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: 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
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%
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
1
1
1:&
itFugitaboutIsAPRRs
IRIRIsCCRs
I
R
I
RIsEARRs
FFDD
F
F
D
D
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$2.32.
• Overvaluation of BM in Aus. = -22%.
• The overvaluation of a commodity in a country reflects the overvaluation of that country’s currency.
PPP across time
• PPP holds at start of year
• PPP holds at end of year
• (Send/Sstart) = (1+Id)/(1+If)
• (1+af) = (1+Id)/(1+If)
• Intuition: A high inflation currency will depreciate.
PPP across time: Formulas
F
DT
TIIT
T
F
DT
TI
TI
S
SIsAPR
eS
SIsCC
I
I
S
SIsEAR
FD
1
1:
:
1
1:
0
0
0
Real Exchange Rate
• Inflation adjusted exchange rate• Must account for two inflation rates:
domestic and foreign• Real FX Rate at t = (Nominal FX Rate at t)
X (1+Foreign Inflation Rate/1+Domestic Inflation Rate) ^ t
• Important over long time horizons when inflation exerts its effect
PPP and Real FX Rates
• PPP implies that real FX rates don’t change• All inflation rates cancel out• Result: real FX rate at end of period =
nominal (and real) FX rate at start of period• Interpretation: If inflation is the sole cause
of a change in FX rates, then the FX rates although changing in nominal terms are constant in real terms.
PPP and Real FX Rates
PPPttREALt
PPPttREALt
PPPttREALt
t
D
FtREALt
t
F
DPPPt
SSSS
SSSS
SSSS
I
ISS
I
ISS
,0,
,0,
,0,
,
0,
1
1
1
1
Thai T-Shirt Tale: application of real FX rate
• Gauge profitability at start vs. end of year• Profitability = Baht profit margin per T-shirt• Two different year end scenarios examined• First scenario: Violation of PPP, nominal
FX rate constant, real FX rate changes• Second scenario: Consistent with PPP,
nominal FX rate changes, real FX rate constant
Thai T-Shirt: First Scenario
• Real value of baht (currency of cost) rises• Real value of C$ (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 Lose
(Thai T-shirt 1st scenario)
Currency of Costs
Lose
(Thai T-shirt 1st scenario)
Gain
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