Tài chính doanh nghiệp - Topic 10: Hedging commodity risk and car l. gattis

1Topic #10Hedging Commodity Risk and CaRL. GattisA Course in Risk ManagementMcdonald 2nd Chapters 4 and 6 covers Commodity Futures and Arbitrage.2What Do Financial Risk Managers Do? (IMM)Identify risks that affects the viability of your firmMarket Risks: Equity, Interest Rates, Currency, Commodity, Liquidity Risk, Basis RiskCredit Risks: Bond and counterparty defaultMeasure exposure to identified risksPositions, VaR/CaR/EaR, Stress TestsMitigate risksLayoff, Accept, Hedge, Hold Capital3Producers and buyers are exposed to commodity price riskFirms convert inputs into goods and services. output input commodity Producer BuyerFirms hedge to protect input costsFirms hedge to protect output prices4Goldiggers, Inc. – Short ForwardGoldiggers is a gold-mining firm planning to sell gold in one year, receiving the spot price of gold on that day. The current spot price of gold is $405/oz The costs of gold mining are $380/oz. Management believes that gold prices will be between $350 and $500 next year with an expected value of $425. The one year forward price of gold is $420.If the company does not hedge the price of gold, what will be the possible profits per ounce.If the company hedges the price of gold, what will be the hedged profits per ounce.StUnhedged ProfitsShort Forward ProfitHedged Profit$350St-380= -30(F-St)=7040$420St-380=+40(F-St)=040$500St-380=120(F-St)=-80405Goldiggers, Inc. – Long PutSuppose a 1-year put option on gold with a strike price of $420 has a premium of $8.77/oz. Be sure to account for the interest expense (r=5%) of the purchased option. Compute the hedged and unhedged profitsStUnhedged ProfitsPut ProfitHedged Profit$350St-380= -3070-9.21=60.7930.74$420St-380=+408.77*1.05=-9.2130.74$500St-380=1208.77*1.05=-9.21 110.766Commodity buyers are short the commodity, so must take a long derivatives position hedgeA buyer that faces price risk on an input has an inherent short position in this commodity.When the price of the input , the firm’s profit . Some strategies to hedge profit:Long forwardLong call7Cashflow at Risk (CaR) measures cashflow (liquidity) riskVaR measures risk of the market value balance sheet CaR measures risk of the cash flow statementCaR is the level of cashflow loss that has a x% probability of being exceeded over the next n periods. CaR is more appropriate for non-financial corporations that rely on operational cashflows for growth and working capital needsCaRs tend to be longer term (3 months – 1 year)8Goldiggers CaRGoldiggers is a gold-mining firm planning to sell gold in one year, receiving the spot price of gold on that day. The current spot price of gold is $405/oz. The costs of gold mining are $380/oz. The one year forward price of gold is $420 and the expected spot price is $429. The monthly volatility of gold prices is 3%. Management wants to know its exposure to gold. Calculate the 95% CaR and the probability of a cashflow shortfall. S0=$405, S1=$429, F0,1=$420, Costs=$380, P=95%, T=1yrCaR(95%, 1yr) = 1.65*(405*.03*SQRT(12))=$69.595% level of Cashflows = (429-380)-69.5= -$20.59Goldiggers CaR95%, 1-year, CaRExpected cashflows in one year = S1-C=429 – 380 = $49.0095% per unit CaR = 1.65*(.03*√12*405) = $69.5095% per unit Cashflow level = $49 - 69.50= -$20.50 “5% prob. loss”Management has determined that the probability of cashflow shortfall is unacceptable due to distress costs; alternative actionsHold $20.50 or more in capital reserves: but costly to issue stock and hold cashHedge All: Enter into short forward contract at $420 and eliminate riskCaR = 0 (selling price does not change)Certain Cashflow = 420-380=40 “but no upside”Hedge Some: short forwards on 50% of exposed quantity (hedge ratio)CaR is reduced by hedge ratio = $69.50 *1/2=$34.7595% Hedged Cashflow = (429-69.50)*.5 + 420*.5 – 380 = $9.75 “Sell half of output at forward price and other half at market price”10Goldiggers CaRGoldigger’s unhedged probability of cashflow shortfall and distress429 - Z*.03*sqrt(12)*405 - 380= 0Z= 1.16 cashflows are negative if more than a 1.16 standard deviations move in spot pricesProbability of distress: 1-.8770=12.3%87.7% Probability of less than 1.16σ move (12.3% prob of 1.16σ move or more11Goldiggers CaRWhat hedge (H) ratio is needed to target a 5% probability of distress (zero or negative cashflows)H is the percent hedged at 420 forward price(1-H) is the percent unhedged (expected spot of 429)Z=1.65 is the 5% probability change420H + (1-H){429-1.65*.03*sqrt(12)*405} - 380= 0420H + (1-H){359.55}-380=060.45H-20.45=0H=.34 (hedge 34% with forwards)You can verify 34% results in 5% chance of cashflows l+c, then the forward curve will show contango This relationship must hold for assets where storage is feasible and there are no supply/demand shocks or seasonal production16Commodity FuturesThe No Arb forward price can only persist if it is feasible to execute a cash and carry arbitrage – buying the asset and financing it at any time (Carry market commodities)Transportation too costly (natural gas)Storage too costly (electricity)Seasonality in supply (corn, oil at time due to OPEC)Seasonality in demand (natural gas)For these reasons, cash and carry arbitrage is difficult to execute and forward prices reflect expectations of future spot prices17Beta and CorrelationIf the prices of the futures contract (Brent Crude) and your Risk (E.g. Jet Fuels) are not perfectly correlated, you cannot eliminate risk.Steps to establish risk minimizing hedge is:Choose hedge instrument with highest correlation to your asset (lowest basis risk: risk that basis change)Compute beta to determine optimal number of contractsHow: Regress asset returns (Y) on index returns (X) and use regression coefficient (beta) and correlation (r-squared)The risk minimizing number of contracts is:18Futures hedges must be tailed due to mark-to-market gains and lossesIf the forward contract risk minimizing hedge ratio of 1, the futures hedge ratio is <1 due to the daily mark-to-market that magnifies gains by allowing the earning of interest on early gainsThe risk minimizing tailing factor is:19Delivery and Cheapest-to-DeliverExchange-traded futures contracts call for delivery of the underlying commodity of specific quality at a specific location on specific dates.The short-party will delivery “the cheapest-to-deliver” assetWhat would you deliver if you were short aBeer FuturesWine FuturesCar FuturesA hedger may require different date, location, or qualityFor this reason, most long futures are not held to maturity20Delivery and Unwinding95% of futures contracts are “unwound” prior to the expiration. (E.g, HSY with a long cocoa futures contract, enters into a short futures just prior to expiration; making a profit on the change in the futures priceAssuming HSY goes long the 1-year futures (Dec) at t=0, and short just prior to delivery (t=12/1) Long Payoff = (F12/1,1 – F0,1) x Multiplier x #ContractsIf spot and December prices rise (remember futures converge to spot near delivery), HSY will unwind, using profits by buy cocoa in the spot marketOn 1/1, long December contract (1-year delivery)On 12/1, short December contract (1 month delivery)21Unwinding at Hershey FoodsSuppose Hershey foods requires high quality Ghana (GH) cocoa in production. Unfortunately, the NYBOT contract allows for a lower quality chocolate for delivery-- primarily grown in the Ivory Coast (IC). The spot price on 5/10/05 for IC cocoa was $1,500 per metric ton. The spot price for GH cocoa was $1,600. Hershey would like to lock into a price of GH cocoa for May 2006 (1 yr) NYBOT cocoa quotes are on the next