Lecture 6 Hedging with Futures Primary Texts Edwards and Ma: Chapters 5 & 6 CME: Chapter 5

Hedging Fundamentals Hedging: The activity of trading futures with the objective of reducing or controlling price risk (due to uncertainty about future price levels) is called hedging. Output Price Risks: A farmer who is growing corn and planning to sell it in six months (after harvest) cannot be certain about what the price of corn will be in six months. Input Price Risks: An airline career that wish to set passenger fares that remain fixed for the next six months cannot be certain about what the price of jet fuel will be in six months. Both output and input price risks can be reduced or controlled by hedging. However, quantity risk cannot be controlled by hedging.

Hedging Fundamentals The Basic Long and Short Hedges Hedging typically involves taking a position in futures that is opposite either to A position that one already has in the cash market, or A futures cash obligation that one has or will incur There are two basic types of hedges: Short hedge and long hedge Short Hedge: A short hedge occurs when a firm which owns or plans to purchase or produce a cash commodity sells futures to hedge the cash position. Cash price risk is declining cash prices Long Hedge: A long hedge occurs when a firm which plans to purchase a cash commodity in either cash or forward market purchase futures to hedge the future cash position. Cash price risk is increasing cash prices

Hedging Fundamentals Short Hedge (with Zero Basis Risk) Suppose it is June 01. A cotton farmer in Lubbock planted cotton in April, and expects to harvest 100,000 lbs of cotton in October. On June 01, the cash price for cotton is 55 cents/lb in the local market and October NYBOT Cotton futures settled at 57 cents/lb. The farmer is worried that cash price of cotton at harvest (in October) may decline significantly. The farmer may hedge against the declining price risk by short hedging. To fully cover her expected cash position at harvest, the cotton farmer needs to short 2 NYBOT Cotton futures (because the size of NYBOT cotton futures is 50,000 lbs.)

DateCash TransactionFutures TransactionBasis June 01Local cash price = ¢/lb Exp. cash position = 100,000 lbs Fut. Price = ¢/lb− 2 ¢/lb Oct. 19Harvest = 100,000 lbs Cash price = ¢/lb Sell cash cotton at ¢/lb Fut. Price = ¢/lb− 2 ¢/lb Gain/Loss Rev./Profit Net Return (Cash Revenue + profit/loss from futures transaction) Net realized price = Net Return /Cash position Perfect Hedging Short Hedge (with Zero Basis Risk)

DateCash TransactionFutures TransactionBasis June 01Local cash price = 55 ¢/lb Exp. cash position = 100,000 lbs Fut. Price = 57 ¢/lb Short 2 NYBOT cotton futures at 57 ¢/lb − 2 ¢/lb Oct. 19Harvest = 100,000 lbs Cash price = 50 ¢/lb Sell cash cotton at 50 ¢/lb Fut. Price = 52 ¢/lb Long 2 NYBOT cotton futures at 52 ¢/lb − 2 ¢/lb Gain/LossLoss = (50−55=) −5 ¢/lbGain = (57−52=) 5 ¢/lb0 Revenue/ProfitRev. = $0.50×100,000 = $50,000 Profit = $0.05× 2×50,000 = $5,000 Net Return (Cash Revenue + profit/loss from futures transaction)$55,000 Net realized price = Net Return /Cash position (= $55,000/100,000)55 ¢/lb Perfect Hedging Short Hedge (with Zero Basis Risk)

Perfect Hedging Long Hedge (with Zero Basis Risk) Suppose that a beef packer in Amarillo has a plant-capacity of slaughtering 1,000 fed cattle per month. Each fed cattle weight approximately 1,200 lbs. It is Oct 19. The cash price for live cattle is 75 cents/lb in the local market, and Feb CME Live Cattle futures settled at 85 cents/lb. The beef packer plans to purchase live cattle in February from the local market, but is worried that cash price for live cattle may increase significantly in February. The beef packer may hedge against the increasing price risk by long hedging. To fully cover her expected cash position in February, the beef packer needs to long 30 CME Live Cattle futures (because the size of CME Live Cattle futures is 40,000 lbs.)

