2Long & Short HedgesA 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 future & want to lock in the priceA short hedge is also appropriate if you currently own the asset and want to be protected against price fluctuations
3Arguments in Favor of Hedging Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables
4Arguments against Hedging Shareholders are usually well diversified and can make their own hedging decisionsIt may increase risk to hedge when competitors do notExplaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult
5Convergence of Futures to Spot PriceSpot PriceFuturesPriceSpot PriceTimeTime(a)(b)
6Basis Risk Basis is the difference between spot & futures Basis risk arises because of the uncertainty about the basis when the hedge is closed out
7Long Hedge Suppose that F1 : Initial Futures Price F2 : Final Futures PriceS2 : Final Asset PriceYou hedge the future purchase of an asset by entering into a long futures contractExposed to basis risk if hedging period does not match maturity date of futures
8Long Hedge Gain on Futures = F2 - F1 Future Spot Price = S2 Cost of Asset = Future Spot Price - Gain on FuturesGain on Futures = F2 - F1Future Spot Price = S2Cost of Asset= S2 - (F2 - F1)Cost of Asset = F1 + Basis2Basis2 = S2 - F2Future basis is uncertainTherefore, effective cost of asset hedged is uncertain
9Short Hedge Suppose that F1 : Initial Futures Price F2 : Final Futures PriceS2 : Final Asset PriceYou hedge the future sale of an asset by entering into a short futures contract
10Short Hedge Gain = F1 - F2 Future Spot Price = S2 Price Realized = Gain on Futures + Future Spot PriceGain = F1 - F2Future Spot Price = S2Price Realized = S2 + F1 - F2Price Realized = F1 + Basis2Basis2 = S2 - F2Price Realized = Cost of AssetSame Formula
11Example Hedging period 3 months Futures contract expires in 4 months We’re exposed to basis riskSuppose F1 = $105 and S1 =100Current basis = = -5Basis in 3 months is uncertainWhat is basis in 4 months?
13Choice of ContractChoose a delivery month that is as close as possible to, but later than, the end of the life of the hedgeWhen there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price.
14Minimum Variance Hedge Ratio Hedge ratio is the ratio of the futures to underlying asset positionA perfect hedge requires that futures and underlying spot asset price changes are perfectly correlatedFor imperfect hedge, set hedge ratio to minimize variance of hedging error
15Minimum Variance Hedge Ratio Proportion of the exposure that should optimally be hedged iswheresS is the standard deviation of DS, the change in the spot price during the hedging period,sF is the standard deviation of DF, the change in the futures price during the hedging periodr is the coefficient of correlation between DS and DF.
16Minimum Variance Hedge Ratio Continued Error =S - hFPerfect hedge: Error = 0 at all timesS = hF + ErrorChoose h to minimize var(Error)Therefore, h = slope of regressionOr h = cov(S, F)/var(F)
17Hedging Using Index Futures P: Current portfolio valueA: Current value of futures contract on indexF: Current futures price of indexS: Current value of underlying indexA = F x multiplierFor S&P 500 futures, multiplier = $250If F=1000, A = 250,000
18Hedging Using Index Futures Naive hedge: N = - P/AMatch dollar value of futures to dollar value of portfolioSuppose you wish to hedge $1M portfolio with S&P 500 hundred futuresSell 1,000,000/250,000 = 4 contracts
19Hedging Using Index Futures Remember total risk can divided up into systematic and unsystematic riskSystematic risk is measured by the portfolio betaHedging with futures allows us to change the systematic riskBut not the unsystematic risk
20Hedging Using Index Futures To hedge the risk in a portfolio the number of contracts that should be shorted iswhere P is the value of the portfolio, b is its beta, and A is the value of the assets underlying one futures contract
21Hedging Stock Portfolios Hedge reduces systematic -- not unsystematic risk is computed with respect to the index underlying the futures contractFutures should be chosen on underlying index that most closely matches the investor’s portfolio
22Changing Beta Let * = desired beta Let = portfolio beta Then N = (* - )(P/A) (N < 0: sell)N > 0: buyIf we adopt the above convention, this formula textbook generalizes
23Reasons for Hedging an Equity Portfolio Desire to be out of the market for a short period of time. (Hedging may be cheaper than selling the portfolio and buying it back.)Desire to hedge systematic risk (Appropriate when you feel that you have picked stocks that will outperform the market.)
24Example Value of S&P 500 is 1,000 Value of Portfolio is $5 million Beta of portfolio is 1.5What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?A = 1000x250 = $.25 MN = (0 – 1.5)(5)/.25 = - 30 contracts (sell)
25Changing BetaWhat position is necessary to reduce the beta of the portfolio to 0.75?N = (.75 – 1.5)(5)/.25 = -15 contracts (sell)What position is necessary to increase the beta of the portfolio to 2.0?N = (2 – 1.5)(5)/.25 = 10 contracts (buy)
26Rolling The Hedge Forward We can use a series of futures contracts to increase the life of a hedgeEach time we switch from 1 futures contract to another we incur a type of basis risk