Hedging Strategies Using Futures

Hedging and Shareholders

Hedging and Competitors

All implications of price changes on a companys profitability should be taken into account in the design of a hedging strategy to protect against the price changes.

= S Fstrengthening of the basisweakening of the basis

Spot priceFutures pricet1t2Figure 3.1 Variation of basic over timeS1F1F2S2b2b1b1 = S1 F1b2 =S2 F2Suppose thatF1 : Initial Futures PriceF2 : Final Futures PriceS2 : Final Asset Price

Long Hedge :You hedge the future purchase of an asset by entering into a long futures contractThe effective price( ) that is paid with hedge is S2 + F1 F2 = F1 + b2Short Hedge :You hedge the future sold of an asset by entering into a short futures contractThe effective price( ) that is obtained for the asset with hedge is S2 + F1 F2 = F1 + b2basis risk()

One key factor affecting basis risk is the choice of the futures contract to be used for hedging. This choice has two components:The choice of the assets underlying the futures contractsThe choice of the delivery monthA contract with a later delivery month is usually chosen in these circumstances.

h* : Hedge ratio that minimizes the variance of the hedgers position.

: Coefficient of correlation between S and FS : Change in spot price, S, during a period of time equal to the life of the hedge.F : Change in future price, F, during a period of time equal to the life of the hedge.

S : Standard deviation of SF : Standard deviation of F

NA : Size of position being hedged (unit) QF : Size of one futures contract (unit) N* : Optimal number of futures contracts for hedging

N*: Optimal number of futures contracts for hedgingP : Current value of the portfolioA : Current value of one futures contract : From the capital asset pricing model to determined the appropriate hedge ratio

Value of S&P 500 index =1000S&P 500 futures price =1010Value of portfolio = $5,000,000Risk-free interest rate = 4% per annumDividend yield on index = 1% per annumBeta of portfolio = 1.5

Time to maturity

Value of index in three months9009501 ,0001,0501,100Futures price of index today1,0101,0101,0101,0101,010Futures price of index in three months9029521,0031,0531,103Gain on futures position810,000435,00052,500 322,500 697,500Return on market 9.750% 4.750%0.250%5.250%10.250%Expected return on portfolio 15.125% 7.625% 0.125%7.375%14.875%Expected portfolio value in three months(including dividends)4,243,7504,618,7504,993,7505,368,7505,743,750Total expected value of position in three months5,053,7505,053,7505,046,2505,046,2505,046,250