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Futures, Options, and Swaps Fin 288 Drake Fin 288 DRAKE UNIVERSITY Derivatives Drake Drake University Fin 288 Basic Definition Any Asset whose value is based upon (or derived from) an underlying asset. The performance of the derivative is dependent upon the performance of the underlying asset. The Derivative Debate Positives Drake Drake University Fin 288 Derivative securities have the potential to allow both financial firms and non-financial firms to greatly decrease risk and increase the efficiency of markets. Example of possible benefits include the ability to: decrease interest rate risk, decrease price risk, decrease transaction costs, increase the efficiency of markets, provide investors with new non replicatable products, and increase information availability. The Derivative Debate Negatives Drake Drake University Fin 288 Use of derivatives has resulted in some dramatic financial losses Financial Firms (loss) – Allied Irish Bank ($700 Million), Barings Bank ($1 Billion), Daiwa Bank (> $1 Billion), Kidder Peabody ($350 Million), LTCM ($4 Billion), Midland Bank ($50 Million), National Westminister Bank ( $130 Million) Non Financial Firms (Loss) – Allied Lyons ($150 Million), Hammersmith and Fulham ($600 million), MG ($1.8 Billion), Orange County ($2 Billion), Shell ($1 Billion), Sumitomo ($2 Billion) The Derivative Debate* Overview Drake Drake University Fin 288 Warren Buffett – “We view them as time bombs, both for the parties that deal in them and the economic system.” “Derivatives are financial weapons of mass destruction, carrying dangers that while now latent, are potentially lethal.” Alan Greenspan“Although the benefits and costs of derivatives remain the subject of great spirited debate, the performance of the economy and the financial system in recent years suggests that those benefits have materially exceeded the costs.” Quotes on slides labled The Deivative Debate were found in "The Great Derivtives Smackdown" www.forbes.com The Derivative Debate Drake Drake University Fin 288 To fully understand the benefits and risks of using derivative requires an understanding of the products available and the markets in which they trade. In class we will focus on the most popular and common forms of derivative products: Futures, Options, and Swaps. We will also focus on the use of derivatives to manage risk and look at what caused the large individual losses outlined above. Two Myths Concerning Derivatives Drake Drake University Fin 288 1) Derivative Securities are a recent development 2) The large losses associated with derivative securities indicate that derivative securities are the equivalent of gambling. Myth 1 Drake Drake University Fin 288 Derivative Securities are a recent development Truth: Derivative contracts can be traced back as far as 2000 B.C. in India and also appeared in Ancient Greece where contracts similar to options were traded on olives during the winter prior to the spring harvest. Brief History of Derivatives Markets* Drake Drake University Fin 288 1100’s Forward contracts were used by Flemish traders who gathered -- a letter de faire- forward contract specifying delivery at a later date 1600’s Japan -- Cho-ai-mai (Rice Trade on Book) Essentially futures contracts on rice designed to manage the volatility in rice prices caused by weather, warfare and other risks. Netherlands -- formal futures markets developed to trade tulip bulbs in 1636 Options also appeared in Amsterdam during the 1600’s *History taken from Darrel Duffie, Futures Markets 1989 Brief History Continued Drake Drake University Fin 288 1700’s – trading in options began in the US and in England, but the exchanges were perceived as being dishonest 1863 -- Confederacy issued 20 year bonds denominated in French francs and convertible to cotton (a dual currency cotton indexed bond) Brief History Continued. Drake Drake University Fin 288 Organized Exchanges in US Chicago Board of Trade Established in 1848 to bring farmers and merchants together. Futures Contracts were first traded on the CBOT in 1865. Developed the first standard contract Chicago Mercantile Exchange Started as the Chicago Produce Exchange in 1874 for trade in perishable agricultural products. In 1919 it became the Chicago Mercantile Exchange (CME). Introduced a contract for S&P 500 futures in 1982. NYMEX 1872 KCBOT 1876 Brief History Continued Drake Drake University Fin 288 Early 1900’s Put and Call Dealers Association formed to bring together buyers and sellers of options, however the organization did not establish a secondary market and there were no contract guarantees. 