPoint PPT Presentation


  • 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 more intuition: effect of sudden lowering of FX interest rateS(RMB/C$) F = Canada, D = China: RD = RF No change in S projectedBank of Canada lowers bank rate; Peoples Bank of China hold interest rate steadyThen RD > RF: Impact on S0, S1?Primary effect: S0 dropsSecondary (more muted) effect: S1 drops[S1 / S0] > 1: a low interest rate FX will appreciate

  • 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%Exact Relation: (1+17%) = (1-14.5%)^-1; (1+C$appreciation)=(1+U$appreciation)^-1One plus appreciation of one currency equals the reciprocal of one plus appreciation of the other currency.

  • Two Useful TransformationsAppreciation in one currency vs. appreciation in the other currency.Rate of return on a security measured in one currency vs. rate of return on the same security measured in another currency.Must know how to transform data provided!The data are provided in the form of percentages.Data must be converted into decimal format before the transformations can be applied.

  • 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

  • Canadian ExporterTransactions Exposure - FX cash flows it will receive over the next 6 months are contractually set.Operating Exposure FX cash flows it may receive beyond the 6-month time horizon from contracts as yet unsigned.More subtle forms of operating exposure in vignettes.

  • Four operating exposure vignettes1. Aspen Skiing: Revenues exhibited positive operating exposure.2. Laker Airways: Ditto, but negative operating exposure.3. Petrleos Mexicanos: Revenues denominated/determined by U$.4. YCF: Revenues denominated in APeso but determined by U$.

  • Aspen SkiingColorado resort: all balance sheet items and cash flows in greenbacks.Yet exposed to C$, FFr, etc.In 1983, U$ appreciated, I.e. C$, FFr depreciated.Domestic and foreign clientele shifted holidays to Banff, Chamonix, Chicopee.

  • Aspen SkiingY-axis: Cash flows in U$; X-axis: S(U$/C$)

  • Aspen Skiing: Lesson GleanedAlthough you operate exclusively domestically, if your clientele has the option of purchasing in a foreign market, you exhibit positive exposure to that foreign markets currency. A U.S. firm with Aspen Skiing as client likewise possesses the same type of exposure.

  • Aspen Skiing: Two HedgesHedge positive operating exposure of cash flows to C$, FFr, etc.Denominate some debt in C$, FFr, etc. Result: negative transactions exposure of debt offsets positive operating exposure of revenues.Buy resorts in Canada, France, etc. Result: some revenue streams rise, other fall with rise in C$, FFr, etc.

  • Laker AirwaysEarly exploiter of air transport deregulation in late 70s. Target market: Price conscious Brit tourists vacationing in Florida.Cost structure: jet fuel U$-denominated.Financed jets with cheap U$-debt provided by US Ex-Im Bank.Steep U$ appreciated in early 80s spelled doom for Laker Airways.

  • Laker Airways ExposuresJet fuel: both transactions and operating exposure to U$.Debt: transactions exposure to U$.Revenues: negative operating exposure to U$. When U$ appreciated target clientele shifted holidays from Florida to Palma de Mallorca, Islas Canarias, Marbella, etc.

  • Laker Airways: Lessons GleanedIf your business involves assisting a domestic clientele purchase goods/services in a foreign country, you have negative operating exposure to that foreign countrys currency.Dollar denomination of debt aggravated the firms negative exposure to the greenback.

  • Sir Freddies Egregious ErrorError: Denominated debt in U$s.Appreciation of U$ resulted in: Sterling value of costs and debt service increasing; Sterling value of revenues decreasing.Sir Freddie got squeezed!Hedges: debt denominated in Sterling; cater to Yank clientele vacationing in UK.

  • Petrleos MexicanosMost of output sold in world oil markets, ergo U$-denominated.Revenues exhibit both transactions and operating exposure to U$.Hedge: debt denominated in U$s.Negative transactions exposure of debt service offsets positive exposure of revenues.

  • Yacimientos Pertrolferos Fiscales (YPF)Most of output sold domestically, i.e., Argentine peso denominated.Debt denomination in U$s also makes sense! Huh??No price controls on domestic oil. PPP applies to oil. If U$ rises, peso price of oil rises.

  • YPFRevenues: currency of denomination is peso but currency of determination is U$.PPP: Ppeso = Pworld(U$) X S(AP/U$).For PPP to hold, Ppeso must rise if S rises.Hedge: debt denominated in U$s. Transactions exposure of debt offsets operating exposure of revenues.

  • Pemex & YPF: Lessons GleanedPemex: Transaction exposure of debt service (denomination of debt in a foreign currency) can offset the positive transactions/operating exposure of a revenue stream.YPF: As in Pemex, but revenue stream possess only positive operating (no transactions) exposure to a foreign currency.

  • Yankee Inc.s ExposuresUS firm exports to UK; major competitor in UK is importer from FranceExport contracts denominated in sterling Yankee faces positive transactions exposure to sterling; X variable is S(USD/BPS)Yankee faces positive operating exposure to the euro; X variable is S(USD/EUR)

  • Canuck Ltd.Canadian firm operating exclusively in Canada.Competitor in Canada sources product in the UK.Canuck Ltd. has positive exposure to the Pound Sterling, PS.

  • Canuck Ltd.s Operating ExposureMeasured as slope of Canucks risk profile.Vertical axis = cash flow measured in reference currency (C$).Horizontal axis = FX rate measured in direct quotation (C$/PS).Somehow calculate slope = PS1.923M, say. Interpret: As if receiving PS1.923M per periodRegression model improves this approach: slope calculation and statistical test.

  • Hedging operating exposureUse denomination of long-term debt.How to determine extent of exposure? Simple regression (use direct quotation).Regress domestic currency CF on FX exchange rate.Or regress domestic currency rate-of-return on %-age appreciation of FX.

  • Measuring Operating ExposureSlope term of simple regression.X-variable: S in direct quotation; also appreciation in S.Y-variable: cash flow in reference currency; also growth rate in cash flow.Critical statistics: slope term, t-statistic for slope term.

  • 3 possible regression specifications:Y = CF in reference currency and X = S (direct quotation) e.g. Tin Man.Y = rate of return on stock measured in reference currency and X = % appreciation of S (direct quotation) e.g. Selamat Malam.Y = growth rate in CF measured in reference currency and X = % appreciation of S (direct quotation) e.g. Marubeni-Iida.

  • Simple Regression SlopeDenominated in units of foreign currency.As if that amount of FX rece


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