Week 3
The Foreign Exchange Markets
Spot quotes, bid
-
ask spreads,
Spot
quotes,
bid
ask
spreads,
triangular arbitrage. Forward rates
FINOPMGT 413
Spot and Forward Markets
• Foreign exchange trading occurs in two separate,
but connected, markets: Spot and the Forward
market.
• Spot market: Buying and selling of f/x with
libidfd
sett
l
ement
i
n 2
b
us
i
ness
d
ays
f
rom to
d
ay.
• Forward market: Settlement occurs at some future
dt
d
a
t
e.
– That is, you may enter into a forward contract to buy 10
million Yen 90 days from today
FINOPMGT 413
million
Yen
90
days
from
today
.
F/X Rate Quotes
• We can view F/X rates as quotes in direct or indirect
terms.
• Direct: a direct f/x quote is in units of domestic currency
per unit of foreign currency [DC/FC].
– For exam
p
le
,
a
q
uote of the USD-British Pound is direct for the
p, q
US$ if it is quoted as 1.9631US$/BP.
• Indirect: an indirect f/x quote is in units of foreign
currency per unit of domestic currency [FC/DC].
– Example: 106.86 Yen/US$ is an indirect quote for the US$ (but
direct quote for the Yen).
• We will interpret every quote as being “direct”:
DC/FC Therefore we will always think of whichever
DC/FC
.
Therefore
,
we
will
always
think
of
whichever
country is in the denominator as being the “foreign”
country. Please always remember this convention.
FINOPMGT 413
Appreciation/Depreciation
• A currency is said to appreciate (depreciate) against a
foreign currency if you can buy more (less) foreign
currency per unit of domestic currency
currency
per
unit
of
domestic
currency
.
• Examples: The WSJ reported the following on Wednesday
– “Yesterday afternoon in New York, the euro was at $1.4635 from
$
1 4827 late Monda ”
The E ro b s less dollars on
Tesda
as
$
1
.
4827
late
Monda
y
”
.
The
E
u
ro
b
uy
s
less
dollars
on
T
u
esda
y
as
opposed to Monday; therefore, the Euro depreciated (and the $
appreciated).
–
If the Yen
-
$ rate changed from
106.86
Yen/$ to
106.74
Y/$, has
If
the
Yen
$
rate
changed
from
106.86
Yen/$
to
106.74
Y/$,
has
the Yen appreciated or depreciated? [Answer: Depreciated]
• When the currency is quoted in direct terms then an
increase
(decrease) in the quote is an
appreciation
increase
(decrease)
in
the
quote
is
an
appreciation
(depreciation) of the foreign currency.
• When its quoted in indirect terms, then an increase in the
rate is an appreciation of the domestic currency
FINOPMGT 413
rate
is
an
appreciation
of
the
domestic
currency
.
Cross Rates
• The cross rate is the exchange rate for converting one
foreign currency to another For example the rate for
foreign
currency
to
another
.
For
example
,
the
rate
for
Yen/BP would be a called a cross rate. If we know the
exchange rate for US$-Yen and US$-BP, we can easily
calculate the cross rate
calculate
the
cross
rate
.
• Example: Friday, Sept 14, 2007
• US$/BP=2.0068, Yen/US$ = 115.30, US$/Euro=1.3878
• What is the Yen/BP cross rate? (Answer: 231.38 Yen/BP)
• What is the Euro/BP cross rate? (Answer: 1.4460 Euro/BP)
•
Qt: Given the rates of the previous week did the Yen
•
Qt:
Given
the
rates
of
the
previous
week
did
the
Yen
appreciate or depreciate against the BP?
FINOPMGT 413
Arbitraging Cross Rates (1/2)
Arbitraging
Cross
Rates
(1/2)
• Suppose a bank quotes you the following rates: US$/BP=
1.8193
,
Yen/US$ = 110.27
,
and 199 Yen/BP.
,
,
• The implied Yen/BP cross rate (from the $/BP, Yen/$
quotes) is 200.61 Yen/BP.