1970’s The uncertainty associate with the economic environment created an increase in the design of new derivative products designed to manage risk, and interest in options increased. Brief History continued Drake Drake University Fin 288 1973 The Chicago Board of Trade forms the Chicago Board of Options Exchange (CBOE). Early 1980’s The daily volume of trading on options exchanges is greater than the daily trading volume of the underlying assets. Options on major indexes and options on futures are developed. Myth 2 Drake Drake University Fin 288 The large losses associated with derivative securities indicate that Derivative Securities are the equivalent of gambling. Truth: Many of the losses were the result of poor operational oversight, excessive speculation, a lack of risk limits, and poor understanding of markets (especially liquidity risk). The Derivative Debate Large Losses and Market Efficiency Drake Drake University Fin 288 Alan Greenspan“Even the largest corporate defaults in history (WorldCom and Enron) and the largest sovereign default in history (Argentina) have not significantly impaired the capital of any major financial intermediary” Warren Buffett“In the energy and utility sectors, companies used derivatives and trading activities to report great ‘earnings’ – until the roof fell in when the actually tried to convert the derivatives related receivables on the balance sheets into cash. ‘Mark to Market’ then turned out to truly be ‘mark to myth’ Legitimate Questions about Derivatives Drake Drake University Fin 288 What are the intended economic benefits and risks? Has the rapid growth in use of derivatives increased the possibility of systematic risk? Has there been a concentration of risk due to a limited number of dealers? Does Regulation do a good job of monitoring and limiting derivative related risk? What happened in the cases of the large losses? Economic Benefits of Derivatives* Drake Drake University Fin 288 Risk Management – given the link to the underlying asset a derivative can be used to decrease or increase the risk of owning the underlying asset Price and Informational Discovery – since many claims are contingent on future events derivative markets can provide information about the markets perception of the future. An Introduction to Derivatives adn Risk Managmetn by Don Chance Economic Benefits Continued Drake Drake University Fin 288 Operational Advantages – generally derivative markets have lower transaction costs and greater liquidity compared to the spot market. Additionally they allow easier short sales helping to “complete” the market. Market Efficiency - Spot market prices are sometimes not consistent with assets true economic value and arbitrage opportunities exist. Derivatives help eliminate arbitrage and increase price efficiency. Some Financial Risks Drake Drake University Fin 288 Legal Risk Default Risk Liquidity Risk Market Risk However all financial assets bear most of these risks. Other Risks Drake Drake University Fin 288 Ability to increase leverage via use of derivatives can cause increased risk when the derivative security is used incorrectly. Sources of this possible problem include: Excess optimism about forecasting ability Excessive speculation instead of risk management Poor understanding of security being traded Lack of liquidity in the market Growth of Derivative Use Drake Drake University Fin 288 Has the rapid growth in use of derivatives increased the possibility of systematic risk? This question is especially relevant for the banking sector which of course spills over to the entire financial sector. Notional value Drake Drake University Fin 288 Approximate Market Capitalization of the Wilshire 5000 (represents 98% of equities traded in US) = $13.6 Trillion Approximate size of outstanding debt in all fixed income markets = $23.5 Trillion The notional value of derivative securities held by commercial banks in the US as of Sept 30, 2004 = $84 Trillion Increase in Derivative use by Commercial banks Drake Drake University Fin 288 Year Notional Value of Derivatives 1996 $20 Trillion 1998 $32.5 Trillion 2000 $40.1 Trillion 2002 $55.4 Trillion 2004 $84 Trillion Concentration Risk Drake Drake University Fin 288 5 banks account for 95% of the total notional amount of derivatives with more than 99% of the total held by the largest 25 banks. Over-the-Counter contracts comprise 92% of the total notional holding and only 8% are exchange traded – increasing credit risk and liquidity risk. During the third quarter of 2004 banks charged off $91 million from derivatives and total past due contracts were at $41 million Size of the Market and Concentration Risk Drake Drake University Fin 288 Notional value is a very misleading measure of risk since the represent the value of the underlying security, not necessarily the value that may be lost in the event of a bad outcome. However, this also makes it very difficult if not impossible to estimate the actual amount of risk that is present especially since such a large percentage are over the counter instruments. The Derivative Debate Concentration Risk Drake Drake University Fin 288 Alan Greenspan – “One development that gives me and others some pause is the decline in the number of major derivative dealers and its potential implications for market liquidity and for concentration of counterparty risk” Warren Buffett“Large mounts of risk, particularly credit risk have become concentrated in the hands of relatively few dealers, who in addition trade excessively with each other.” Regulation Drake Drake University Fin 288 Does