Currency Forwards
FINC 456
Currency Forward Markets:
Why do we care?
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Currency forwards are some of the most widely used
and most liquid risk management products available.
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Trade 24 hours a day, nearly 365 days a year somewhere in
the OTC market
The most liquid currencies tend to be the large European
countries, but recently banks have aggressively begun
selling forwards on much more “exotic” currencies, at least
for short (1 year and less) maturities.
The concept is relatively simple…if the company is
receiving or paying a certain amount of currency in
the future, the company can lock in the value today.
Simple Currency Hedging
Situations: Importers
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Suppose your computer company has contracted to
buy 100,000 memory chips from Japan in 6 months,
at 500 yen per chip.
At an exchange rate of 120 yen/dollar, that’s $416,667.
If the exchange rate goes to 150/dollar it’s $333,333.
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Is this a depreciation of the yen or an appreciation?
If the exchange rate goes to 100 yen/dollar, that’s $500,000.
So your company’s risk is to movements in the yen,
specifically when the yen/dollar rate decreases…
So what to do?
Simple Currency Hedging
Situations: Exporters
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Suppose that you are selling your computers in
Europe, all 25,000 of them at €1000 and expect to
receive the euros in a year.
At an exchange rate of 1.25 ($/euro), that’s $31,250,000.
If the rate goes to 1.40, you receive $35 million.
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Is this a depreciation or an appreciation of the euro?
If the rate goes to 1, you receive $25,000,000.
So your risk is to movements in the Euro rate,
specifically to decreases in the rate…
So what do you do?
Hedging exchange rate risk
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If you are receiving the foreign currency, you are at
risk from a devaluation (or depreciation).
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That’s because each unit of the currency will be worth less
in dollar terms.
To hedge this risk, you sell the currency forward and lock
in today’s rate.
If you are spending the foreign currency in the
future, you are at risk from a re-valuation (or
appreciation).
That’s because each foreign currency unit will require
more dollars to buy.
To hedge this risk, you buy the currency forward…
Currency forwards: the market
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Currency forwards are quoted in forward points, or
the amount that you’d add or subtract to the spot
rate to get the forward rate for that period.
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The number of decimals is just considered “known,” that
is, 2 for the yen, 5 for most other liquid currencies…
The actual forward rate is know as the outright.
Currency forwards are essentially interest rate
products (as we’ll see in a few slides) and as such
are available wherever and to whatever maturity
liquid deposit markets exist in that currency.
Digression:
LIBOR and deposit markets
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LIBOR, or the London Inter-Bank Offer Rate, is
the interest rate of choice for real world currency
forward applications.
LIBOR fixings are quoted daily at 11:00 a.m.
London time for terms of up to 1 year.
The most liquid LIBOR’s are the 3 and 6 month
fixings
LIBOR is quoted in many currencies:
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For example GBP; USD; EUR; JPY; CHF; CAD, etc.
LIBOR rates are annually compounded on an
ACT/360 basis…
Pricing Currency Forwards
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If we think about currencies as any other
commodity, it is not so strange to think of a
currency “growing” at its interest rate.
And if that’s the case, the relevant formula is:
F0 = S 0 e
( rd − r f )T
Note that q, the growth rate, has been replaced by
rf, the foreign interest rate
This formula presumes, requires, has to have,spot rates
quoted as the spot price in dollars of one unit of foreign
currency
$
That is,
S≡
Foreign
Another way of thinking about
currency forwards
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Suppose that the yen is trading at 105 and the 1 year
forward is –200 points.
I have two investments available for my $1000:
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I can invest my dollars here for 2%
I can buy yen today, invest the yen at .5%, and then sell a
forward contract to deliver the yen for dollars in a year.
In a year, my dollars are worth $1020.20 (cont. comp).
I buy 105,000 yen, and in a year, these are worth
105,526.31 yen, which I sell at 103, giving me $1024.53.
If the forward rate is 100 do I have more or fewer dollars?
Arbitrage in Euros
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Suppose that I sell Euros forward at 1.20 for 2 years,
and the spot rate today is 1.25, and US rates are 2%.
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This means I must deliver the Euros in 2 years and receive
1.25 dollars.
For instance if I sell 100,000 euros forward, I’ll receive for
sure $120,000 in 2 years.
How many Euros do I need to buy today in order to
have 100,000 of them in 2 years if euro rates are 3%?
How about 94,176 euros…or $117,721?
If I just invested the dollars I’d have $122,524 in two years…
Is the forward cheap or expensive?
Arbitrage in Euros, con’t
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Can I make some money here?
How about if I buy the Euros forward at 1.05…
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So, maybe I can pay them back to someone…
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But what is my risk here…I’ll have Euros in 2 years and I
really don’t want them!
Why don’t I borrow Euros today (I’ll need to pay back
100,000 of them, so borrow 94,176).
I’ll sell them at the spot rate, and get $117,721.
And invest that amount at 2% here…to get $122,525.
In 2 years, I earn $2,525 for sure…so I keep buying
forwards!
The Money Market Hedge
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If I sell Euros forward, I’ll receive dollars for Euros in
the future.
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I could also receive dollars and pay Euros by:
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Do this to hedge depreciation or appreciation risk?
Borrowing Euros
Selling the borrowed Euros in the spot market to get dollars
Lending out the dollars
The difference in interest rates essentially locks in a
forward rate!
When I get my Euros in the future, I use them to pay back
the loan…
So what do forward markets tell us
about interest rates?
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If the forward implies a depreciation, of the
currency, interest rates in that country are higher
than in the US.
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What’s the intuition here?
If the forward implies an appreciation of the
currency, interest rates in that country are lower
than in the US.
What’s a good example here?
Currency Forward Markets:
The real world
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Often, especially in emerging markets, there are
impediments to one side of the arbitrage
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For instance, before the Mexican devaluation, it was
difficult/impossible to borrow pesos and difficult to sell in the
spot market…
The continuing restrictions in Argentina are another perfect
example…
Banks or companies with significant operations “in country”
have advantages, since they can use the currency, and
observe deposit flows
Occasionally, non-delivery forwards are offered to circumvent
these restrictions
These are cash-settled, and either hedged using futures,
correlated markets, or by selling products to investors
Currency Markets:
The real world formula
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If we are not in the continuously compounded
world, the money-market deposit version of the
forward pricing formula is:
(
(
)
)
 1 + rUS t

basis 
F0 = S 0 

 1+ r t
f

basis 
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And remember, with the bid/ask spread, the second
rule of finance…you as the consumer always lose
money to the bank.