•
If the implied cross rate does not equal the quoted cross
•
If
the
implied
cross
rate
does
not
equal
the
quoted
cross
rate, there there exists an arbitrage opportunity (in this
case, the arbitrage opportunity has a specific name -
“triangular arbitrage”)
“triangular
arbitrage”)
.
• How would you actually implement such an arbitrage?
Buy low, sell high.
• In other words, you buy the currency where it is cheaper,
and sell where it is more expensive.
FINOPMGT 413
Arbitra
g
in
g
Cross Rates
(
1/2
)
gg ( )
• The Yen is cheaper at 200.61 Y/BP and more expensive at
199 Yen/BP.
• So you buy Yen @ 200.61 (sell BP) and sell Yen @ 199
(buy BP).
•
How do you implement the arbitrage trade? You
•
How
do
you
implement
the
arbitrage
trade?
You
simultaneously make the following trades:
• Buy Yen for US$ @110.27, Sell Yen for BP @199 , Sell
f S$ @ 1 8193
BP
f
or U
S$
@
1
.
8193
.
– US$ 1 => 110.27 Yen (@110.27Yen/$)
– Yen 110.27 => (110.27/199) = 0.5541 BP (@ 199 Yen/BP)
– BP 0.5541=> 1.0081 US$ (@1.8193$/BP)
• You make gains of $8,100 for every $1 million in capital.
FINOPMGT 413
Summarizing Steps in Triangular Arbitrage
Summarizing
Steps
in
Triangular
Arbitrage
• Assume that the three currencies are the US$ and two other foreign
c rrencies and that o ant to make o r arbitrage in US$
c
u
rrencies
and
that
y
o
u w
ant
to
make
y
o
u
r
arbitrage
in
US$
.
• 1. Identify the weaker non-US currency between implied cross rate and
quoted cross rate.
–
Yen is weaker at im
p
lied cross rate of 200.61 Yen/BP as com
p
ared with
pp
actual quote of 199 Yen/BP.
• 2. Buy the weak currency low.
– Buy Yen @ 110.27 Y/US$.
$1 => 110 27 Yen
–
$1
=>
110
.
27
Yen
• 3. Sell the currency you bought in (2.) high at the cross-rate to buy the
other currency cheap
– Sell Yen @ 199 Yen/BP.
–
110.27 Yen =>0.5541 BP
• 4. Sell the currency high to buy the US$ cheap.
– Sell BP @ 1.8193 US$/BP
–
0 5541 BP
=
> $1 0081
FINOPMGT 413
–
0
.
5541
BP
>
$1
.
0081
Bid-Ask Spreads
• As the dealer who trades forei
g
n currenc
y
with
y
ou has to
gyy
make money, there is a bid-ask spread associated with the
quote, i.e. the price for buying the foreign currency is
different from the price for selling the currency
different
from
the
price
for
selling
the
currency
.
• Bid: the price at which the dealer is willing to buy the
foreign currency
• Ask or Offer: the price at which the dealer is willing to
sell the foreign currency.
FINOPMGT 413
Examples of Bid
Ask Spreads
Examples
of
Bid
-
Ask
Spreads
•
BP
-
US$: 1 8220
-
1 8229 $/BP
BP
-
US$:
1
.
8220
-
1
.
8229
$/BP
• The quote of 1.8220 is the bid or the price at which the
dealer will buy the BP (foreign currency) and 1.8229 is the
ask price.
• Qt: On a $1,000,000 round-trip transaction with the BP,
what is the cost that you incur because of the bid
-
ask
what
is
the
cost
that
you
incur
because
of
the
bid
-
ask
spread on BP? Ans: $494
FINOPMGT 413
Bid
AkR dIdi Q
Bid
-
A
s
k
R
ates an
d
I
n
di
rect
Q
uotes
•Su
pp
ose the rate is
q
uoted in indirect terms. What is the bid
pp q
(ask)?
