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1、Using Futures for Managing Risk,Front,nearby,Distant,deferred,End of day,Size of market,No of contracts still to be delivered,Every open and close position,The Basis,Basis=Current Spot Price Futures PriceAt the delivery date bases=0Futures p=spot price,Hedging,Using futures to manage risk,Inventory
2、Hedging vs.Anticipatory Hedging,different types of hedgesone involves an existing position in the cash market the other is where a cash position has not been taken but is expected to be taken in the future.hedging in the financial markets is mostly of the anticipatory type,i.e.,hedging the interest
3、rate at which one will borrow or lend,Micro vs.Macro hedging,micro hedge-futures position is matched against a specific asset or liability macro hedge-hedge is structured to offset the net(i.e.,combined)risk associated with the hedgers overall asset/liability mixbank that uses interest rate futures
4、to equate the duration of the asset and liability sides of its balance sheet,Short and Long Hedge,A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the priceA short futures hedge is appropriate when you know you will sell an asset in the f
5、uture&want to lock in the price,Short Hedge,On May 15,the producer of crude oil negotiated a contract to sell 1 mil.barrels price on August 15.If the p goes up for 1c he gains 10.000 USD,if it goes down 1c he lose 10.000 USDMaybe to hedge?What are+and of this?,Pro,Companies should focus on the main
6、business they are in and take steps to minimize risks arising from interest rates,exchange rates,and other market variables,Against,Shareholders are usually well diversified and can make their own hedging decisionsIt may increase risk to hedge when competitors do notExplaining a situation where ther
7、e is a loss on the hedge and a gain on the underlying can be difficult,So,what if we hedge?,Long Hedge,A copper fabricator knows he needs 100.000 pounds of copper on May 15.Spot p is 120c/pound and futures for May delivery is 120c/pound.Each contract is 25,000 pounds(NYMEX),Cross Hedging,Two assets
8、are differentExample Lufthansa No jet fuel futures,so need to use something else,Constructing the Hedge,the hedge ratio(HR,h*)HR is the number of units of futures necessary to hedge one unit of the cash position“naive approach”1:1,not for cross hedging,Optimal Hedge Ratio,Proportion of the exposure
9、that should optimally be hedged issS is the standard deviation of S,the change in the spot price during the hedging period,sF is the standard deviation of F,the change in the futures price during the hedging periodr is the coefficient of correlation between S and F.,4.17,Then we need to know No of c
10、ontractsNa sized of position being heldQf size of one futures contractN optimal number of futures contracts for hedging,Example,Lufthansa needs to buy 2 mil.gallons of jet fuel in one month from now.They use heating oil to hedge position.Excel table gives p for last 15 months.Calculate the number of
11、 contracts for short hedge,Cost-of-Carry Arbitrage,Occurs when the spot price is too low relative to the futures price.Money can be made by simultaneously buying the spot asset and establishing a short futures position,then holding(i.e.,carrying)the commodity until delivery At T1 you deliver the ass
12、et against your futures obligation.,F0,t=S0(1+C)F0,t-futures price observed today for delivery at time t,S0-spot price observed todayC-expected net cost of carry,Reverse cost-of-carry arbitrage,simultaneously go short the commodity and long the futures positionF0,t=S0ebT e-exponential function b-exp
13、ected net cost of carry expressed as a rate,T-time between today and the delivery date,Risk free rate,Repo rateImplied repo rate,Example:,There is No.2 Red Wheat in a Chicago warehouse.The current spot price is 300 cents per bushel.The current one-month repo rate is 6 percent,and the cost of storing
14、 and insuring one bushel of wheat is 4 cents per month.Price of todays futures contract calling for delivery in one month?,You could buy wheat today at the spot price and then store it for one month,3001+(30/360)(.06)+4=305.5 cents per bushelIf the futures price is above 305.5,you could short the fu
15、tures,buy wheat today,store it for one month,and make a riskless arbitrage profit!,AIRR-Annualized Implied Repo Rate,3001+(30/360)(AIRR)+4=306.5 cents per bushel.AIRR=(360/30)(306.5/304)-1=9.87%Since the implied repo rate from this risk-free opportunity exceeds the opportunity cost of using your money for other ventures of equivalent risk,that is,the actual repo rate,then we have identified an arbitrage opportunity.,
