Forwards • Forward contract - an agreement between two parties involving the future delivery of a particular quantity of an asset at a price agreed upon today. • Buyers and sellers are obliged to deliver or take delivery. • No money is exchanged until settlement. • This may introduce default risk for some forward contracts.
Example • Example: You buy a forward contract to receive delivery of Euros at an exchange rate of 1 $/€ in three months. • If in three months the spot rate is 1.2 $/€, you gain, since you get 1 Euro for each dollar through your forward contract, but the Euros are currently worth more: 1.2 dollars for each Euro. • To think about it another way, you get one Euro for each dollar, whereas if you had waited, your dollar would have bought only 0.83 Euros.
Futures • Futures contract - similar to a forward contract but it is entered into on an organized exchange and has standardized features (contract size, delivery date, acceptable grade of the commodity, etc.) • They have very low transactions costs. Commissions can run as low as .05% of the value of the contract.
History • Rice contracts - 17th Century Japan • 1848 CBOT established • Financial Futures • 1972 foreign currencies at CME • 1975 interest rate futures at CBOT • 1982 stock index futures at KBT, CME, NYFE
Foreign Exchange Futures • Futures markets • Chicago Mercantile (International Monetary Market) • London International Financial Futures Exchange • MidAmerica Commodity Exchange • Active forward market
Types of Contracts • Agricultural commodities • Metals and minerals (including energy contracts) • Foreign currencies • Financial futures • Interest rate futures • Stock index futures futures contract specifications can be found on: http://www.duke.edu/~charvey/options/futures/f_idx.htm
Frozen Pork Bellies FuturesTicker Symbol: PB Trading Unit': 40,000 lbs. USDA-inspected 12-14, 14-16 pound or 16-18 pound (at a 21/2c discount) Pork Bellies Price Quote: $ per hundred pounds (or cents/pound) Min Price Fluct: $.025 $10.00/tick Daily Price Limit: $2.00 $800.00/contract Contract Months: Feb, Mar, May, Jul, Aug Trading Hours: 9:10 am-1:00 pm (Chicago Time) Last day: 9:10 am-12:00 pm Last Day of Trading: The business day immediately preceding the last 5 business days of the contract month. Delivery Days: Any business day of the contract month. Delivery Points: The CME Clearing House or a current list of approved warehouses.
Key Terms for Futures Contracts • Futures price - agreed-upon price at maturity • Note that this is different than the price of a security, which is the price paid today for the security. A futures contract involves no exchange of money at the outset. • Long position - agree to purchase • Short position - agree to sell • Profits on positions at maturity Long = future spot price minus futures price Short = futures price minus future spot price
Key Difference in Futures • Secondary trading - liquidity. • Standardized contract units. • Clearinghouse warrants performance. • Unlike forwards, there is no default risk with futures. • Sellers do not have to be concerned about evaluating the credit risk of every different buyer, since the clearing house guarantees all transactions.
Trading Mechanics • Clearinghouse - acts as the counterparty to all buyers and sellers. • Obligated to deliver or supply delivery • Stands in the middle of the transaction between the long and short position $ $ Long Position Short Position Clearinghouse commodity ? commodity ?
Margin Accounts • When buying a contract, the buyer must post a performance bond; that is, deposit money in a margin account, usually 20 percent of the value of the contract. • Note that this margin account is NOT the same as a stock margin account in which a buyer is making a down payment and borrowing funds from the broker to complete the sale. • Since the account earns interest, there is no cost to you, the buyer, of posting the performance bond.
Margin and Trading Arrangements • Initial Margin - funds deposited to provide capital to absorb losses(more than one-day price moves) • Marking to Market - each day the profits or losses from the new futures price are reflected in the account (“daily settlement.”).This is calculated by taking the difference between the closing futures price at the end of the day minus the previous closing price. • Maintenance or variation margin - an established value below which a trader’s margin may not fall.