• Example: Yen/USD 107.66 – 107.72
•
We have to be careful of how the currency is quoted to
•
We
have
to
be
careful
of
how
the
currency
is
quoted
to
figure out the bid and ask (using the principle that the dealer
will buy foreign currency low and sell FC high).
Th h d l ill b (
b
id) Y 107 72 d ll
•
Th
us: t
h
e
d
ea
l
er w
ill
b
uy
(
b
id)
Y
en at
107
.
72
an
d
se
ll
(offer) at 107.66 (and the dealer will buy USD at 107.66 and
sell at 107.72.)
• If the currency is quoted in direct (indirect) then the lower
(higher) number is the bid.
•
A word of warning: Its easy to get confused unless you
FINOPMGT 413
A
word
of
warning:
Its
easy
to
get
confused
unless
you
always use one convention.
Bid-Ask and Cross Rates (1/2)
bk
$/ d
• Suppose a US
b
an
k
quotes 1.7019-36
$/
BP, an
d
0.9850-67
$/Euro. What would be the cross rate for Euro/BP in
Frankfurt?
• In Frankfurt, the dealer will buy BP at the lower rate and
sell BP at a higher rate (in terms of the Euro). So the cross
t ill fl t thi
ra
t
e w
ill
re
fl
ec
t
thi
s.
• Bid: the dealer buys BP at $1.7019 (lower price, bid), and
sells Euro at 0.9867
(
hi
g
her
p
rice
,
ask
)
=
(g p , )
1.7019/0.9867=1.7250 Euro/BP.
FINOPMGT 413
Bid-Ask and Cross Rates (2/2)
i il l h ff h d l ill ll h
•S
i
m
il
ar
l
y, to get t
h
e o
ff
er rate: t
h
e
d
ea
l
er w
ill
se
ll
BP at t
h
e
higher rate (in terms of Euro).
•
So: Dealer sells BP for USD at offer or ask rate of
So:
Dealer
sells
BP
for
USD
at
offer
or
ask
rate
of
US$1.7036/BP, and buys Euro at bid rate of $0.9850. So
the offer rate for Euro/BP is:1.7036/0.9850=1.7295
E/BP
E
uro
/BP
.
• Therefore: the cross rate is 1.7250-1.7295 Euro/BP.
FINOPMGT 413
Triangular Arbitrage with Bid-Ask Spreads (1/2)
•
1
1 7019
36 $/BP
•
1
.
1
.
7019
-
36
$/BP
•2. 0.9850-67$/Euro
•
3
1 7200
1 7300 Euro/BP
•
3
.
1
.
7200
-
1
.
7300
Euro/BP
• The implied cross rate is 1.7248-95 Euro/BP.
D thi tit t t i l bit ?
•
D
oes
thi
s cons
tit
u
t
e a
t
r
i
angu
l
ar ar
bit
rage
?
FINOPMGT 413
Triangular Arbitrage with Bid-Ask Spreads (2/2)
• For there to be a trian
g
ular arbitra
g
e
,
y
ou have to be able to
gg,y
buy low and sell high.
• Dealer 1 (implied cross rate): 1.7248-95
• Dealer 2 : 1.7200-1.7300.
• Can you buy the BP low and sell it high?
No Because one dealer sells you BP @ 1 7290 while the second
–
No
.
Because
one
dealer
sells
you
BP
@
1
.
7290
while
the
second
buys @ 1.7200. You cannot reverse the transaction also because
the second dealer will sell you at 1.7300, and the first dealer buys
at 1.7248. In each case, you lose money.
at
1.7248.
In
each
case,
you
lose
money.
• Qt: Can you give examples of a quote that would allow for
arbitrage? Provide two examples, one where the BP is
id l d h ii id hih
FINOPMGT 413
p
r
i
ce
d
too
l
ow, an
d
one w
h
ere
i
t
i
s pr
i
ce
d
too
hi
g
h
.
Forward Rate Basics (1/2)
• What is a
f
orward rate a
g
reement?
fg
• The forward exchange contract is an agreement to
exchange currencies in the future at a fixed exchange rate.
•
H
ow does one determine the forward exchange rate?