DateCash TransactionFutures TransactionBasis Oct 22Local cash price = ¢/lb Exp. cash position = 1,200,000 lbs Futures Price = ¢/lb Feb 01Local cash price = 80 ¢/lb Purchase 1, ¢/lb Futures Price = ¢/lb Gain/LossLoss = ¢/lbGain = ¢/lb Payment/ProfitPayment = = Profit = = Net Payment (Cash payment - profit/loss from futures transaction) Net price paid = Net Payment /Cash position (= ) ¢/lb Perfect Hedging Long Hedge (with Zero Basis Risk)

DateCash TransactionFutures TransactionBasis Oct 22Local cash price = 75 ¢/lb Exp. cash position = 1,200,000 lbs Fut. Price = 85 ¢/lb Long 30 CME LC futures 85 ¢/lb − 10 ¢/lb Feb 01Local cash price = 80 ¢/lb Purchase 1, ¢/lb Fut. Price = 90 ¢ Short 30 CME LC fut. 90 ¢/lb − 10 ¢/lb Gain/LossLoss = (75−80=) −5 ¢/lbGain = (90−85=) 5 ¢/lb0 Payment/ProfitPayment = $0.80×1,200,000 = $960,000 Profit=$0.05×30×40,000 = $60,000 Net Payment (Cash payment - profit/loss from futures transaction)$900,000 Net price paid = Net Payment /Cash position (= 900,000/1,200,000)75 ¢/lb

Hedging with Basis Risk When the basis remains unchanged, it is simple to construct predictable, no-risk hedge. Unfortunately, perfect hedging is not usual in reality Like cash and futures prices, basis may change as well Basis may expand (absolute basis becomes larger) or shrink (absolute basis becomes smaller) However, a change in the basis can affect the results of hedging Short Hedge Basis expands – net realized price is lower than the initial cash price Basis shrinks – net realized price is higher than the initial cash price Long Hedge Basis expands – net price paid is lower than the initial cash price Basis shrinks – net price paid is higher than the initial cash price

DateCash TransactionFutures TransactionBasis June 01Local cash price = 55 ¢/lb Exp. cash position = 100,000 lbs Fut. Price = 57 ¢/lb− 2 ¢/lb Oct. 22Harvest = 100,000 lbs Cash price = 50 ¢/lb Sell cash cotton at 50 ¢/lb Fut. Price = ¢/lb ¢/lb Gain/Loss Revenue/Profit Net Return (Cash Revenue + profit/loss from futures transaction) Net realized price = Net Return /Cash position Short Hedge (with Basis Risk) Basis Expands Change in Basis = Long Basis – Short Basis

DateCash TransactionFutures TransactionBasis June 01Local cash price = 55 ¢/lb Exp. cash position = 100,000 lbs Fut. Price = 57 ¢/lb Short 2 NYBOT cotton futures at 57 ¢/lb − 2 ¢/lb Oct. 22Harvest = 100,000 lbs Cash price = 50 ¢/lb Sell cash cotton at 50 ¢/lb Fut. Price = 54 ¢/lb Long 2 NYBOT cotton futures at 54 ¢/lb − 4 ¢/lb Gain/LossLoss = (50−55=) −5 ¢/lbGain = (57−54=) 3 ¢/lb− 2 ¢/lb Revenue/ProfitRev. = $0.50×100,000 = $50,000 Profit = $0.03× 2×50,000 = $3,000 Net Return (Cash Revenue + profit/loss from futures transaction)$53,000 Net realized price = Net Return /Cash position (= $53,000/100,000)53 ¢/lb Short Hedge (with Basis Risk) Basis Expands Change in Basis = Long Basis – Short Basis

DateCash TransactionFutures TransactionBasis June 01Local cash price = 55 ¢/lb Exp. cash position = 100,000 lbs Fut. Price = 57 ¢/lb− 2 ¢/lb Oct. 22Harvest = 100,000 lbs Cash price = 50 ¢/lb Sell cash cotton at 50 ¢/lb Fut. Price = ¢/lb ¢/lb Gain/Loss Revenue/Profit Net Return (Cash Revenue + profit/loss from futures transaction) Net realized price = Net Return /Cash position Short Hedge (with Basis Risk) Basis Shrinks Change in Basis = Long Basis – Short Basis

DateCash TransactionFutures TransactionBasis June 01Local cash price = 55 ¢/lb Exp. cash position = 100,000 lbs Fut. Price = 57 ¢/lb Short 2 NYBOT cotton futures at 57 ¢/lb − 2 ¢/lb Oct. 22Harvest = 100,000 lbs Cash price = 50 ¢/lb Sell cash cotton at 50 ¢/lb Fut. Price = 51 ¢/lb Long 2 NYBOT cotton futures at 51 ¢/lb − 1 ¢/lb Gain/LossLoss = (50−55=) −5 ¢/lbGain = (57−51=) 6 ¢/lb+ 1 ¢/lb Revenue/ProfitRev. = $0.50×100,000 = $50,000 Profit = $0.06× 2×50,000 = $6,000 Net Return (Cash Revenue + profit/loss from futures transaction)$56,000 Net realized price = Net Return /Cash position (= $56,000/100,000)56 ¢/lb Short Hedge (with Basis Risk) Basis Shrinks Change in Basis = Long Basis – Short Basis