Clearinghouse • Bears any residual credit risk, that exists because: 1) futures prices move so dramatically that the amount required to mark to market is larger than the balance of an individual's margin account, and 2) the individual defaults on payment of the balance.
Daily Settlement - an example • Suppose that the current futures price of gold for delivery 4 days from now is $293.50 per ounce. • Over the next 3 days, the price evolves as follows, and the daily settlements are calculated accordingly for a long position:Day Futures Price Profit (loss)/ounce 1 295.20 +1.70 2 294.60 -0.60 3 293.00 -1.60Net Profit = -0.50
Suppose an Australian futures speculator buys one SPI (share price index) futures contract on the Sydney Futures Exchange (SFE) at 11:00am on June 6. At that time, the futures price is 2300. At the close of trading on June 6, the futures price has fallen to 2290 (what causes futures prices to move is discussed below). Underlying one futures contract is $25 x Index, so the buyer's position has changed by $25(2290-2300)=-$250. Since the buyer has bought the futures contract and the price has gone down, he has lost money on the day and his broker will immediately take $250 out of his account. This immediate reflection of the gain or loss is known as marking to market.
Where does the $250 go? • On the opposite side of the buyer's buy order, there was a seller, who has made a gain of $250 (note that futures trading is a zero-sum game - whatever one party loses, the counterparty gains). • The $250 is credited to the seller's account. • Suppose that at the close of trading the following day, the futures price is 2310. Since the buyer has bought the futures and the price has gone up, he makes money. • In particular, $25(2310-2290)=+$500 is credited to his account. This money, of course, comes from the seller's account.
Forwards and FuturesProfits and Losses • A futures contract can be considered a series of one-day forward contracts. • It’s as if you close out your position each day and then open up a new position. • The price of a futures contract will approach the spot price as the futures contract nears its maturity date. • The capital gains and losses on the futures contract are realized over the life of the contract rather than at the end, which is the case with a forward.
Closing out Positions • Option One: You can reverse the trade • Go long (enter into a contract to buy) if closing out a short position. • Go short (enter into a contract to sell) if closing out a long position. • The difference in the prices in the two contracts will be your profit. • Example: you have been long corn futures for 5 days. You want out. You enter into a short contract for the same amount. The long and short positions cancel at the clearinghouse.
Closing out Positions • Option Two: You can take or make delivery. • Financial futures though are “cash settled.” • Most trades are reversed and do not involve actual delivery.
Deliverable quality: Greasy wool futures. Delivery must be made at approved warehouses in the major wool selling centres throughout Australia. For wool to be deliverable, it must possess the relevant measurement certificates issued by the Australian Wool Testing Authority (AWTA) and appraisal certificates issued by the Australian Wool Exchange Limited (AWEX). In particular, it must be good topmaking merino fleece with average fibre diameter of 21.0 microns, with measured mean staple strength of 35 n/ktx, mean staple length of 90mm, of good colour with less than 1.0% vegetable matter.
Because any particular bale of wool is unlikely to exactly match these specifications, wool within some prespecified tolerance is deliverable. • In particular, 2,400 to 2,600 clean weight kilograms of merino fleece wool, of good topmaking style or better, good colour, with average micron between 19.6 and 22.5 micron, measured staple length between 80mm and 100mm, measured staple strength greater than 30 n/ktx, less than 2.0% vegetable matter is deliverable. • Premiums and discounts for delivery that does not match the exact specifications of the underlying contract are fixed on the Friday prior to the last day of trading for all deliverable wools above and below the standard, quoted in cents per kilogram clean.
