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

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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