Regulation do a good job of monitoring and limiting derivative related risk? There has been increased reporting requirements relating to derivative securities for both financial and non-financial firms, increasing transparency. The amount of off balance sheet securities has come under increased scrutiny in the banking sector. The Derivative Debate Regulation Drake Drake University Fin 288 Warren Buffett – There is no central bank assigned to the job of preventing the dominoes from toppling in insurance or derivatives. (total return swaps ) and other kinds of derivatives severely curtail the ability of regulators to curb leverage and get their arms around the risk profiles of banks, insurers and other financial institutions. The Derivative Debate Regulation Drake Drake University Fin 288 Alan Greenspan – Except where market discipline is undermined by moral hazard owing for example to federal guarantees of private debt, private regulation generally is far better at constraining excessive risk taking than is government regulation. This Class. Drake Drake University Fin 288 Our goal is to explain the functioning of derivative markets in detail and then introduce how they can be used by business to manage both financial and non-financial risk. Basic Types of Derivative Contracts Drake Drake University Fin 288 Forward Contracts Agreement between two parties to purchase and sell something at a later date at a price agreed upon today Futures Contract Same idea as a forward, but the contract trades on an exchange and the counter party is not set. Basic Types of Derivative Contracts Drake Drake University Fin 288 Options Contract - Agreement that gives the holder the right, but not the obligation, to buy or sell a security in the future as a designated price. the Swaps Contract – An agreement between two entities to exchange cash flow streams based upon a prearranged formula. Other Derivatives Drake Drake University Fin 288 Options on futures: The right to buy or sell a futures contract at a later date Swaption: The option to enter into a swap at a future date Collateralized Mortgage Obligation (CMO) A mortgage backed security where investors are divided into classes and there are rules outlining the repayment of principal to each class. Indexed currency option notes: Bonds where the amount received but the holder at maturity varies with an exchange (usually a foreign exchange rate) Credit, Weather, Electricity and other derivative classes Forward Contracts Drake Drake University Fin 288 Agreement between two parties to purchase (and sell) something at a later date at a price agreed upon today. Legal contract where both parties have the obligation to either buy or sell a specific product in the future at the designated price. Largest risk is the risk of default. Payoff on Forward Contracts Drake Drake University Fin 288 Long Position Agreeing to buy a specified amount (The Contract Size) of a given commodity or asset at a set point in time in the future (The Delivery Date) at a set price (The Delivery Price) Payoff The payoff will depend upon the spot (Cash) price at the delivery date. Payoff = Spot Price – Delivery Price Example Drake Drake University Fin 288 Assume you have agreed to buy €1,000,000 in 3 months at a rate of €1 = $1.6196 Spot Rate $1.65 $1.6169 $1.55 Spot – Delivery Price Payoff $1.65-$1.6196=$0.0304 $30,400 $1.6196-$1.6196=0 0 $1.55-$1.6196=$0.0696 -$69,600 Example Graphically Drake Drake University Fin 288 Payoff .0304 1.55 -.0696 1.6196 1.650 Spot Price Payoff: Short Position Drake Drake University Fin 288 Agreeing to sell a specified amount (The Contract Size) of a given commodity or asset at a point of time in the future (The Delivery Date) at a set price (The Delivery Price). Payoff on Short position Since the position is profitable when the price declines the payoff becomes: Payoff = The Delivery Price – The Spot Price Long vs. Short Drake Drake University Fin 288 For a long position to exist (someone agreeing to buy) there must be an offsetting short position (someone agreeing to sell). Assume that you held the short position for the previous example: sell L 1,000,000 in 3 mos at a rate of L1 = $1.6196 Spot Rate Spot – Delivery Price Payoff $1.65 $1.6196-$1.65=-$0.0304 -$30,400 $1.6169 $1.6196-$1.6196=0 0 $1.55 $1.6196-$1.55= $0.0696 $69,600 Example Graphically Payoff Drake Drake University Fin 288 .0304 1.55 -.0696 1.6196 1.650 Spot Price Zero Sum Game Drake Drake University Fin 288 The contract and many other derivative securities are often referred to as a “zero sum game” In the contract above the combined profit of the long and short position is zero. One party gains and the other looses by an equal amount. Contract Goals Drake Drake University Fin 288 The goal of the contract is to decrease risk, assume that you had to pay L1,000,000 in 3 months for the shipment of an input. You are afraid that the $ price will increase and you will pay a higher price. Similarly the other party may be afraid that the $ price will decrease (maybe they are receiving a payment in 3 months). Both parties can hedge by entering into the forward