1. Lecture 4 Cash vs. Futures Prices Primary Texts Edwards and Ma: Chapter 4

2. Futures Prices Convention of reporting futures prices The relationship between futures prices and the cash price of the underlying commodity the relationships between the prices of futures contracts with different delivery dates Cost-of-Carry pricing relationship Key concepts: Basis, convenience yield, contango, backwardation, arbitrage, speculation, spreading, hedging

3. Live Cattle CME (40,000lbs; cents/lbs), Aug 27, 2009 Reported by Financial Times Cont. Month Settlement Price Day’s ChangeHighLow Vol. (000s) Open Int. (000s) Aug85.1750.10085.90084.9501.43.3 Oct87.5750.20088.00087.25020.8111.3 Dec87.7000.12588.00087.2506.770.3 Feb88.0250.15088.20087.6503.028.6 Total34.4243.1 Settlement Price: The settlement price is usually determined by a formula using a range of prices recorded within the closing period (such as the last minute of trading) – it is not usually the last trading price of the day

4. Convention of Reporting Futures Prices Day’s Change: The difference between today’s settlement price and yesterday’s settlement price – can be either positive or negative Day’s change = today’s settlement – yesterday’s settlement High: The highest price of a trade recorded during the day Low: The lowest price of a trade recorded during the day Volume: The total number of futures contracts that are traded during the day. Open Interest: The number of futures contracts that are open at the close of the previous day’s trading. The actual figures for open interest and trading volume usually lag price quotations by one day

5. The Relationship between Cash and Futures Prices Cash closing price and futures settlement prices for live cattle on 23 February 1998 Cash/FuturesClosing/SettlementCash - Futures (cents/lb) Cash 59.50 April 98 Futures 63.87− 4.37 June 98 Futures 66.05− 6.55 August 98 Futures 67.82−8.32 October 98 Futures 69.00− 9.50 December 98 Futures 70.27−10.77 Note that the cash closing prices for live cattle reported in Table 1 are national averages. The cash market for a commodity may be geographically segmented and there may be more than one cash price for a commodity at a moment in time.

8. There are several obvious features of the cash and futures price relationship shown in Figures 1 and 2: Futures settlement prices are higher than cash closing prices Futures Price (FP t, T ) > Cash Price (CP t ) A distant-month futures price is higher than a near-month futures price FP t, Dec > FP t, NM > CP t The difference between the cash and futures price depends on, and increases with, the time to delivery |CP t – FP t, T | increases with T−t (the time to delivery) The futures prices slowly but inevitably converges to the cash prices as the delivery date approaches FP t, T → CP t as t → T These relationships exist regardless of the level of cash price. The Relationship between Cash and Futures Prices

9. Cost-of-Carry: The cost-of-carry refers to the costs of purchasing and carrying (or holding) a commodity for a specified period of time. Cost-of-Carry = financing costs + storage costs + insurance costs + shipping cost + other miscellaneous costs CC T-t = CP t × R t, T × (T-t)/365 + G t, T + I t, T + S + D Where CP t = the cash price at time t R t, T = the annualized riskless interest rate at which funds can be borrowed at time t for period (T − t) G t, T = the cost of storing the physical commodity per unit for the time period from purchase (at t) to delivery (at T) I t, T = the cost of insuring the physical commodity per unit for the time period from purchase (at t) to delivery (at T) S = The costs of shipping and handling the commodity D = Other miscellaneous costs (e.g., depreciation, etc.) The Cost-of-Carry Price Relationship

10. The cost-of-carry formula is based on simple interest financing cost. It does not allow for continuous compounding interest costs. The formula assumes that there are no information or transaction costs associated with buying or selling either futures or physical commodity, credit risks, taxes, and so on. The Full-Carry Futures Price: The full-carry futures price of a commodity refers to the estimated futures price using the following formula. FP* = CP t + CC T-t Thus, at any given time t the estimated futures price with delivery time T is equal to the cash price plus the cost of carrying the commodity for the period of T-t. The Cost-of-Carry Price Relationship

11. Example: Cost-of-Carry and Full-carry Futures Price Date: Feb 02, 2010 Cash price of wheat in Lubbock (CP t ):550.50 cents per bushel Simple interest rate (R t, T ):10% Storage and Ins. costs (G t, T +I t, T ):5 cents per bushel per month Shipping costs (S)0 Other Costs (D):0 September 2010 Wheat CME Futures Contract: Cost-of-Carry (CC t,T ): Full-Carry Futures Price (FP*) Calculating the Cost-of-Carry and Full-Carry Futures Price

12. The Convenience Yield The convenience yield refers to an implied yield (or return) from simply holding a commodity. This yield need not be a directly measurable or pecuniary return. It could be the implicit return that a firm places on its ability to use its inventory. Ownership of the physical commodity enables a manufacturer to keep a production process running and perhaps profit from temporary local shortages. Y t, T = FP* − FP t, T = CP t + CC T−t − FP t, T If we observe a relationship where the actual futures price (FP t, T ) is less than the full-carry futures price (FP*), the actual futures price (FP t, T ) is said to have an implicit convenience yield. Example: Y t, T = FP* − FP t, T = 617.61 − 612.75 = 4.86 cents/bushel.