DateCash TransactionFutures TransactionBasis Oct 22Local cash price = 75 ¢/lb Exp. cash position = 1,200,000 lbs Fut. Price = 85 ¢/lb Feb 01Local cash price = 80 ¢/lb Purchase 1, ¢/lb Fut. Price = ¢/lb Gain/LossLoss = ¢/lbGain = ¢/lb Payment/ProfitPayment =0.80×1,200,000 = $960,000 Profit = $ × 30×40,000 = $ Net Payment (Cash payment - profit/loss from futures transaction) Net price paid = Net Payment /Cash position (= ) ¢/lb Long Hedge (with Basis Risk) Basis Expands Change in Basis = Short Basis – Long Basis

DateCash TransactionFutures TransactionBasis Oct 22Local cash price = 75 ¢/lb Exp. cash position = 1,200,000 lbs Fut. Price = 85 ¢/lb Long 30 CME LC futures 85 ¢/lb − 10 ¢/lb Feb 01Local cash price = 80 ¢/lb Purchase 1, ¢/lb Fut. Price = 92 ¢ Short 30 CME LC fut. 90 ¢/lb − 12 ¢/lb Gain/LossLoss = (75−80=) −5 ¢/lbGain = (92−85=) 7 ¢/lb− 2 ¢/lb Payment/ProfitPayment = $0.80×1,200,000 = $960,000 Profit=$0.07×30×40,000 = $84,000 Net Payment (Cash payment - profit/loss from futures transaction)$876,000 Net price paid = Net Payment /Cash position (= 876,000/1,200,000)73 ¢/lb Long Hedge (with Basis Risk) Basis Expands Change in Basis = Short Basis – Long Basis

DateCash TransactionFutures TransactionBasis Oct 22Local cash price = 75 ¢/lb Exp. cash position = 1,200,000 lbs Fut. Price = 85 ¢/lb Feb 01Local cash price = 80 ¢/lb Purchase 1, ¢/lb Fut. Price = ¢/lb Gain/LossLoss = ¢/lbGain = ¢/lb Payment/ProfitPayment =0.80×1,200,000 = $960,000 Profit = $ × 30×40,000 = $ Net Payment (Cash payment - profit/loss from futures transaction) Net price paid = Net Payment /Cash position (= ) ¢/lb Long Hedge (with Basis Risk) Basis Shrinks Change in Basis = Short Basis – Long Basis

DateCash TransactionFutures TransactionBasis Oct 22Local cash price = 75 ¢/lb Exp. cash position = 1,200,000 lbs Fut. Price = 85 ¢/lb Long 30 CME LC futures 85 ¢/lb − 10 ¢/lb Feb 01Local cash price = 80 ¢/lb Purchase 1, ¢/lb Fut. Price = 87 ¢ Short 30 CME LC fut. 90 ¢/lb − 7 ¢/lb Gain/LossLoss = (75−80=) −5 ¢/lbGain = (87−85=) 2 ¢/lb+ 3 ¢/lb Payment/ProfitPayment = $0.80×1,200,000 = $960,000 Profit=$0.02×30×40,000 = $24,000 Net Payment (Cash payment - profit/loss from futures transaction)$936,000 Net price paid = Net Payment /Cash position (= 936,000/1,200,000)78 ¢/lb Long Hedge (with Basis Risk) Basis Shrinks Change in Basis = Short Basis – Long Basis

Hedging Fundamentals Price Risk versus Basis Risk While the objective of hedging is to reduce exposure to price risk, hedgers trade price risk for basis risk (assumes basis risk). Hedging => reduces exposure to cash price risk, but increases exposure to basis risk Cash Price Risk => the magnitude by which the cash price may deviate from the mean (cash price) Typically measured by the variance (or by standard deviation) Basis risk => the magnitude by which the basis deviates from the mean (basis) Typically measured by the variance (or by standard deviation) Basis:B t, T = CP t − FP t, T Change in the basis:∆B t, T = ∆CP t − ∆FP t, T

