Exchange Rate  the exchange rate represents the number
of units of one currency that exchanges for a unit of another. There are
two ways to express an exchange rate between two currencies (e.g. the
$ and £ [pound]). One can either write $/£ or £/$ . These
are reciprocals of each other. Thus if E is the $/£ exchange rate
and V is the £/$ exchange rate then E = 1/V.
For Example, on Jan 8, 1997 the following exchange rates prevailed,
E_{$/£} = 1.69 which implies V_{£/$
}= 0.59
V_{¥/$} = 116. which implies E_{$/¥
}= 0.0086
Currency Value
It is important to note that the value of a currency is always given in terms of another currency.
Thus the value of a US dollar in terms of British pounds is the £/$ exchange rate. The value of
the Japanese yen in terms of dollar is the $/¥ exchange rate.
[Note: we always express the value of all items in terms of something
else. Thus, the value of a quart of milk is given in dollars, not in milk
units. The value of car is also given in dollar terms, not in terms of
cars. Similarly, the value of a dollar is given in terms of something
else, usually another currency. Hence the rupee/$ exchange rate gives
us the value of the dollar in terms of rupees.]
This definition is especially useful to remember when one is dealing
with unfamiliar currencies. Thus the value of the euro (€) in terms
of British pounds is given as the £/€ exchange rate.
The peso/€ exchange rate refers to the value of the euro in terms
of pesos.
Currency appreciation  a currency appreciates with respect to another when its value rises in
terms of the other. The dollar appreciates with respect to the yen if the ¥/$ exchange rate rises.
Currency depreciation  a currency depreciates with respect to another when its value falls in
terms of the other. The dollar depreciates with respect to the yen if the ¥/$ exchange rate falls.
Note that if the ¥/$ rate rises, then its reciprocal, the $/¥ rate falls. Since the $/¥ rate represents
the value of the yen in terms of dollars, this means that when the dollar appreciates with respect to
the yen, the yen must depreciate with respect to the dollar.
The rate of appreciation (or depreciation) is the percentage change in the value of a currency
over some period of time.
Example #1:
On Jan. 8 1997, E_{¥/$} = 116
On Jan. 8 1996, E_{¥/$} = 105
Use percentage change formula: (New value  Old value)/Old Value
Multiply by 100 to write as a percentage to get,
0.105 x 100 = +10.5%
Since we have calculated the change in the value of the $, in terms of yen, and since the
percentage change is positive, this means that the dollar has appreciated by 10.5% with respect to
the yen during the past year.
Example #2:
On Jan. 8 1997, E_{£/$} = 0.59
On Jan. 8 1996, E_{£/$} = 0.65
Use percentage change formula: (New value  Old value)/Old Value
Multiply by 100 to write as a percentage to get,
0.092 x 100 = 9.2%
Since we have calculated the change in the value of the $, in terms of pounds, and since the
percentage change is negative, this means that the dollar has depreciated by 9.2% with respect to
the pound during the past year.
Arbitrage  arbitrage, generally means buying a product when its price is low and then reselling it
after its price rises in order to make a profit. Currency arbitrage means buying a currency in one
market (say New York) at a low price and reselling, moments later, in another market at a higher
price.
Spot Exchange Rate  the spot exchange rate refers to the exchange rate that prevails on the spot,
that is, for trades to take place immediately.
Forward Exchange Rate  the forward exchange rate refers to the rate which appears on a
contract to exchange currencies either 30, 60, 90 or 180 days in the future.
For example a corporation might sign a contract with a bank to buy DMs for dollars 60 days from
now at a predetermined ER. The predetermined rate is called the 60day forward rate. Forward
contracts can be used to reduce exchange rate risk.
For example suppose an importer of BMWs is expecting a shipment in 60 days.
Suppose that upon arrival the importer must pay €1,000,000. The current
spot ER is 1.20 $/€ thus if the payment were made today it would
cost $1,200,000. Suppose further that the importer is fearful of a $ depreciation.
He doesn't currently have the $1,200,000 but expects to earn more than
enough in sales over the next two months. If the $ falls in value to,
say, 1.3 $/€ in 60 days time, how much would cost the importer in
dollars to purchase the BMW shipment?
A. The shipment would still cost €1,000,000. To find out how much
this is in dollars multiply €1,000,000 by 1.3 $/€ = $1,300,000.
Note this is $100.000 more for the cars simply because the $ value changed.
One way the importer could protect himself against this potential loss
is to purchase a forward contract to buy € for $ in 60 days. The
ER on the forward contract will likely be different from the current spot
ER. In part its value will reflect market expectations about the degree
to which currency values will change in the next two months. Suppose the
current 60day forward ER is 1.25 $/€ reflecting the expectation
that the $ value will fall. If the importer purchases a 60day contract
to buy €1,000,000 it will cost him (1,000,000 x 1.25) = $1,250,000.
Although this is higher than what it would cost if the exchange were made
today, the importer does not have the cash available to make the trade
today, and the forward contract would protect the importer from even an
even greater $depreciation.
When the forward ER is such that a forward trade costs more than a spot trade today costs, there
is said to be a forward premium. If the reverse were true, such that the forward trade were
cheaper than a spot trade then there is a forward discount.
Hedging  a currency trader is hedging if he or she
enters into a forward contract to protect oneself from a downside loss.
However by hedging the trader also forfeits the potential for an upside
gain. Suppose in the story above that the spot ER falls rather than falls.
Suppose the ER fell to 1.10 $/€ . In this case, had the importer
waited the €1,000,000 would only have cost (1,000,000 x 1.10) = $1,100,000.
Thus, hedging protects against loss but at the same time eliminaters potential
unexpected gain.
