Lecture 2: Exchange Rate Concepts
An exchange rate can be quoted in two ways:
Direct: The price of the foreign currency in terms of dollars
(以本國貨幣表示之外國貨幣價格)
Indirect: The price of dollars in terms of the foreign currency
(以外國貨幣表示之本國貨幣價格)
1. International Financial Market
See the quotes on Financial Times (midpoint between bid and offer rates) and Wall
Street Journal (offer or selling rate).
The worldwide volume of foreign exchange trading is enormous, and it has ballooned
in recent years. The Bank for International Settlements estimated the trading value
was close to $600 billion per day, and reached $1.2 trillion per day in 1998.
New technologies, such as Internet links, are used among the major foreign exchange
trading centers (London, New York, Tokyo, Frankfurt, and Singapore).
Vehicle currency: determined primarily by transactions costs.
Whenever the indirect exchange costs through the vehicle are less than direct
exchange costs between two non-vehicle currencies. Example: Peso-USD and
USD-Won vs. Peso-Won.
Quotes in European terms (goes up, domestic currency appreciation)
American terms (goes up, domestic currency depreciation)
Types of Transaction:
a. Spot: Apply to exchange currencies “on the spot”
b. Forward: Apply to exchange currencies on some future date at a prenegotiated
exchange rate
c. Future: The buyer buys a promise that a specified amount of foreign currency
will be delivered on a specified date in the future.
d. Option: The owner has the right to buy or sell a specified amount of foreign
currency at a specified price at any time up to a specified expiration date.
e. Swap: Spot sales of a currency combined with a forward repurchase of the
currency. They make up a significant proportion of all foreign exchange
trading.
f. NDF( Non-delivery forward): Purchase/Sale Agreement is a contractual
obligation to compensate the affected counterpart in the event of any
difference between the market rate on any given date and the agreed rate,
taking into account the contracted amount of the product (e.g., US$). At no
time is there physical delivery of the product.
Arbitrage: The process of buying a currency cheap and selling it dear.
Triangular arbitrage
Assume there are no transactions costs,
S1  S 3x S 2
The dollar price of pound (=1.60), the euro price of the pound (=1.55), and the dollar
price of the euro (=1.10) respectively. Begin with 1.60 dollars and end up with
1.705 dollars.
Related Articles: *Taiwan’s exchange market (1) (2) (3)*
2. Average Exchange Rates
(Effective Exchange Rate Index)
Nominal: A nominal effective exchange rate is the exchange rate of the domestic
currency vis-à-vis other currencies weighted by their share in either the country
international trade or payments.
Fed’s index has weights based on the various nations’ relative sizes in world trade
IMF bases its weights on the various volume of trade with the United States
Real: Real effective exchange rates take account of price level differences between
trading partners. Movements in real effective exchange rates provide an indication of
the evolution of a country’s aggregate external price competitiveness.
3. Real Exchange Rates
PT / PNT
PCPI / PW PI
Terms of Trade:
Px / Pm
4. Purchasing Power Parity
LOP: law of one price
Absolute PPP
Relative PPP
OECD: Purchasing Power Parities (PPPs) are currency conversion rates that both
convert to a common currency and equalise the purchasing power of different
currencies. In other words, they eliminate the differences in price levels between
countries in the process of conversion.
How many products are included in the basket of goods and services used for the
PPP calculation?
The final products list for the 1999 comparison covered around 2,500 consumer goods and
services, 34 occupations in government, education and health services, 186 types of
equipment goods and 20 construction projects? The large number of price specifications is to
enable as many countries as possible to identify goods and services which are representative
of their domestic expenditures. However, countries are expected to provide only a relatively
small subset of these prices (several hundred in general).
Big Mac Parity
Exchange rate Pass Through
Related Articles: * (4)(5)(6)(7)*
5. PPP and Non-Traded Goods
Assume that price level is the linear combination of the prices of tradables and
non-tradables. (natural log)
P  1   PT  PNT
e及P為
對數型式
*
P *  1   PT*  PNT
PPP holds for tradable goods:
e  PT  PT*
Real exchange rate:
q  e  P*  P
*
q  PT  PT*  1   PT*  PNT
 1   PT  PNT
*
 PT* 
  PNT  PT    PNT
Z NT
*
Z NT
Balassa (1964) and Samuelson (1964), two-sector model, free labor mobility within
the country, perfect competition, and different productivities:
PT 
W
AT
，
PT* 
W*
AT*
，
PNT 
*
PNT

W
ANT
W*
*
ANT
lnPNT PT   ln AT ANT   Z NT
W：表示工資率
A：生產力
不同部門之工資率相同




*
*
*
ln PNT
PT*  ln AT* ANT
 Z NT

*
q   ln  AT ANT  +  ln AT* ANT

6. Interest Parity
Eurocurrency: a foreign currency denominated deposit at a bank located outside the
country where the currency is used as legal tender.
London Interbank Offer Rate (LIBOR): the rate at which banks are willing to lend to
the most creditworthy banks participating in the London Interbank market.
Covered Interest Parity
1  it  (1  it )
Ft
St
Example:
1 + 0.0678 > (1 + 0.0422)
0.9961
= 1.0178
1.0200
There is arbitrage profit.
Logarithmic approximation,
it  it  f t  st
Uncovered Interest Parity
1  it  (1  it )
S te1
St
6. Forward Premium Puzzles
Market efficiency and rational expectation
Assume that covered interest rate parity (IRP):
1  it  (1  it )
Ft
 i  i  f  s
St
If there is rational expectation with risk–free economic agent, market efficiency
implies that the hypothesis test in the regression coefficients of
st 1  st     ( f t 1  st )   t 1 is   0,   1.
Most empirical studies reject the null hypothesis.
Possible explanations:
a. Risk premium
i  i   ( f  s)  
b. Peso problem
One-period-ahead rationally expected future spot rate is
Et ( st 1 )  ps1  (1  p) s0
s0 , fixed; s1 , uncredible
If the forward exchange rate is the market’s expected future spot rate, we have a
rational explanation for the forward premium bias. Although the forecast errors are
serially correlated, they are not useful in predicting the future depreciation.
c. Noise traders
The market participants are not fully rational. Some (noise) traders are unable to
distinguish between pseudo-signals and news. Short-horizon rational investors bear
the risk that they may be required to liquidate their positions at a time when noise
traders have pushed asset prices even farther away from the fundamental value.