Five Parity Conditions
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Transcript of 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.
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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).
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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.
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UIP: Intuition
• RF>RD implies S1<S0. A high interest rate currency will depreciate (IRP: exhibit forward discount).
• Similarly, a low interest rate currency will appreciate (IRP: exhibit a forward premium).
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UIP more intuition: effect of sudden lowering of FX interest rate
• S(RMB/C$) F = Canada, D = China: RD = RF
• No change in S projected• Bank of Canada lowers bank rate; People’s Bank
of China hold interest rate steady• Then RD > RF: Impact on S0, S1?• Primary effect: S0 drops• Secondary (more muted) effect: S1 drops• [S1 / S0] > 1: a low interest rate FX will appreciate
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UIP: Formulas
F
DT
TRRT
T
F
DT
TR
TR
S
SRsAPR
eS
SRsCC
R
R
S
SRsEAR
FD
1
1:
:
1
1:
0
0
0
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Ex-post application of uncovered interest parity.
• True ex-post by definition.
• Split up domestic currency rate of return on a foreign security into two components: rate of return of the foreign security and the appreciation of the foreign currency.
• Investment in a foreign security means investment in two different factors.
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Application of ex-post uncovered interest parity
• CAC 40 rose by 53.64 %, euro depreciated by 14.94% (vis-à-vis C$)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$’s, 53.64%
measured in euros.
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Who ripped off Charlie Canuck?
• Focus: S&P500 for 2003.
• RU$, 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$: (.737/.63)-1=17%.
• (1+19%)=(1+1.7%)(1+17%)
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Charlie Canuck continued
• What’s depreciation of U$? 17%? Not!!• Jan’03:C$1.587 vs. Dec’03:C$1.357.• U$appreciation=(1.357/1.587)-1= -14.5%• Exact Relation: (1+17%) = (1-14.5%)^-1;
(1+C$appreciation)=(1+U$appreciation)^-1• One plus appreciation of one currency
equals the reciprocal of one plus appreciation of the other currency.
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Two Useful Transformations• Appreciation 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.
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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).
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RIP: Formulas
!:&
:&
1
1
1
1:&
itFugitaboutIsAPRRs
IRIRIsCCRs
I
R
I
RIsEARRs
FFDD
F
F
D
D
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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.
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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%.
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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$2.32.
• Overvaluation of BM in Aus. = -22%.
• The overvaluation of a commodity in a country reflects the overvaluation of that country’s currency.
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PPP across time
• PPP holds at start of year
• PPP holds at end of year
• (Send/Sstart) = (1+Id)/(1+If)
• (1+af) = (1+Id)/(1+If)
• Intuition: A high inflation currency will depreciate.
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PPP across time: Formulas
F
DT
TIIT
T
F
DT
TI
TI
S
SIsAPR
eS
SIsCC
I
I
S
SIsEAR
FD
1
1:
:
1
1:
0
0
0
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Canadian Exporter
• Transactions Exposure - FX cash flows it will receive over the next 6 months are contractually set.
• Operating Exposure – FX cash flows it may receive beyond the 6-month time horizon from contracts as yet unsigned.
• More subtle forms of operating exposure in vignettes.
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Four operating exposure vignettes
• 1. Aspen Skiing: Revenues exhibited positive operating exposure.
• 2. Laker Airways: Ditto, but negative operating exposure.
• 3. Petróleos Mexicanos: Revenues denominated/determined by U$.
• 4. YCF: Revenues denominated in APeso but determined by U$.
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Aspen Skiing
• Colorado resort: all balance sheet items and cash flows in greenbacks.
• Yet exposed to C$, FFr, etc.
• In 1983, U$ appreciated, I.e. C$, FFr depreciated.
• Domestic and foreign clientele shifted holidays to Banff, Chamonix, Chicopee.
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Aspen Skiing
Y-axis: Cash flows in U$; X-axis: S(U$/C$)
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Aspen Skiing: Lesson Gleaned
Although you operate exclusively domestically, if your clientele has the option of purchasing in a foreign market, you exhibit positive exposure to that foreign market’s currency. A U.S. firm with Aspen Skiing as client likewise possesses the same type of exposure.
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Aspen Skiing: Two Hedges
• Hedge 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$, FFr, etc.
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Laker Airways
• Early exploiter of air transport deregulation in late 70’s. Target market: Price conscious Brit tourists vacationing in Florida.
• Cost structure: jet fuel U$-denominated.• Financed jets with cheap U$-debt provided
by US Ex-Im Bank.• Steep U$ appreciated in early 80’s spelled
doom for Laker Airways.
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Laker Airways’ Exposures
• Jet 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.
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Laker Airways: Lessons Gleaned
• If your business involves assisting a domestic clientele purchase goods/services in a foreign country, you have negative operating exposure to that foreign country’s currency.
• Dollar denomination of debt aggravated the firm’s negative exposure to the greenback.
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Sir Freddie’s Egregious Error
• Error: 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.
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Petróleos Mexicanos
• Most of output sold in world oil markets, ergo U$-denominated.
