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Futures Markets: Futures and Forwards

• Futures and forwards can be used for two diverse reasons:– Hedging

– Speculation

• Unlike with Options, Futures and Forwards carry an obligation to fulfill the contract!

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Forward Contracts

• A forward contract is a contract made today for the future delivery of an asset at a pre-specified price

• No money or assets change hands prior to maturity

• Forwards are traded OTC directly between two parties

• The buyer is said to have the “Long Position”

• The buyer must take delivery at maturity

• The buyer must pay the agreed upon price

• The seller is said to have the “short position”

• The seller must Deliver at maturity

• The seller must accept the agreed upon price

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Why Enter a Forwards Contract?

• Allows you to invest money before you need an asset

• However, you give up any claims to the asset until ownership changes hands

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How Do You Value the Forward?

• Once again, we will use the concept of replication• We could follow one of two strategies

– Buy an asset today and then sell it at an agreed upon forward price 3 months from now

– Invest the share price in a risk free asset for the same period of time

– Assuming the asset pays no dividends or other interest, these two strategies should be identical, so you should be able to use on to price the other

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An Example of Valuing a Forward Contract

• Assume the following:– A share of stock sells today for $25– It pays no dividends in the next three months– The risk free rate is 6% per annum with quarterly

compounding

• You buy the share of stock today for $25 and enter a forward contract to sell it in 3 months:– What are the cash flows from buying one share of stock

today? What are the cash flows from the Forward contract today?

– What are the cash flows 3 months from now?

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An Example of Valuing a Forward Contract

• Alternatively, you could invest the value of the share at the risk free rate– What are the cash flows from this strategy today?

– Three months from now?

• If these portfolios have an identical return, what is the value of the Forward contract today?

• What are the cash flows of both strategies if the Forward pays a dividend of $2 at the end of the 3 month period? What is the value of the Forward contract now?

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So, How Do You Value the Forward?

• You would consider 2 portfolios

• Portfolio I– Buy a stock at S0, and sell a share forward for F

• Portfolio II– Invest the value of stock at S0 at the risk free

rate

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What Are the cash flows of These Strategies?

Today 3 Months Portfolio I Stock

Forward Net

- S0

0 - S0

St + Dt F – St F + Dt

Portfolio II - S0 S0(1+rf)

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Formula For Valuing a Forward

F = S0 (1+rf) - Dt

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Futures Contracts

• Futures contracts are standardized contracts

• Futures contracts are traded on organized exchanges

• The ‘other’ side of a ‘position’ is typically held by the brokerage house

• Must be a buyer for every seller

• Both the buyer and seller must post margin

• Futures contracts are marked to market daily and consequently there are daily cash flows

• Traders normally ‘reverse’ there position just piro to maturity

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Futures Contracts• Long Position – the trader who commits to buying

an asset– The long position profits when the price goes up

• Short Position – the trader who commits to deliver the asset– The short position profits when the price goes down

• The Price at Maturity = the Spot Price at maturity• Profit to buyer = Spot Price at maturity – Original

Futures Price• Profit to seller = Original Futures price – Spot

Price at maturity • Futures prices are a zero sum game!

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What Sort of Futures Exist?

• You can get a futures contract on:– Agricultural products and livestock

– Metals and petroleum

– Interest rates

– Currencies

– Stock Market indices

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Marking to Market

• How does the margin account work?– Traders have an account with the brokerage house

– Both buyer and seller post margin

– Each day, the clearinghouse caclulates gains or loses on the contracts

– Should the margin reach a trigger level called the maintenance or variation margin, the margin account must be replenished

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Marking to Market – An Example

• Assume the following:– You want to buy a futures contract on corn– Each contract is for 5,000 bushels– The price is 245 3/5 or $2.456 per bushel

• What is the value of the contract?• If the margin requirement is 10% what must the

margin be?• On November 3, the price of corn goes from

$2.3587 to $2.3823– What is the actual gain or loss on the day– What is the return on the original investment?

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The Convergence Property

• Futures prices on the delivery date will be equal to the spot price at the time of maturity– As the maturity date nears, the futures price and the

spot price converge!

• Basis – Basis is the difference between the forward or futures price and the spot price– Another way to think of convexity is to say that at

maturity, the basis must be zero!