13. The Cost-of-Carry and Convenience Yield Pricing Relationship: Based on the cost-of-carry and convenience yield concepts, the fundamental pricing formula for commodity futures is given by FP t, T = CP t + CC T-t − Y t,T FP t, T − CP t + Y t,T = CC T-t If Y t,T = 0,FP t, T − CP t = CC T-t =>FP t, T = FP* If Y t,T > 0,FP t, T − CP t FP t, T < FP* Futures price cannot exceed the spot price by more than the cost-of- carry, FP t, T − CP t ≤ CC T-t Thus, actual Futures price cannot exceed the full-carry futures price =>FP t, T ≤ FP*

14. No-Risk Cash-Futures Arbitrage What happens if the futures price of a commodity is too far above the spot price? FP t,T > FP* => Arbitrage: Short Futures, Buy Cash Commodity Short Futures => Supply of Futures ↑ => Futures Price ↓ Buy cash comm. => Demand for Comm. ↑ => Cash Price ↑ Arbitrage => FP t,T − CP t ↓ => FP t,T − CP t ≈ CC t,T What happens if the futures price of a commodity is too far below the spot price? FP t,T Arbitrage: Long Futures, Sell Cash Commodity Long Futures => Demand for Futures ↑ => Futures Price ↑ Sell cash comm. => Supply of Comm. ↑ => Cash Price ↓ Arbitrage => FP t,T − CP t ↓ => FP t,T − CP t ≈ CC t,T

15. Cash-Futures Arbitrage Example: Observed Futures Price is Greater than Full-Carry Futures Price

16. Cash-Futures Arbitrage: FP t,T > FP* Date: Cash price Interest rate Costs of storage and insurance Full-carry futures price Observed futures price ActivitiesCash Flows Date: Sell futures @ Borrow @ 10% interest Buy Cash commodity @ Date: Deliver cash commodity Pay Back the Loan - Principal Interest ( ) Storage and Insurance Cost Net Arbitrage profit

17. Cash-Futures Arbitrage Example: Observed Futures Price is much lower than Full-Carry Futures Price

18. Cash-Futures Arbitrage: FP t,T << FP* Date: Cash price Interest rate Costs of storage and insurance Full-carry futures price Observed futures price ActivitiesCash Flows Date: Buy futures @ Sell cash commodity @ Invest proceeds @ 10% interest Date: Take delivery of cash commodity Withdraw cash from investment Principal Interest Net Arbitrage profit

19. The Basis The basis is defined as the difference between cash and futures prices. The basis can either be negative, or positive, or zero. In particular, B t, T = CP t − FP t, T = Y t, T − CC T−t For Y t, T ≥ 0 and CC t,T ≥ 0, a negative basis reflects that the convenience yield is lower than the cost-of-carry. B t, T CP t Y t, T < CC T−t The basis is positive when the futures price is lower than the cash price. In this case, the convenience is higher than the cost-of-carry. B t, T > 0 => CP t > FP t, T => Y t, T > CC T−t The basis is zero when the convenience yield and cost-of-carry are equal or when both the convenience yield and cost-of-carry are zero. B t, T = 0 => CP t = FP t, T => Y t, T = CC T−t or Y t, T = 0 = CC T−t

20. Contango Markets Contango: A market condition is referred to as in contango when, at a particular point in time, futures prices rise progressively with the time to delivery, i.e. the futures price of a distant delivery month is higher than the futures price of a near delivery month. Contango => FP t, T+n > FP t, T where n=1,….., N A contango is normal for a non-perishable commodity which has a positive cost-of-carry.

21. Contango Market Condition On 02 February 2009, the wheat futures market was in contango.

22. Backwardation Markets Backwardation is commonly referred to a market condition in which, at a particular point in time, futures prices fall progressively with the time to delivery, i.e. the futures price of a distant delivery month is lower than the futures price of a near delivery month.. Backwardation => FP t, T+n < FP t, T where n=1,….., N Backwardation is characterized by a shortage of the physical commodity. Backwardation often occurs at times when cash prices are high and have been rising sharply, a manifestation of a shortage in the market. In such cases, the underlying commodity is said to have a positive convenience yield.

23. Backwardation Market Condition On 02 February 2009, the soybean meal futures market was in backwardation.