• Revenues exhibit both transactions and operating exposure to U$.
• Hedge: debt denominated in U$’s.• Negative transactions exposure of debt
service offsets positive exposure of revenues.
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Yacimientos Pertrolíferos Fiscales (YPF)
• Most of output sold domestically, i.e., Argentine peso denominated.
• Debt denomination in U$´s also makes sense! Huh??
• No price controls on domestic oil.
• PPP applies to oil. If U$ rises, peso price of oil rises.
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YPF
• Revenues: 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.
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Pemex & YPF: Lessons Gleaned
• Pemex: 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.
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Yankee Inc.’s Exposures
• US firm exports to UK; major competitor in UK is importer from France
• Export 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)
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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.
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Canuck Ltd.’s Operating Exposure
• Measured as slope of Canuck’s 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 period• Regression model improves this approach: slope
calculation and statistical test.
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Hedging operating exposure
• Use 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.
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Measuring Operating Exposure
• Slope 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.
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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.
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Simple Regression Slope
• Denominated in units of foreign currency.
• As if that amount of FX received per period.
• Null hypothesis: slope = 0, I.e., no operating exposure.
• Alternative hypothesis: slope not = 0, I.e., operating exposure exists.
• Reject null: absolute value of t statistic > 2.
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Ballad of the Tin Man
• Application of regression approach.• Simple regression slope coefficient is not
significant. Ergo, no operating exposure to PS, PS denominated debt not appropriate.
• Although the acquired company generates PS CF’s, debt employed in acquisition should be U$ denominated.
• Ballad’s: currency of denomination is PS, currency of determination is U$.
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Tin Man: Possible Conclusions
Value of t Exposure to Pound Sterling?
Currency of Determination
<2
(Observed)
No U.S. Dollar
>2
(Not observed)
Yes Pound Sterling
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Tin Man: effects of different debt denominations
• Message of regression: CF(gross of debt service) in U$’s not affected by FX rate.
• With PS debt: Rise in PS causes a reduction in U$ net of debt service CF.
• With U$ debt: Rise in PS causes no change in U$ net of debt service CF.
• PS debt causes negative exposure to PS.
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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
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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.
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PPP and Real FX Rates
PPPttREALt
PPPttREALt
PPPttREALt
t
D
FtREALt
t
F
DPPPt
SSSS
SSSS
SSSS
I
ISS
I
ISS
,0,
,0,
,0,
,
0,
1
1
1
1
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Nexus: PPP & Real FX Rate
• Real FX appreciation means the FX appreciated too much or depreciated too little.
• Real FX depreciation means the FX depreciated too much or appreciated too little.
• Too much or too little using PPP as benchmark. • No change in real FX rate means the FX behaved
exactly in accordance with PPP.
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Compare aobserved with appp
• (1+ aobserved )^T= ST / So
• (1+ aPPP )^T= ST,PPP / So
• really = in real terms
• aobserved > appp: FX really appreciated
• aobserved < appp: FX really depreciated
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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
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Thai T-Shirt Manufacturer• Incurs costs in baht• Exports to Canada, revenues in C$• Faces Canada-based competitors in Canada• Default assumption in this course: exporter based
in country X (Thailand) faces competitors in country Y (Canada) who are based in country Y
• Paradigm: 2 firms competing in same market (Canada) but sourcing in 2 different countries (Canada, Thailand)
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Thai T-Shirt: First Scenario
• Real value of baht (currency of cost) rises• Real value of C$ (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
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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.
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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
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To assess competitive advantage, get real!! (not nominal)
Real Appreciation
Real Depreciation
Currency of Revenues
Gain Lose
(Thai T-shirt 1st scenario)
Currency of Costs
Lose
(Thai T-shirt 1st scenario)
Gain
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Mean-Reversion of Real FX Rates
• Empirical evidence: real FX rates are mean-reverting, i.e., real appreciation (depreciation) is followed sooner or later by real depreciation (appreciation)
• Consistent with PPP holding in the long run i.e., real FX rates don’t change in the long run
• Implication: Episode of competitive advantage gain (loss) will sooner or later be followed by competitive advantage loss (gain)
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Accounting Exposure
• Accounting rules for the determination of FX exposure found in Section 1650 of CICA Handbook
• Applies to both GAAP and IFRS• Emphasizes transactions exposure, tending to
ignore operating exposure• Accounting = Transactions Exposure• May yield an inaccurate view of a firm’s true FX
exposure
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Accounting vs. Transactions/Operating Exposure• Canadian firm with operating exposure to
sterling creates transactions exposure to establish a perfect hedge.
• Operating exposure: C$ revenue stream positively exposed to sterling (Canadian competitors import from UK).
• Transactions exposure: debt denominated in sterling.
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Accounting vs. Transactions/Operating Exposure• Canadian firm based on accounting rules
(accounting exposure) is damaged by the rise in sterling.
• In fact, market value of stockholder wealth is not affected.
• Accounting exposure does not yield a true picture of Canadian firm’s FX exposure.