Trading Strategies • Speculation - • You go short if you believe price will fall. • You golong if you believe price will rise. • Hedging - • long hedge - protecting against a rise in price • e.g. for an input to production • short hedge - protecting against a fall in price • e.g. for an output commodity
Corn Example • You are a farmer who wants to sell your corn harvest in September. You would like to lock into a price now. • The current futures price is $2.26 ¼ per bushel, and you think that this is an acceptable lock-in price. • Contract size is 5000 bushels. • You go short 10 contracts and deposit (.2)(10×5000)(2.26 1/4) = $22,625 in a margin account. • This means you agree to sell 50,000 bushels of corn to the CBOT on September for 2.26 ¼ per bushel.
Corn Example • September comes around and the current corn price is $1. • You sell your corn to a buyer for $1. • But you make money on your futures contract. • Since the futures price equals the spot price when the contract comes due, the futures price is also $1. • At this point your margin account will have gained value by the amount (2.26 1/4 - 1)(50,000). • So at this point you enter into a long contract. The two contracts (one long and one short) cancel out, you don’t have to deliver any corn to the CBOT, and you pocket the gain to your margin account.
Forward and Futures Pricing • There are two ways to acquire an asset for some date in the future • Purchase it now and store it • Take a long position in futures • These two strategies must have the same market determined costs. • Otherwise we could do arbitrage.
Determining Forward Prices • Consider a perfect hedge: • Hold an underlying asset and short a forward contract on that asset. • This combined position has no risk! • You knew the terms of the contract from the start. • At the maturity date, you deliver the underlying asset in exchange for the forward price. • Therefore, a perfect hedge should return the riskless rate of return. • This idea can be used to develop a relationship between forward (or futures) prices and spot prices.
Basis & Convergence Property • On the delivery date, the futures price = spot price or FT = PTor FT - PT = 0 • gain or loss (marking to market) on a long position = FT - FT-1 • the sum of all daily settlements = FT - F0 • given convergence, this means sum of all daily settlements = PT - F0
Futures prices Contango Expectations Hypothesis Normal Backwardation Time Delivery date Futures prices versus expected future spot price
Futures Prices vs. Expected Spot • Expectations Hypothesis • Normal Backwardation • Contango • Modern Portfolio Theory Suppliers are natural hedgers F < E[PT] Purchasers are the natural hedgers => F > E[PT] P0 = E[PT]/(1+k)T P0 = F/(1+Rf)T E[PT]/(1+k)T = F/(1+Rf)T E[PT]* (1+Rf)T /(1+k)T = F If beta > 0, then k > Rf F < E[PT]
Are forward and future prices the same? • Marking to market complicates valuation for futures • However if interest rats do not change then forwards and futures should have the same price • We are going to assume that interest rates do not change.
Hedge Example • An investor owns an S&P 500 fund that has a current value equal to the index level of 1000. • Assume dividends of $26 will be paid on the index at the end of the year. • Assume that the futures price for a contract that calls for delivery in one year is $1050. • The investor hedges by shorting one futures contract.
Rate of Return for the Hedge • If we denote the one-year futures price today in the market by F0, the dividend by D, and the spot price by S0, we can write the return on the strategy as: • The way to understand this is to think about $ in and $ out. • He gets F0 when he delivers his S&P fund. He gets D in dividends, and he pays S0 for the fund. • Plugging in the numbers from the example we get.
General Spot-Futures Parity • Since this strategy is risk-free, its return must be equal to the risk free rate. • Rearranging terms, we get • Continues compounding should be used…how would the formula look then?
Intuition behind the Pricing Formula • One can interpret the formula F0=S0(1+rf -d)as follows. • If the futures contract is priced correctly, you should be indifferent between: • arranging today to buy the underlying asset at a cost of F0 one year from now; and, • paying S0 to buy the asset today, foregoing interest of rfS0 on your money (over the next year), but receiving dS0(at the end of the year) as a benefit to holding on to the asset for the year.
Arbitrage Opportunities • If spot-futures parity is not observed, then arbitrage is possible. • If the futures price is too high: • Short the futures • Borrow the cost of the stocks at the risk free rate • Buy the index For example, if F0=1055, this strategy would yield 1055+26-1000(1.076) = 5.