agreement – however after the 3 months, one party will actually be “worse off” compared to not hedging Determining the delivery price Drake Drake University Fin 288 The delivery price will be determined by the participants expectations about the future price and their willingness to enter into the contract. (Today’s spot price most likely does not equal the delivery price). What else should be considered? They should both also consider the time value of money Storage costs especailly if the asset is a commodity Future and Forward contracts Drake Drake University Fin 288 Both Futures and Forward contracts are contracts entered into by two parties who agree to buy and sell a given commodity or asset (for example a T- Bill) at a specified point of time in the future at a set price. Futures vs. Forwards Drake Drake University Fin 288 Future contracts are traded on an exchange, Forward contracts are privately negotiated overthe-counter arrangements between two parties. Both set a price to be paid in the future for a specified contract. Forward Contracts are subject to counter party default risk, The futures exchange attempts to limit or eliminate the amount of counter party default risk. Other Forward Contract Risks Drake Drake University Fin 288 One goal of the negotiation is to specify exactly the type, quantity, and means of delivery of the underlying asset. The chance that an asset different than anticipated might be delivered should be eliminated by the contract. Futures contracts attempt to account for this problem via standardization of the contract. Futures Contracts Drake Drake University Fin 288 Long Position: Agreeing to purchase a specified amount of a given commodity or asset at a point in time in the future at a set price (the futures price) Short Position: Agreeing to sell a specified amount of a given commodity or asset at a point of time in the future for a set price (the futures price). Option Contracts Drake Drake University Fin 288 The first difference between an option and a future (or forward) contract is that the holder of the option has the right to buy or sell a product but is not obligated to do so. They have the choice to not exercise the option. The second main difference is that the holder of the option pays an initial price for the right to buy or sell. Option Terminology Drake Drake University Fin 288 Call Option – the right to buy an asset at some point in the future for a designated price. Put Option – the right to sell an asset at some point in the future at a given price Option Terminology Drake Drake University Fin 288 Expiration Date The last day the option can be exercised (American Option) also called the strike date, maturity, and exercise date Exercise Price The price specified in the contract American Option Can be exercised at any time up to the expiration date European Option Can be exercised only on the expiration date Option Terminology Drake Drake University Fin 288 Long position: Buying an option Long Call: Bought the right to buy the asset Long Put: Bought the right to sell the asset Short Position: Writing or Selling the option Short Call - Agreed to sell the other party the right to buy the underlying asset, if the other party exercises the option you deliver the asset. Short Put - Agreed to buy the underlying asset from the other party if they decide to exercise the option. Risk to the Writer of the Option Drake Drake University Fin 288 The writer of the call option accepts all of the risk since the buyer will not exercise if there would be a loss. Call Option Profit Drake Drake University Fin 288 Call option – as the price of the asset increases the option is more profitable. Once the price is above the exercise price (strike price) the option will be exercised If the price of the underlying asset is below the exercise price it won’t be exercised – you only loose the cost of the option. The Profit earned is equal to the gain or loss on the option minus the initial cost. Profit Diagram Call Option (Long Call Position) Profit S-X-C S Cost X Spot Price Drake Drake University Fin 288 Example: Naked Call Option Drake Drake University Fin 288 Assume that you can purchase a share of stock in one month with an exercise price of $100. Assume that the option is currently at the money (the current price of the stock is also $100) and selling for $3. What are the possible payoffs if you bought the option and held it until maturity? Five possible results Drake Drake University Fin 288 The price of the stock at maturity of the option is $100. The buyer looses the entire purchase price, no reason to exercise. The price of the stock at maturity is less than $100. The buyer looses the $3 option price and does not exercise the option. Five Possible Results continued Drake Drake University Fin 288 The price of the stock at maturity is greater than $100, but less than $103. The buyer will exercise the option and recover a portion of the option cost. The price of the stock is equal to $103. The buyer will exercise the option and recover the cost of the option. The price of the stock is greater than $103. The buyer