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.
• 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 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.
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).
UIP more intuition: effect of sudden
lowering of FX interest rate
• S(RMB/C$) F = Canada, D = China: RD = RF
• No change in S projected
• Bank of Canada lowers bank rate; People’s Bank
of China hold interest rate steady
• Then RD > RF: Impact on S0, S1?
• Primary effect: S0 drops
• Secondary (more muted) effect: S1 drops
• [S1 / S0] > 1: a low interest rate FX will appreciate
UIP: Formulas
ST 1  RD 
RsEAR :


S 0 1  RF 
ST
 RD  RF T
RsCC :
e
S0
T
ST 1  TRD 
RsAPR :


S 0 1  TRF 
Ex-post application of uncovered
interest parity.
• True ex-post by definition.
• Split up domestic currency rate of return on
a foreign security into two components: rate
of return of the foreign security and the
appreciation of the foreign currency.
• Investment in a foreign security means
investment in two different factors.
Application of ex-post uncovered
interest parity
• CAC 40 rose by 53.64 %, euro depreciated
by 14.94% (vis-à-vis C$)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$’s, 53.64%
measured in euros.
Who ripped off Charlie Canuck?
•
•
•
•
•
•
Focus: S&P500 for 2003.
RU$, 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$: (.737/.63)-1=17%.
(1+19%)=(1+1.7%)(1+17%)
Charlie Canuck continued
•
•
•
•
What’s depreciation of U$? 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.
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.
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).
RIP: Formulas
1  RD 1  RF
Rs & IsEAR :

1 ID 1 IF
Rs & IsCC : RD  I D  RF  I F
Rs & IsAPR : Fugitaboutit!
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.
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%.
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$2.32.
• Overvaluation of BM in Aus. = -22%.
• The overvaluation of a commodity in a
country reflects the overvaluation of that
country’s currency.
PPP across time
•
•
•
•
•
PPP holds at start of year
PPP holds at end of year
(Send/Sstart) = (1+Id)/(1+If)
(1+af) = (1+Id)/(1+If)
Intuition: A high inflation currency will
depreciate.
PPP across time: Formulas
ST 1  I D 
IsEAR :


S 0 1  I F 
ST
IsCC :
 e  I D  I F T
S0
T
ST 1  TI D 
IsAPR :


S 0 1  TI F 
Canadian Exporter
• Transactions Exposure - FX cash flows it
will receive over the next 6 months are
contractually set.
• Operating Exposure – FX cash flows it may
receive beyond the 6-month time horizon
from contracts as yet unsigned.
• More subtle forms of operating exposure in
vignettes.
Four operating exposure
vignettes
• 1. Aspen Skiing: Revenues exhibited
positive operating exposure.
• 2. Laker Airways: Ditto, but negative
operating exposure.
• 3. Petróleos Mexicanos: Revenues
denominated/determined by U$.
• 4. YCF: Revenues denominated in APeso
but determined by U$.
Aspen Skiing
• Colorado resort: all balance sheet items and
cash flows in greenbacks.
• Yet exposed to C$, FFr, etc.
• In 1983, U$ appreciated, I.e. C$, FFr
depreciated.
• Domestic and foreign clientele shifted
holidays to Banff, Chamonix, Chicopee.
Aspen Skiing
Y-axis: Cash flows in U$; X-axis: S(U$/C$)
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.
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$, FFr, etc.
Laker Airways
• Early exploiter of air transport deregulation
in late 70’s. Target market: Price conscious
Brit tourists vacationing in Florida.
• Cost structure: jet fuel U$-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.
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.
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.
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.
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$’s.
• Negative transactions exposure of debt
service offsets positive exposure of
revenues.
Yacimientos Pertrolíferos
Fiscales (YPF)
• Most of output sold domestically, i.e.,
Argentine peso denominated.
• Debt denomination in U$´s also makes
sense! Huh??
• No price controls on domestic oil.
• PPP applies to oil. If U$ rises, peso price of
oil rises.
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.
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.
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)
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
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.
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.
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.
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 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.
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$.
Tin Man: Possible Conclusions
Value of t
Exposure to
Pound Sterling?
Currency of
Determination
<2
(Observed)
No
U.S. Dollar
>2
(Not observed)
Yes
Pound Sterling
Tin Man: effects of different debt
denominations
• Message of regression: CF(gross of debt
service) in U$’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.
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
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.
PPP and Real FX Rates
S t , PPP
1 ID 

 S 0 
1 IF 
t
t
1 IF 

S t , REAL  S t 
1 ID 
S t , REAL  S 0  St  St , PPP
S t , REAL  S 0  S t  St , PPP
S t , REAL  S 0  St  St , PPP
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.
Compare aobserved with appp
•
•
•
•
•
(1+ aobserved )^T= ST / S
(1+ aPPP )^T= ST,PPP / S
really = in real terms
aobserved > appp: FX really appreciated
aobserved < appp: FX really depreciated
o
o
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
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)
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
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.
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
To assess competitive advantage,
get real!! (not nominal)
Real
Appreciation
Real
Depreciation
Currency of
Revenues
Gain
Currency of
Costs
Lose
(Thai T-shirt 1st
scenario)
Lose
(Thai T-shirt 1st
scenario)
Gain
Mean-Reversion of Real FX Rates
• Empirical evidence: real FX rates are meanreverting, 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)
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
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.
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.