Arbitrage Opportunities • If the futures price is too low, the reverse is true: • Go long futures • Short the index • Invest the proceeds at the risk free rate. For example, if F0=1045, this strategy would yield 1000(1.076)-1045-26 = 5.
Stock Index Contracts • Available on both domestic and international indexes. • Advantages over direct stock purchase: • lower transaction costs • better for timing or allocation strategies • takes less time to acquire the portfolio
Using Stock Index Contracts to Create Synthetic Positions • We have seen how to create a synthetic lending strategy by holding the index and taking a short position in index futures. • By playing with this relationship, we can see how to create a synthetic index purchase: • Go long the index future and lend. • Also, we can see that being long a forward or futures contract is equivalent to buying the underlying stocks in the index and borrowing to finance this purchase.
Using Stock Index Futures as a Partial Hedge • We saw how to create a completely riskless portfolio by combining a long position in stocks with a short position in index futures. • A portfolio manager may also want to take a short position in an index futures contract to reduce temporarily the portfolio's exposure to the market (but not eliminate all exposure). • This allows the manager to take advantage of her superior stock-picking ability, and avoids the triggering of high transaction costs (from selling off stock and buying it again later) and of capital gains taxes.
Using Stock Index Futures as a Partial Hedge • The number of futures contracts to go long or short is determined by how much you want to change the portfolio’s level of risk. • You can measure the change in risk by the amount you want to change the portfolio’s beta or by the amount you want to change the portfolio’s level of total investment. • These two approaches are equivalent.
Using Stock Index Futures as a Partial Hedge • Changing beta • Changing value
Example • A portfolio manager whose $450 million portfolio currently has a beta of 1.2believes that the market may fall in the next couple of months andwants to reduce the portfolio beta to 0.8. • How many contracts should she short? • Assume that the S&P 500 is now at 1000. • If the market falls by 1%, the S&P index will fall by 10 points.
Example • Since S&P futures contracts come in multiples of $500(per point), the drop translates into a change of $5,000 per contract. • The manager's portfolio would fall by • $5.4 million (=1.2*450*1%) if the beta stayed at 1.2, • $3.6 million (=0.8*450*1%) if beta falls to 0.8. • Thus, to reduce the loss by $1.8 million (= 5.4-3.6), the manager should short 360 contracts (1,800,000/5,000).
Hedging Foreign Exchange Risk A US firm wants to protect against a decline in profit that would result from a decline in the pound: • Estimated profit loss of $200,000 if the pound declines by $.10. • Short or sell pounds for future delivery to avoid the exposure.
Pricing on Foreign Exchange Futures Interest rate parity theorem Developed using the US Dollar and British Pound where F0 is the forward price E0 is the current exchange rate
Text Pricing Example rus = 5% ruk = 6% E0 = $1.60 per pound T = 1 yr If the futures price varies from $1.58 per pound arbitrage opportunities will be present.
Hedge Ratio for Foreign Exchange Example Hedge Ratio in pounds =ch. in value of unprotected position / profit on 1 futures position $200,000 per $.10 change in the pound/dollar exchange rate $.10 profit per pound delivered per $.10 in exchange rate = 2,000,000 pounds to be delivered Hedge Ratio in contacts Each contract is for 62,500 pounds or $6,250 per a $.10 change $200,000 / $6,250 = 32 contracts
Interest Rate Futures • Idea: to separate security-specific decisions from bets on movements in the entire structure of interest rates • Domestic interest rate contracts • T-bills, notes and bonds • municipal bonds • International contracts • Eurodollar • Hedging • Underwriters • Firms issuing debt
Uses of Interest Rate Hedges • Owners of fixed-income portfolios protecting against a rise in rates. • Corporations planning to issue debt securities protecting against a rise in rates. • Investor hedging against a decline in rates for a planned future investment. • Exposure for a fixed-income portfolio is proportional to modified duration.