slide.HersheyGhana CocoaS0,GH=1600NYBOTI.C. CocoaS0,IC=1500Ghana-IC Basis is $10022I.C. CocoaS0,IC=1500F0,IC=1579Ghana CocoaS0,GH=160023Basis Risk at Hershey FoodsSuppose Hershey enters into 1 long contract and the spot price of IC cocoa in May 2006 is $2000. (St=Ft,t=$2000)If the IC-GH basis is unchanged, what is the hedged and unhedged cost of cocoa per ton. Assume no margin requirements and Hershey sells (unwinds) the contract just prior to settlement (assume the futures price converges to the spot price at maturity)24Unwinding at Hershey FoodsTime 0Time TCashflows at TIvory CoastCocoaSpot = $1500F0T = $1579Go long futuresSpot = $2000FTT = $2000Go short futures Profit on futures2000-1579=421GhanaCocoaSpot = $1600Basis = $100Spot = 2100Basis = $100Buy 1 ton-2100Totals-1,679=F+basis1579+100=167925Basis Risk at Hershey Foods Time 0Time TCashflows at TIvory CoastCocoaSpot = $1500F0T = $1579long futuresSpot = $2000FTT = $2000short futures 421GhanaCocoaSpot = $1600Basis = $100Spot = 2140Basis = $140Buy 1 ton2140Buy GH Cocoa in spot marketsTotals1719=1579+140Recalculate if the basis widened by $40 due to particularly dry weather in Ghana.26Strip HedgeIf Hershey wants to lock into the price of cocoa for 1 ton per month for the next year, it could simply enter into 1 contract at each maturity.This is called a strip hedge, hedging a stream of obligations by offsetting each with a futures contract matching the maturity and quantity27Stack HedgeIf Hershey wants to lock into the price of cocoa for 1 ton per month for the next year, it could also enter into a contract with a single maturity. Eg. 12 contracts in near term monthThis is called a stack hedgeStack and RollIf Hershey chooses a stack hedge of 12 contracts, it would unwind all contracts prior to the first months contract expiration, and put on a new stack hedge of 11 contracts in the new near term month.This process is also called “rolling the futures”28Stack vs. Strip Hedge ExampleManufacturing firm requires oil in one and two years. The spot price is $10 and the firm is concerned about price increases. There is no convenience, storage or lease rates. The continuously compounded return is 10%. The market prices of forwards allow no arbitrage. The firm takes long positions in forwards at t=0, unwinding at St just before maturity.S0=10, F01=10e.1=11.05, F02=10e.1x2=12.21St=20: spot prices rise after the firm hedgesUnhedged Costs to Acquire oil at t=1,2 = $20Strip Hedge Cost:Year 1: (St-F)-St = (20-11.05)-20=-11.05Year 2: (St-F)-St = (20-12.21)-20=-12.2129Stack vs. Strip Hedge ExampleStrip Hedged Cost:Year 1: (St-F)-St = (20-11.05)-20=-11.05Year 2: (St-F)-St = (20-12.21)-20=-12.21Stack and Roll Hedged CostLong two 1-year contracts @ 11.05, unwinding before deliveryYear 1Contract #1 unwind and buy@spot: (St-F)-St = (20-11.05)x-20=-11.05Contract #2: unwind and roll (St-F) = (20-11.05) = +8.95 which is investedTake long position in F12 = 20e.1=22.10 Year 2Unwind and buy@spot: (St-F)-St = (20-22.10)-20=-22.10Add value of profits from previous year: +8.95e.1=+$9.89Total Cost in year 2: 9.89 – 22.10 = -$12.21Strip and stack will yield identical payoffs as long as the forward is prices according to No Arb price and cost of carry is unchanged.30Why Stack and RollLong-term contracts unavailableLow liquidity in long-term contractsLong-term forward prices higher than no-arb priceBetting on a flattening of the forward curvePut on strip after flattening31Closing Out AlternativesHold Futures to maturity and Take Delivery or Receive Cash Settlement (contract will specify)Unwind Futures by taking opposite position in same contractExchange Futures for Physical Delivery (EFP), (a.k.a., Against Actual or A/A)Negotiate with a producer a contract where he/she exchanges your futures or forward contract for physical delivery contract (Physical)32Problems