• Answer: by the basic pricing principle that the forward
exchange rate should be such that it does not allow for
exchange
rate
should
be
such
that
it
does
not
allow
for
arbitrage.
FINOPMGT 413
Basics (2/2)
Basics
(2/2)
•
According to the WSJ, on
2/6/2008,
the
spot for
According
to
the
WSJ,
on
2/6/2008,
the
spot
for
the Japanese Yen was at 106.86, the 3 month
forward was at 106.24, the 6-month forward at
105.76.
• Thus, the Yen traded at a premium (was stronger)
in the futures market.
– Does the futures prices indicate that the market expects
the Yen to appreciate over the next year?
the
Yen
to
appreciate
over
the
next
year?
FINOPMGT 413
What determines the Forward Rate
What
determines
the
Forward
Rate
•
Expectations do not determine the forward exchange rate
•
Expectations
do
not
determine
the
forward
exchange
rate
.
It does not matter that people think or feel that the currency
is going to depreciate or appreciate.
• What determines the forward exchange rate? The forward
exchange rate only depends on the relative interest rates.
FINOPMGT 413
Th F d E h R t
Th
e
F
orwar
d
E
xc
h
an
g
e
R
a
t
e
• The forward exchange rate only depends on the
li i
re
l
at
i
ve
i
nterest rates.
• Here are the Euro-currency interest rates as of
2/6/2008
(from the CME):
2/6/2008
(from
the
CME):
• June Eurodollar = 2.43%
•
June
Euro
-
yen
=
0 67%
June
Euro
yen
0
.
67%
We shall see that the Yen forward is at a premium
to the s
p
ot
(
Yen is stron
g
er
)
b
ecause the interest
p( g)
rates in Yen are lower that the interest rates in
US$.
FINOPMGT 413
An example to motivate the pricing of the
fd/f
f
orwar
d/f
uture
• Suppose, as an importer of Japanese goods, you need to
make a payment in Yen exactly one year from today.
However, you don’t want to take any exchange rate risk:
how can you eliminate exchange risk? You have two
how
can
you
eliminate
exchange
risk?
You
have
two
options:
• 1. Enter into a forward contract today - this will guarantee
you an exchange rate of F, where F is the forward
exchange rate.
•
2 Buy Yen today at the spot rate S and hold the Yen
2
.
Buy
Yen
today
at
the
spot
rate
,
S
,
and
hold
the
Yen
until you need it in the future.
FINOPMGT 413
Determinin
g
the forward rate
g
• Which option will you prefer?
Ahldbidiffbh
•
A
nswer: you s
h
ou
ld
b
e
i
n
diff
erent
b
etween t
h
e two,
because if they are priced such that you prefer one over the
other,
y
ou can make an arbitra
g
e
p
rofit.
ygp
• Consider the first option, when you enter into a forward
contract today at F Y/$. If you start off with $1 today, then
this will guarantee you 1(1 + r(US) ) F Yen/USD This
this
will
guarantee
you
1(1
+
r(US)
)
F
Yen/USD
.
This
assumes that you invest your $1 in an US bank and earn
the US interest rate.
FINOPMGT 413
• Alternativel
y,
y
ou can use
y
our
$
1 to bu
y
S
y
en toda
y,
and
y, y y $ y y y,
invest these S yen in a Japanese bank, earning an interest
rate of r(JP). This will guarantee you an amount of S(1 +
r(JP) after a year
r(JP)
after
a
year
.
• It must be that in either case you have the same amount of
money, so that:
• F (1 + r(US)) = S(1+r(JP)) Yen/US$
• F = S(1+r(JP))/(1 + r(US)) Yen/US$
FINOPMGT 413
The Forward Rate when Exchange Rates are quoted
The
Forward
Rate
when
Exchange
Rates
are
quoted
in Direct Terms
• It is im
p
ortant to note the units: is it DC/FC or FC/DC.
p
• Suppose the rate is quoted in direct terms: $/Yen.
