Definitions: Forwards vs. Futures

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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Definitions Forwards vs. Futures A forward
contract is a binding arrangement that requires
the long (or buying) party to pay a specified sum
to the short (or selling) party on a given date,
in exchange for delivery of a certain quantity of
a specified good. A futures contract is like a
forward contract except that it is a
standardized, traded security. Also, to reduce
counterparty risk (the chance that they might not
pay up), a future is marked to market with cash
payments every day.
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Example Pork Bellies in May I know that I will
be very hungry for Pork Bellies in May (I always
am at that time of year). Im afraid that the
price of good bellies will go up between now and
then. If that happens, I will not be able to
afford all the pork bellies I want. How can I
ensure that I will be able to eat 40,000 pounds
of bellies in May? The Wall Street Journal lists
a settling price of 95.12 for Pork Bellies to be
delivered in May. If I go long (i.e. buy) this
contract, I will be obligated to buy 40,000lbs of
bellies on the specified delivery date in May.
The price will be fixed today, so that no matter
how much the spot price might rise, I will be
able to buy the bellies I want.
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Futures Contracts The Details Futures contracts
are in zero net supply. (i.e. The total of
long positions is equal to the of short
positions at all times.) To close out a long
position I can sell it. To close out a short
position I can buy it back. If I do not close
out a position in this way by the end of the
period I will either have to physically take or
provide delivery. Commodities futures are
based on particular grades of quality and all the
details are specified. For example, you cant
just provide insect infested old corn and say,
pick it up at my house on the delivery date.
Delivered products must meet the CME, etc.,
standards or you will be penalized by the
exchange.
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Futures Contracts More Details Although futures
contracts are designed to be worth net zero at
inception and at the close of each day (marking
to market), exchanges do not allow unlimited
leverage. The exchange will require traders to
put up margin of about 5 of the market price
of their contracts. As prices move you might end
up with excess margin (which can be taken out as
cash) or inadequate margin, in which case a
broker will make a margin call.
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Futures Contracts What Drives Prices? You might
think that futures prices reflect market
expectations for demand of a given commodity.
For example, if people use more heating oil in
the winter then prices for winter delivery will
be higher. But, suppose that futures prices were
much higher for December than for August. I
could buy the cheap August contracts and take
delivery of the oil just after I drain my pool
for the summer. Meanwhile, I sell the expensive
December contracts. From August to December I
stash a lot of heating oil in my swimming pool,
then deliver it when the December contracts come
due. This is an arbitrage! But there is no
arbitrage in this cold, cruel world!
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999

• Futures Contracts If Demand Doesnt Drive
  Prices, ...What does?
• There are three factors that influence most
  commodity futures
• risk free rate Rf
• convenience yield (CY)
• storage cost (SC)
• General equation for prices of commodities
• Futures Price F (1 Rf)T (Spot Price
  PV(SC) - PV(CY))

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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Futures Contracts Pricing Lets use an example
Brealey Myers Corporate Finance Textbook
futures contracts are traded on the Sloan
Commodities Exchange. The size of the contract
is 1 book and the delivery period is in 1 year.
It is currently the start of the school year.
The SCE requires that books are the latest
edition in new condition and that delivery must
be made to the Tang lobby. Spot Price 84 Rf
5 on 1 year treasuries Storage Cost 1 /
book Convenience Yield 30 / year (This is
the benefit of physically having the
textbook in your hands, say on the
day before the final)
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Futures Contracts Pricing Futures Price F
(1 Rf)T (Spot Price PV(SC) - PV(CY)) F
(1 0.05)1 (84 1 / (1.05) - 30 /
(1.05)) 59.2 This, by the way, is a
backwardation since the spot price is above the
futures price.
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Futures Contracts Pricing Another way to write
the Futures Price Equation is F Spot (1
Rf NCY) Where NCY is the Net Convenience
Yield, defined by PV(NCY) PV(CY) - PV(SC)
The simplified futures price
equation only works for single periods, and only
if the net convenience yield can be considered to
be a single lump sum payment at the end of period
T.
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Futures Contracts Currency Forward
Pricing Currencies cost nothing to store but
provide a different sort of dividend yield than
we have thought of so far. Suppose we agree to
buy 2 Deutschemarks next year in exchange for 1.
The dividend yield that we are giving up in this
case is the interest we could have earned in
Germany if we had bought spot instead of forward.
This suggests a relationship for pricing
currency forwards and futures F (1 Rf)T
(Spot - PV(CY)) and PV(CY) Spot (1
Rj)T / (1 Rf)T So F Spot (1
Rf)T / (1 Rj)T Where Rf is the local
interest rate and Rj is the foreign interest
rate, and Spot is expressed in terms of
local/foreign currencies. (e.g. 0.5 dollars per
deutschmark)
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Swaps A swap is an agreement with another party
to exchange one stream of asset payments for
another. Two of the most common examples are
currency swaps and interest rate swaps.
Currency swaps are typically set up like the
following example On January 1, 2000, I sign a
contract with you to exchange Rupiahs (Indonesia)
for Dong (Vietnam). On that day and on the 1st
of every June and January for the next 5 years I
will give you 100 Rupiahs in exchange for 100
Dong. For this particular example to work,
the interest rates in Indonesia and Vietnam must
be the same and the exchange rate must be 11.
A currency swap is the equivalent of a series
of forward contracts.
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Currency Swap Example Suppose the current
forward rates for Dong/Rupiah are as
follows Spot 1.0000 1 yr. 1.0500 2
yr. 1.1025 3 yr. 1.1576 The current yield
curve in Vietnam is flat at Rv10. What is the
yield curve (Ri) like in Indonesia (hint its
flat) Using 3 yr. rate F 1.1576
(1Rv)3 1.0000 / (1Ri)3 Ri 4.76
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Currency Swap Example Spot 1.0000 1
yr. 1.0500 2 yr. 1.1025 3 yr. 1.1576 How
much would a three year Dong/Rupiah swap (in
which you give away 100 Rupiah for 100 dong at
the end of each year) be worth in present value
terms in Dong? Answer Calculate the
present value of the Rupiah payments and subtract
it from the PV of the Dong receipts. Or note
that you could buy 100 contracts forward for each
year at the posted prices. Your cost would be
105 dong in year 1, 110.3 dong in year 2, and
115.76 dong in year 3. Since you get back 100
dong, your net loss is 5, 10.3, and 15.76 in each
year. Simply discount these back at Rv 10.
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Interest Rate Swap (Example) Interest rate
swaps are the most common variety. A typical
rate swap will involve one party paying a fixed
interest rate and the other paying a floating
rate. Example What is the value (to party A) of
a 2 year swap with biannual payments where party
A agrees to pay party B a fixed rate of 5 in
exchange for a floating rate of 1 over
treasuries. The treasury yield curve is
currently flat at 5. The swaps notional value
is 100. Assume there is no payment at
t0. Answer The value from As perspective is
simply the PV of the stream it is receiving
minus the PV of the stream it is paying.
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Forwards, Futures Swaps Stephen Chadwick May 5,
1999
Interest Rate Swap Example Value 3 /
1.050.5 3 / 1.05 3 / 1.05(3/2) 3 /
1.052 - 2.5 / 1.050.5 2.5
/ 1.05 2.5 / 1.05(3/2) 2.5 / 1.052
1.88