Hedging Fundamentals Price Risk versus Basis Risk If the cash and futures prices always change by exactly the same amount, there is no basis risk because the change in the basis is zero. When changes in the cash and futures prices are not equal, there is basis risk. Basis risk is defined as the variance of the basis. Where = Var(B ) = E[B 2 ] – (E[B]) 2 = Var(CP − FP ) = Var(CP) + Var(FP ) – 2Cov(CP, FP) = Var(CP ) = E[CP 2 ] – (E[CP]) 2 = Var(FP) = E[FP 2 ] – (E[FP]) 2 ρ = Correlation coefficient between CP and FP = Cov(CP, FP ) = E[CP×FP] – E[CP]× E[FP]

Hedging Fundamentals Price Risk versus Basis Risk Basis risk is defined as the variance of the basis. = 0, if and ρ = 1 > 0, if The magnitude of the basis risk depends mainly on the degree of correlation between cash and futures prices Higher ρ =>Lower basis risk Lower ρ => Higher basis risk For a hedge to be attractive, the basis risk should be significantly less than the hedger’s cash price risk.

Hedging Fundamentals Anticipated Hedging Effectiveness One measure of anticipated hedging effectiveness is to compare the basis risk that the hedgers expect to assume with the price risk they expect to eliminate. The smaller the anticipated basis risk is compared to the anticipated price risk, the more effective is the hedge. This measure of effectiveness can be stated formally as The closer HE is to 1, the more effective is the hedge. The higher the cash price risk relative to the basis risk (i.e., higher variance of cash price relative to lower variance of the basis), the more effective is the hedge.

Hedging Fundamentals Anticipated Hedging Effectiveness => HE = 0 => no potential benefit from hedging => HE > 0 => hedging may be beneficial => HE hedging incurs a potential loss Anticipated hedging effectiveness is higher the lower is the basis risk. The basis risk is lower the higher the correlation between the cash and futures prices. ρ↑=>σ 2 B ↓=>HE ↑

Devising a Hedging Strategy A hedger faces three initial decisions: What kind of futures to use, Which contract month of that futures to use, and How many contracts to hedge with Which Futures Contract A hedger wants to maximize hedging effectiveness ρ↑ => σ 2 B ↓ => HE ↑ The hedger chooses a futures contract the price of which is highly correlated with the cash prices of the commodity (or asset) to be hedged Futures and cash prices of the same commodity are generally highly correlated. When hedging a commodity on which no futures contract is traded, a closely related commodity is used on which futures contract is traded – cross-hedging

Devising a Hedging Strategy Which Contract Month Typically, the prices of the nearest month futures contract are the most highly correlated with cash prices. Thus, using the near month futures contract reduces the basis risk the most. When hedging a continuous cash obligation for a long period of time, hedgers have to decide between two alternatives: hedging with a nearby futures contract and rolling the hedge forward Rolling the hedge often entails greater brokerage and execution costs. hedging with a more distant futures contract and rolling the hedge less frequently. Using a more distant futures contract usually increases basis risk, since its price would be less correlated with cash prices.

Devising a Hedging Strategy How Many Futures Contracts Decide about the optimal futures position to assume - the number of futures contract times the quantity represented by each contract In general, the number is determined by the hedge ratio – the ratio of the size of the futures position to the size of the cash position. Q c = the quantity of the cash commodity that is being hedged. Q f = the size (quantity) of the futures position = NFC×Q fc Q fc = the size of the futures contract NFC = Number of futures contracts The hedge ratio that minimizes risk is defined as Where, Q * f = the quantity of the commodity futures that minimize risk

Devising a Hedging Strategy ∆V H = ∆CP× Q c − ∆FP× Q f ∆V H = the change in value of the total hedged position ∆CP = The change in the cash price ∆FP = the change in the futures price If the change in the value of the hedged position is set equal to zero (making variability equal to zero), then But, Where, NFC * = the number of contracts that minimize risk Q fc = the size of the futures contract

Devising a Hedging Strategy The number of futures contract with which to hedge in order to achieve the minimum variance hedge is given by Estimating the Hedge Ratio There are two general techniques to estimate the hedge ratio: the naïve method and the regression analysis. Both procedures use historical price data to estimate the hedge ratio.

Devising a Hedging Strategy Estimating the Hedge Ratio The naïve method: The regression analysis: Another way of obtaining the estimate of the (regression analysis) hedge ratio is to use the following formula σ ∆CP = standard deviation of the changes in cash price (∆CP) σ ∆FP = standard deviation of the changes in futures price (∆FP) ρ ∆ = Correlation coefficient between ∆CP and ∆FP