will make a profit of S-$100-$3. Profit Diagram Call Option (Long Call Position) Profit S-100-3 103 -3 100 S Spot Price Drake Drake University Fin 288 Profit Diagram Call Option (Short Call Position) Profit X C+X-S S Spot Price Drake Drake University Fin 288 Put option payoffs Drake Drake University Fin 288 The writer of the put option will profit if the option is not exercised or if it is exercised and the spot price is less than the exercise price plus cost of the option. In the previous example the writer will profit as long as the spot price is less than $103. What if the spot price is equal to $103? Put Option Profits Drake Drake University Fin 288 Put option – as the price of the asset decreases the option is more profitable. Once the price is below the exercise price (strike price) the option will be exercised If the price of the underlying asset is above the exercise price it won’t be exercised – you only loose the cost of the option. Profit Diagram Put Option Drake Drake University Profit X-S-C Spot Price S Cost X Fin 288 More Terminology Drake Drake University Fin 288 In - the - money options when the spot price of the underlying asset for a call (put) is greater (less) than the exercise price Out - of - the - money options when the spot price of the underlying asset for a call (put) is less (greater) than the exercise price At – the - money options when the exercise price and spot price are equal. Swap Introduction Drake Drake University Fin 288 An agreement between two parties to exchange cash flows in the future. The agreement specifies the dates that the cash flows are to be paid and the way that they are to be calculated. A forward contract is an example of a simple swap. With a forward contract, the result is an exchange of cash flows at a single given date in the future. In the case of a swap the cash flows occur at several dates in the future. In other words, you can think of a swap as a portfolio of forward contracts. Mechanics of Swaps Drake Drake University Fin 288 The most common used swap agreement is an exchange of cash flows based upon a fixed and floating rate. Often referred to a “plain vanilla” swap, the agreement consists of one party paying a fixed interest rate on a notional principal amount in exchange for the other party paying a floating rate on the same notional principal amount for a set period of time. In this case the currency of the agreement is the same for both parties. Notional Principal Drake Drake University The term notional principal implies that the principal itself is not exchanged. If it was exchanged at the end of the swap, the exact same cash flows would result. Fin 288 An Example Drake Drake University Fin 288 Company B agrees to pay A 5% per annum on a notional principal of $100 million Company A Agrees to pay B the 6 month LIBOR rate prevailing 6 months prior to each payment date, on $100 million. (generally the floating rate is set at the beginning of the period for which it is to be paid) The Fixed Side Drake Drake University Fin 288 We assume that the exchange of cash flows should occur each six months (using a fixed rate of 5% compounded semi annually). Company B will pay: ($100M)(.025) = $2.5 Million to Firm A each 6 months. Drake Summary of Cash Flows for Firm B Date 3-1-98 9-1-98 3-1-99 9-1-99 3-1-00 9-1-00 3-1-01 LIBOR 4.2% 4.8% 5.3% 5.5% 5.6% 5.9% 6.4% Cash Flow Received 2.10 2.40 2.65 2.75 2.80 2.95 Drake University Fin 288 Cash Flow Net Paid Cash Flow 2.5 2.5 2.5 2.5 2.5 2.5 -0.4 -0.1 0.15 0.25 0.30 0.45 Drake Swap Diagram Drake University Fin 288 LIBOR Company A Company B 5% Offsetting Spot Position Drake Drake University Fin 288 Assume that A has a commitment to borrow at a fixed rate of 5.2% and that B has a commitment to borrow at a rate of LIBOR + .8% Company A Borrows (pays) 5.2% Pays LIBOR Receives 5% Net LIBOR+.2% Company B Borrows (pays) LIBOR+.8% Receives LIBOR Pays 5% Net 5.8% Drake Swap Diagram 5.2% Drake University Fin 288 LIBOR Company A LIBOR +.2% 5% Company B LIBOR+.8% 5.8% The swap in effect transforms a fixed rate liability or asset to a floating rate liability or asset (and vice versa) for the firms respectively. Options on Futures Drake Drake University Fin 288 Options on futures are as popular or even more popular than on the actual asset. Options on futures do not require payments for accrued interest. The likelihood of delivery squeezes is less. Current prices for futures are readily available, they are more difficult to find for bonds. Useful Concepts / Terminology Drake Drake University Fin 288 The language of derivative markets can be confusing. Some basic principles apply to all of the markets and instruments that we will cover. Risk Preferences Drake Drake University Fin 288 Risk Loving vs. Risk Neutral vs. Risk Adverse Assume you are faced with two equally likely outcomes: A gain of $10 and a loss of $5. How much would you be willing to pay to accept the risk of the possible loss? Risk Preferences Drake Drake University Fin 288 Risk Neutral: If you are willing to pay $2.50, you are willing to pay a “fair price” to accept the risk. (If you repeated