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## Futures Prices

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**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**Live Cattle CME (40,000lbs; cents/lbs), Aug 27, 2009Reported**by Financial Times • 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**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**The Relationship between Cash and Futures PricesCash closing**price and futures settlement prices for live cattle on 23 February 1998 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.**The Relationship between Cash and Futures Prices**• 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 (FPt, T) > Cash Price (CPt) • A distant-month futures price is higher than a near-month futures price FPt, Dec > FPt, NM > CPt • The difference between the cash and futures price depends on, and increases with, the time to delivery |CPt – FPt, 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 FPt, T→ CPt as t → T • These relationships exist regardless of the level of cash price.**The Cost-of-Carry Price Relationship**• 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 • CCT-t= CPt × Rt, T × (T-t)/365 + Gt, T + It, T + S + D Where • CPt= the cash price at time t • Rt, T= the annualized riskless interest rate at which funds can be borrowed at time t for period Tminus t • Gt, T = the cost of storing the physical commodity per unit for the time period from purchase (at t) to delivery (at T) • It, 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**• The cost-of-carryformula 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* = CPt + CCT-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 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. Yt,T = FP*−FPt, T = CPt + CCT-t − FPt, T • If we observe a relationship where the actual futures price (FPt, T) is less than the full-carry futures price (FP*), the actual futures price (FPt, T) is said to have an implicit convenience yield. Example: Yt,T = FP*−FPt, T = 617.61 − 612.75 = 4.86 cents/bushel.**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 • FPt, T = CPt + CCT-t − Yt,T • FPt, T − CPt + Yt,T = CCT-t • If Yt,T = 0, FPt, T − CPt = CCT-t=> FPt, T = FP* • If Yt,T > 0, FPt, T − CPt < CCT-t=> FPt, T < FP* • Futures price cannot exceed the spot price by more than the cost-of-carry, FPt, T − CPt≤ CCT-t • Thus, actual Futures price cannot exceed the full-carry futures price => FPt, T ≤ FP***No-Risk Cash-Futures Arbitrage**• What happens if the futures price of a commodity is too far above the spot price? • FPt,T > FP*=>Arbitrage: Short Futures, Buy Cash Commodity • Short Futures => Supply of Futures ↑ => Futures Price ↓ • Buy cash comm. => Demand for Comm. ↑=> Cash Price ↑ • Arbitrage =>FPt,T − CPt↓ =>FPt,T − CPt≈CCt,T • What happens if the futures price of a commodity is too far below the spot price? • FPt,T << FP*=>Arbitrage: Long Futures, Sell Cash Commodity • Long Futures => Demand for Futures ↑ => Futures Price ↑ • Sell cash comm. => Supply of Comm. ↑=> Cash Price ↓ • Arbitrage =>FPt,T − CPt↓ =>FPt,T − CPt≈CCt,T**Cash-Futures Arbitrage Example: Observed Futures Price is**Greater than Full-Carry Futures Price**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, Bt, T = CPt − FPt, T = Yt, T − CCt, T • For Yt, T≥ 0 and CCt,T ≥ 0, a negative basis reflects that the convenience yield is lower than the cost-of-carry. • Bt, T < 0 => CPt < FPt, T => Yt, T < CCt,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. • Bt, T > 0 => CPt > FPt, T => Yt, T > CCt,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. • Bt, T = 0 => CPt = FPt, T => Yt, T = CCt,T or Yt, T= 0 = CCt,T**Contango Markets**• Contango: A market condition is referred to as in contangowhen, 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 =>FPt, T+n > FPt, Twhere n=1,….., N • A contango is normal for a non-perishable commodity which has a positivecost-of-carry.**Contango Market Condition**• On 02 February 2009, the wheat futures market was in contango.**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 =>FPt, T+n < FPt, 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.**Backwardation Market Condition**• On 02 February 2009, the soybean meal futures market was in backwardation.