• Then the 1-year forward price would be:
• F = S(1 + r(US))/(1 + r(JP)) $/Yen
• In general for n days (when we use the Eurocurrency
it t t )
i
n
t
eres
t
ra
t
es
)
:
• F = S(1 + r(US) (n/360) )/ (1 + r(JP) (n/360))
•
We will use the notation that
*
represents the interest rate
We
will
use
the
notation
that
represents
the
interest
rate
in the foreign currency, so that we can also write:
• F = S(1 + r(n/360) )/ (1 + r* (n/360))
FINOPMGT 413
CME Eurocurency Quotes
• Note: The CME quotes the interest rate contracts
as (100-r)%, where r is the interest rate.
– If the December Eurodollar rate is 2.43%, the futures
contract will be quoted at 100 - 2.43 = 97.57.
Th t t th i t t t f th f t
•
Th
us,
t
o ge
t
th
e
i
n
t
eres
t
ra
t
e
f
rom
th
e
f
u
t
ures
contract price, subtract the futures price from 100.
If the futures price is 95 285 then the interest rate is
–
If
the
futures
price
is
95
.
285
,
then
the
interest
rate
is
(100-95.285)=4.715%.
FINOPMGT 413
Pricing the Currency Future
• The spot on 2/6/2008 is 106.57 Yen/US$. The June Euro-yen
contract is at =99.33, and the June Euro-dollar contract is at
97 57
97
.
57
.
• From the price of the futures contract, the interest rates are:
–
US$ interest rate =
(
100
–
97.570
)
=2.43%.
(
)
– Yen interest rate = (100 – 99.330) = 0.67%
• What would be the price of the June‘08 $-Yen futures
contract?
contract?
• The contract expires on the second business day before the
third Wed of the month. Thus, the expiration date is June 16.
hf h
ldd lf ii
T
h
ere
f
ore, t
h
ere are 131 ca
l
en
d
ar
d
ays
l
e
f
t to exp
i
rat
i
on.
• The June Futures price is computed as:
•
F
=
106 57
*
(1+0 0067
x
131/360
)/(1+
0 0243
x
131/360
)
=
FINOPMGT 413
F
106
.
57 (1+0
.
0067
x
131/360
)/(1+
0
.
0243
x
131/360
)
105.89 Yen/$
An approximation for the forward premium
• Suppose n=360 (1-year). Then with some algebraic
manipulation, we can write the forward premium as
(where F, S are quoted in direct terms):
• (F – S)/S = (r – r*)/(1 + r*)
•
For low levels of interest rates we can
approximate
this
For
low
levels
of
interest
rates
,
we
can
approximate
this
as:
• (F-S)/S ~ r – r*
hi
h
fdii il
•T
h
at
i
s, t
h
e one-year
f
orwar
d
prem
i
um
i
s approx
i
mate
l
y
equal to the difference in interest rates.
• If the forward is
q
uotes for n da
y
s
,
we can annualize it:
qy,
(360/n)(F-S)/S ~ r – r*
• Thus, if the Japanese interest rates are 2% lower than US
interest rates then the 1
-
year Yen forward will be
FINOPMGT 413
interest
rates
,
then
the
1
year
Yen
forward
will
be
(approximately) at a premium of 2% over the spot.
Forward Premium/Discount
• If F >S
,
then we sa
y
that the forei
g
n currenc
y
is tradin
g
at
,y gyg
a premium.
• F < S, then we say that the foreign currency is trading at a
di t
di
scoun
t
.
• Note that F>S (F<S) also implies that r>r* (r<r*).
FINOPMGT 413
Forward Contracts and Arbitrage in the Money
Forward
Contracts
and
Arbitrage
in
the
Money
Markets
• If the forward contract is not correctl
y
p
riced
,
then
y
ou
yp , y
may be able to make arbitrage profits from this: this is
called covered interest arbitrage.
