Ch.14 Forward and Futures Prices - PDF Document

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  1. Financial Economics Spring 2011 Ch.14 Forward and Futures Prices ü 14. 1 Distinctions between Forward and Futures Contracts ü Forward Contract ・Two parties agree to exchange some item in the future at a delivery price specified now. ・The forward price is defined as the delivery price that makes the current market value of the contract zero. ・No money is paid in the present by either party to the other. ・The face value is the quantity of the item specified in the contract times the forward price. ・The party who agrees to buy is said to take long position. The other party is said to take short position. ü Futures Contract ・Standardized contracts are traded on exchanges. ・The exchange specifies the exact commodity, the contract size and where and when delivery will be made. fl It is easy to for traders with open positions to close out their positions. ・Traders have contracts with the exchange rather than each other. ・The futures contracts have mechanisms to make sure that the parties to futures contracts do not default. The exchange requires that there be enough collateral posted in each trader's account to cover any losses. This require- ment is called the margin requirement. ü Marking to market All accounts are marked to market at the end of each trading day. Marking to market means that position of your account is evaluated by a settlement price and that your calculated profit is added to your account. Suppose that you buy a futures contract in the morning. You end trading day with long position. After you trade,transactions continue and futures price fluctuates. After the trading hours, your long position is evalu- ated by the settlement price. The last transaction prices are used as the settlement price. Evaluating your position means that they calculate how much profit or loss you would have, if you close your position using the settlement price. Calculated profit of your long position is equal to the settlement price minus your buying price. Positive profit is added to your account. Every trading day, this process is repeated. What happen if you lose? Calculated loss is subtracted from your account. If the collateral in your account falls below a prespecified level, you will receive a margin call from the broker. The broker asks you to add money to your account. If you do not respond immediately, then the broker liquidates your position at the prevailing market price. In other words, the broker sells your long position. Loss is determined. You will receive leftover collateral. This process of daily realization of gains and losses minimizes the possibility of contract default. Because of the margin requirement and process of marking to the market, individuals and firms can use the futures markets without checking credit rating of the contracting parties. ü 14. 2 The Economic Function of Futures Markets ・function of futures market in general It can reallocate exposure to price risk from hedgers to speculator. ・additional function of commodity futures market It makes possible to decide, without taking price risk, how much to sell now and how much to store for the future. What is "Cost of Carry" ? Storing commodity costs you; warehousing, spoilage and interest. Delayed revenue costs you interest on the borrowing. The cost of carry plays important role to set futures price. 1 2011-0622Ch14a.nb

  2. Financial Economics Spring 2011 ü Example on p380 Suppose that a distributor of wheat has a ton of wheat. It is less than one month until the next harvest. He is wondering whether (1) he should sell his wheat in the spot market now or (2) selling it in the future. Let S be spot price today and F be one month futures price. Suppose that cost of carry to keep wheat for a month is C. Farmer' s decision : If S + C < F, then he chooses to store the commodity and to sell it in the future. If S + C > F, then he sells wheat in the spot market now. Storing facilities may be different among the distributors. So may be storage cost and hence cost of carry. For given spot and futures prices, those who have lower storage cost have inventory. Others would sell in the spot market. Spread which is defined F-S tells on average cost of carry. ü 14. 3 The Role of Speculator Speculator: taking risk in pursuit of expected profit Hedger: trying to reduce risk Speculative activity in futures markets is not economic equivalent of gambling at casino. 1.Commodity speculators' activities make futures prices better predictors of the direction of change of spot prices. (This comment in 14.3 on p. 382 looks contradicting to explanation in 14.9 on p.389. It depends on the commodity. ) 2.Their activities make futures markets more liquid than they would otherwise be. Hedgers can find the other side easily. Speculators take the opposite side of a hedger's trade when there are not enough hedgers on the opposite side. ü 14.4 Relation between Commodity Spot and Futures Price Suppose you are looking for an opportunity to arbitrage in wheat markets. If F > S + (cost of carry ), then arbitration is possible. today: spot market: You buy wheat and store it. futures market: You sell short a futures contract at a price F. a month later: You pay storage cost. You deliver wheat and receive amount F of cash. Your profit = F - ( S + cost of buying spot wheat and storing it) If F > S + (cost of carry ), then arbitration is possible. Many traders will do the same. So such an opportunity will not last long. The inequality, F>S+ (cost of carry ), will disappear soon. Hence we will observe the following; F § S + C Futures price is upper-bounded by spot price and cost of carry. ü 14.5 Extracting Information from Commodity Futures Prices Can futures price provide information about investor expectations of spot prices in the future? 1. There is no storage. The spot and forward prices are not linked precisely through an arbitrage-pricing relation. 2. There is storage of wheat. By force of arbitration,the forward price is set by the spot price and cost of carry. Forward and futures price depends on the nature of underlying commodity. Cost to store commodity while keeping quality unchanged varies depending commodity. • Gold: No change in quality forever. Storage is possible. "Forward-spot price parity" holds. 2 2011-0622Ch14a.nb

