Forwards, Futures & Swaps
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Forwards, Futures & Swaps Stephen Chadwick May 5, 1999. Definitions: Forwards vs. Futures

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Definitions: Forwards vs. Futures

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Definitions forwards vs futures

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.


Definitions forwards vs futures

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). I’m 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.


Definitions forwards vs futures

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 can’t 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.


Definitions forwards vs futures

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.”


Definitions forwards vs futures

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!


Definitions forwards vs futures

Forwards, Futures & Swaps

Stephen Chadwick

May 5, 1999

  • Futures Contracts: If Demand Doesn’t 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))


  • Definitions forwards vs futures

    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)


    Definitions forwards vs futures

    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.


    Definitions forwards vs futures

    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.


    Definitions forwards vs futures

    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)


    Definitions forwards vs futures

    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 1:1. ]

    A currency swap is the equivalent of a series of forward contracts.


    Definitions forwards vs futures

    Forwards, Futures & Swaps

    Stephen Chadwick

    May 5, 1999

    Currency Swap Example:

    Suppose the current forward rates for Dong/Rupiah are as follows:

    Spot1.0000

    1 yr.1.0500

    2 yr.1.1025

    3 yr.1.1576

    The current yield curve in Vietnam is flat at Rv=10%. What is the yield curve (Ri) like in Indonesia (hint: its flat):

    Using 3 yr. rate: F = 1.1576 = (1+Rv)^3 * 1.0000 / (1+Ri)^3

    Ri = 4.76%


    Definitions forwards vs futures

    Forwards, Futures & Swaps

    Stephen Chadwick

    May 5, 1999

    Currency Swap Example:

    Spot1.0000

    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%.


    Definitions forwards vs futures

    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 paymentswhere 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 swap’s notional value is $100. Assume there is no payment at t=0.

    Answer:The value from A’s perspective is simply the PV of the stream it is receiving minus the PV of the stream it is paying.


    Definitions forwards vs futures

    Forwards, Futures & Swaps

    Stephen Chadwick

    May 5, 1999

    Interest Rate Swap Example:

    Value = [ $3 / 1.05^0.5 + $3 / 1.05 + $3 / 1.05^(3/2) + $3 / 1.05^2 ] -

    [ $2.5 / 1.05^0.5 + $2.5 / 1.05 + $2.5 / 1.05^(3/2) + $2.5 / 1.05^2 ]

    = $1.88


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