FINOPMGT 413
Covered Interest Arbitrage
• You have the followin
g
data:
g
• 90 day interest rates:
• 1. BP (r*) : 4.20-4.30% (lending-borrowing rates)
• 2. Dollar (r): 1.70-1.85% (lending-borrowing rates)
• Exchange Rates:
$
• Spot (S) : 1.5200-1.5300
$
/BP
• 90 day forward (F) : 1.5150-1.5200 - $/BP
•
Is there an arbitrage?
•
Is
there
an
arbitrage?
FINOPMGT 413
The Mechanics of the Arbitrage
• 1. Borrow 1US
$
at 1.85% for three months - so
y
ou need
$
y
to repay $1 + 0.0185(90/360) = $1.004625 after three
months.
2 B BP t ff i t t 1/1 53 0 6536 BP
•
2
.
B
uy
BP
a
t
o
ff
er pr
i
ce
t
o ge
t
1/1
.
53
=
0
.
6536
BP
.
• 3. Lend BP for three months at lending rate of 4.20% - so
at
e
n
d
o
f
t
hr
ee
m
o
n
t
h
s
you
h
ave
0.6536(
1 +
at e d o t ee o t s you ave 0.6536(
0.042*90/360)=0.660458 BP.
• 4. Sell BP 0.660458 in the forward market at bid of
$1 515/BP $1 000593
$1
.
515/BP
to get
$1
.
000593
.
• Net gain: $(1.000593-1.0045) < 0.
•
So there is no arbitrage
FINOPMGT 413
•
So
there
is
no
arbitrage
.
• Now construct an example to demonstrate an arbitrage.
Summarizing the conditions for absence of arbitrage
• To ensure that there is no arbitrage in either
direction, it must be that:
• 1. (F_bid/S_ask)(1 + r*_l n/360)/(1+r_b n/360) <
1
• 2. (S_bid/F_ask)(1+r_l n/360)/(1 +r*_b n/360) < 1
• Note that “_l” represents the lending interest rate,
and “_b” represents the borrowing interest rate.
FINOPMGT 413
Cti thtiit tt
C
rea
ti
ng a syn
th
e
ti
c
i
n
t
eres
t
ra
t
e
• By borrowing/lending in a currency and then hedging your
exposure with a forward contract can effectively allow you
to get different effective interest rates.
•
The synthetic net cost of lending or borrowing can be
•
The
synthetic
net
cost
of
lending
or
borrowing
can
be
quickly calculated precisely in the following manner. We
can re-write the relation between F, S, r and r*, as follows:
• (1 + [F-S]/S)(1 + r*) = 1 + r
•[or 1 + (swap points) /S)(1 + r*) = 1 + r . ]
S( hi)(1(F
S)/S)(1 *)
1
•
S
o r
(
synt
h
et
i
c
)
=
(1
+
(F
-
S)/S)(1
+r
*)
-
1
• Note that you again have to be careful of bid/ask,
borrowing/lending rates
FINOPMGT 413
borrowing/lending
rates
Forward Quotation in terms of Swap Spreads
• Often the forward market
q
uotation is
p
rovided in terms of
qp
a “swap” spread: F-S.
• A swap is an exchange - in this case, it is an exchange of
th t f th f d ( i )
th
e spo
t
f
or
th
e
f
orwar
d
(
or v
i
ce versa.
)
• Example: Spot Yen: $0.007540/Yen
•
6 Month Swap Rate: 0 00020 premium
•
6
Month
Swap
Rate:
0
.
00020
premium
• Forward = (0.007540+0.00020)=0.007740
•
The foreign currency (Yen) is quoted at a premium
.
The
foreign
currency
(Yen)
is
quoted
at
a
premium
.
FINOPMGT 413
S R t ith Bid
AkS d
S
wap
R
a
t
e w
ith
Bid
-
A
s
k
S
prea
d
s
• Suppose the spot for the BP is quoted at $1.5235-
1.5340/BP, with the one month swap spread at
0.0041-0.0039, and the three month swap spread
at 0 0114
-
0 0119
at
0
.
0114
-
0
.
0119
.
• How do we get the bid-ask spread for the forward?
We use the rule that the bi
d
-ask s
p
reads should
p
increase in the forward market.