  3. Financial Economics Spring 2011 • Agricultural products: Storage cost can be high. Storage may not be paid off. "Forward-spot price parity" may not hold. ü 14.6 Forward-Spot Price Parity for Gold ¤ Forward and spot prices of gold are set together so that no arbitrage is possible. Suppose you have S dollars to invest. Spot gold price is S dollars per ounce. You expect that price of gold will rise during the next one year. There are two methods of speculation: • method 1: buy gold, store it and sell it a year later • method 2: invest in synthetic gold and sell it a year later Method 1: today: You buy gold at spot price S and store it. Suppose that storage cost is proportional to gold price. Let s be cost of storing as ratio. Cost of carry as $ amount is given by s S. Cash inflow = -S 1 year later: You pay storage fee sS & sell gold at spot price S1; cash inflow = -sS + S1 1 + rate of return  sS  S1 S Method 2: investing in synthetic gold today: You buy futures at F, deposit S of money at interest rate r. Cash flow = -S 1 year later: You pay F, receive gold and sell it at spot price S1. You withdraw deposit.You receive principal and interest; S + rS. Cash inflow = -F +S1 +S +rS 1+rate of return = -F +S1+S +rS S In both methods, you have gold a year later. And also in both cases you can sell gold at spot price S1. By Law of One price, these two equivalent methods should have the same rate of return. Arbitration will bring the same rate of return. Hence, we have -sS+S1 S S From the above equality, we have forward-spot price parity for gold; F = ( 1 + s + r ) S ü 14. 7 Financial Futures = -F +S1+S +rS Unlike commodities such as wheat or gold, financial securities are not consumed nor used as inputs to physical production. They are held for their own sake. Storage cost is negligible. Let's suppose there is a stock called S&P. It is a share of investment fund whose value moves together with S&P 500 stock index. In another words, it is a share of "exchange traded fund" which monitors S&P 500 stock index. You like to invest in this stock. You like to have this stock one year later. Buying it in the spot market today is not only method available. You can own this stock either by "buying Stock" or "constructingsynthetic stock". Suppose that S&P stock's current spot price is S. One year forward price is F. We denote spot price one year later by S1. We can construct synthetic stock as follows. today • buy a pure discount bond with face value F; paying PV(F) = F 1r • buy it forward at F 1 year later • Bond is due. You receive F. • Pay F to receive a share of stock. By these transactions, you own a share of stock one year later for sure. With this regard, it is equivalent to buying stock today at spot price S. By Law of One Price, two method should require the same cost. It 3 2011-0622Ch14a.nb

  4. Financial Economics Spring 2011 F implies that S = 1+r should hold. Forward price, also futures price are given by F = (1+r) S ü Homework No.9, due June 29th, 2011 Q1. Numerical example on p380. Modify this example so that you take short position. Then what is the answer to Quick Check 14-1? Q2. Chapter 14, Problem 4 Q3. Chapter 14, Problem 5 Q4. Chapter 14, Problem 8 4 2011-0622Ch14a.nb