the event over and over on average you would receive your $2.50) Risk Averse: If you are willing to pay less than 2.50 lets say 2.00, you are risk averse. The $.50 represents a risk premium, the additional return you expect to earn for accepting the risk. The lower the amount you are willing to pay the more risk averse you are. Short Selling Drake Drake University Fin 288 The investor is selling an asset that he / she does not want. This is accomplished by borrowing an asset from a broker and selling it. The anticipation is that the price of the asset will decline. The investor is obligated to buy back the asset in the future and return it to the broker. Short selling of derivatives is much simpler than short selling stock. Often selling short can offset risk in other positions. Risk Preferences Drake Drake University Fin 288 In pricing derivative products we often will assume that the participants are risk neutral. In other words the value of the securities represent their “fair price” Risk and Return Drake Drake University Fin 288 Generally, increased risk results in increase return. Based on the idea of a “risk free” rate which is the return you require on an investment with a guaranteed payoff. In derivative markets the value of the assets will often be priced based on the use of a risk free rate. In a perfect world the derivative contract would eliminate the risk associated with the fluctuation in the underlying asset. Therefore the combination of the two provides a risk free return and provide a return comparable to the risk free rate. Market Efficiency Drake Drake University Fin 288 Market efficiency occurs when the price of an asset reflects it “true economic value”. You can think of this as the theoretical fair value of the asset (think about the CAPM providing a fair value…). A good portion of the class is placed on valuing derivatives, just like valuing of assets you have done in other classes. The value or price of the derivative will assume that markets are efficient. Types of Traders Drake Drake University Fin 288 Hedger - A participant in a derivatives transaction who is attempting to decrease the risk associate with a spot position by taking the opposite position in a derivatives market. Speculator- Unlike hedgers speculators are attempting to profit from the future movement of the market. Arbitrageurs Drake Drake University Fin 288 Participants who can lock in an immediate profit by simultaneously entering into transactions in two or more markets. A basic assumption throughout the course is that arbitrage opportunities do not exist. The basis for this argument is that if they did exist, the laws of supply and demand will quickly eliminate them as participants attempt to take advantage of the opportunity – the quicker arbitrage opportunities leave the market the more efficient the market is. Arbitrage and the Law of one price Drake Drake University Fin 288 Assume you have two stocks A and B. There are two possible outcomes one month from now. 1) If the first outcome occurs Stock A is worth $100 and Stock B is worth $50 2) If the second outcome occurs, Stock A is worth $80 and stock B is worth $40. From the example it looks like one share of stock A is worth two shares of stock B. In other words by buying two shares of stock B today you should be able to get the same outcome as one share of stock A. Law of one Price Drake Drake University Fin 288 What if stock A is selling for $85 today and B is selling for $39 You could sell short stock A and receive $85 use the proceeds to buy two shares of B (total cost $78) and have a positive cash flow of $7. In one month you could sell your two shares of B and buy one of A returning it to the broker -- You are ahead the $7 plus any interest you received. Market Reaction Drake Drake University Fin 288 If this condition existed the price of stock B would increase (everyone buys it) the price of A would decrease (everyone is short selling it). The two prices would move until the opportunity no longer exists. This is sometimes referred to as the law of one price (the arbitrage opportunity must be eliminated quickly) The Law of One Price Drake Drake University Fin 288 Assuming the law of one price is correct: Investors will prefer more wealth to less If two investment opportunities have the same outcome they must have the same price An investment that produces the same return in all states is risk free and should earn the risk free rate. Investors will prefer an opportunity if it produces a higher return in at least one state and equivalent returns in all other states. Storage, Delivery, and Settlement Drake Drake University Fin 288 Storing an asset entails risk since the spot price of the commodity fluctuates. This risk can be eliminated through the use of derivatives, implying that in the absence of storage costs the investment should earn the risk free rate. Similarly since at expiration the contract is identical to a spot transaction the mechanism for delivery of a commodity and settlement of the contract (via delivery or cash) plays a key role in determining the price of the derivative.