•So we subtract the swap spread if the bid is higher
hhff d
dd
if h bid i l h h
t
h
an t
h
e o
ff
er, an
d
a
dd
if
t
h
e
bid
i
s
l
ower t
h
an t
h
e
offer. Thus: one month forward: 1.5194-1.5301
and the three month forward is: 1.5449
-
1.5459.
FINOPMGT 413
and
the
three
month
forward
is:
1.5449
1.5459.
Using Futures : How many contracts? (1/4)
•Su
pp
ose
y
ou need to make a
p
a
y
ment of
pp y p y
100,000,000 Yen in a few days.
• Today you decide to hedge against exchange rate
ikb b i h
r
i
s
k
b
y
b
uy
i
ng futures contract on t
h
e CME.
• Qt: how many contracts will you buy?
Ylk th dt ifiti th
•
Y
ou
l
oo
k
up
th
e pro
d
uc
t
spec
ifi
ca
ti
ons on
th
e
CME, and find that each futures contact is equal to
12
,
500
,
000 Y
e
n
.
,, e.
• So you need to buy 100/12.5=8 contracts.
FINOPMGT 413
Using Futures : Marking to market (2/4)
• The futures contact is market to market on a dail
y
basis.
y
Thus, if have to book any gains or loss at settlement on a
daily basis.
•
Suppose the futures price increases by
“
36
”
from the
Suppose
the
futures
price
increases
by
36
from
the
previous day. Recall that the Yen contract is quoted in
1/1000000, so that the change in the price is equal to
$0 000036
$0
.
000036
.
• How much do you gain per contract?
• For each “1”= 0.000001 change in the contract, the value
f h h b 12 500 000 0 000001 $12 50
o
f
t
h
e contract c
h
anges
b
y
12
,
500
,
000
x
0
.
000001
=
$12
.
50
.
• Thus for a change of “36”, the value of the contract
chan
g
es b
y
$450. In this case, as the value of the futures
FINOPMGT 413
gy
increases (the Yen appreciates) you make $450 per
contract.
Using Futures : The hedge (3/4)
• The Yen futures on Monda
y
, Tue and Wed settles at 8110,
y
8146, 8155. You own 8 contracts.
• On Tuesday, you make $450 x 8 = $3600.
•
On Wed you make $112 50x8=$900
•
On
Wed
,
you
make
$112
.
50
x
8
=
$900
.
• Suppose the futures matures also on Wed, so you take
delivery of the 12,500,000 x 8 = 100,000,000 Yen at the
f 0 008155$/Y Y $815 500 f h Y
rate o
f
0
.
008155$/Y
en.
Y
ou pay
$815
,
500
f
or t
h
e
Y
en.
• What is the net rate you get?
•
Your total net cash flow is 12,500,000
-
3600
-
Your
total
net
cash
flow
is
12,500,000
3600
900=$811,000.
• As expected, the net rate you get for your 100 million Yen
is 0 008110$/Y because you hedged on Monday at that
FINOPMGT 413
is
0
.
008110$/Y
,
because
you
hedged
on
Monday
at
that
price.
Using Futures : Other Issues (4/4)
• It is ver
y
likel
y
that
y
ou ma
y
not be able to match either
yyy y
the maturity or the amount with a futures contract. You
have to be careful you don’t end up increasing risk, instead
of reducin
g
risk.
g
• Because futures are marked to market, you have to be
careful that you have the liquidity to make your margin
calls in case the market moves against you Thus if you
calls
,
in
case
the
market
moves
against
you
.
Thus
,
if
you
don’t have the cash to may your payments, you may be
forced to close out your position prematurely.
To see the effect of liquidity assume that to hedge your
–
To
see
the
effect
of
liquidity
,
assume
that
to
hedge
your
Yen liabilities, you have to hold a (long) 100 million
Yen futures position for 1 year. Suppose now the Yen
depreciates by 50% Examine how your cash flow
FINOPMGT 413
depreciates
by
50%
.
Examine
how
your
cash
flow
changes.
