Hedging with futures contractBasis risk, optimal hedge ratio and hedging multi-period purchases*

COVERAGEMany of the participants use futures markets to reduce a particular risk that they face (hedgers). We discuss general issues associated with the way hedges are set up using futures contractsWhich position in futures is appropriate to set the hedgeWhich tenure to be used ? (basis risk)What is the optimal size for reducing risk (Hedge ratio)Tailing the hedgeHow to roll a hedge forwardUse of stock index futuresArguments for and against hedging*Basis risk, liquidity risk and tailing the hedge are the major factors

Futures contractsAgreement between 2 parties to buy or sell an asset at a certain time in the future for a certain price(similar to forward)

Forward contractFutures contractNatureOTC (contract b/w 2 private parties)Traded on an exchange Contract termsTailor-madeHighly standardizedAny credit risks Some at the time of settlementVirtually none as contracts are settled dailyDelivery datesUsually one specific delivery date Range of delivery datesDelivery arrangementsDelivery or final cash settlement usually happensContract is usually closed out prior to maturity

*Examples of Futures ContractsOn 25-Jun-15, Agreement to:Buy 100 shares of Infosys Limited at Rs.1,006.70 in 27-Aug-15 (NSE)Buy 10 grams of Gold at Rs.26,533 in 05-Aug-2015 (MCX)Buy 1 barrel of Crude oil at Rs.3,830 in 20-Jul-2015 (MCX)Buy 1,000 @ Rs. 100.9125 in 27-Aug-2015 (MCX-SX)

Buy 100 oz. of gold @ US$1,280/oz. in Oct (NYMEX) Sell 62,500 @ 1.6500 US$/ in June (CME)Sell 1,000 bbl. of oil @ US$114/bbl. in April (NYMEX)

*Futures ContractsFutures price are determined in the same way as other prices (i.e., by the laws of supply and demand). If more traders want to go long than short, the price goes up;If the reverse is true, then the price goes down.

To make trading possible, the exchange specifies certain standardized features and Futures prices are regularly reported live and in the financial press.Tick sizeDelivery dateContract size

*Specific issues in FuturesThe two parties do not necessarily know each other Margining mechanism (daily settlement procedures) is devised to assure both parties a guarantee that the contract will be honoured.Other specific issues with futures aredelivery procedures, bid-offer spreads, and the role of the exchange clearing house

Why we cant lock into Spot price?A perfect hedge is one that eliminates hedger's risk. It can just lead to a more certain outcome. Does not always lead to better outcome than imperfect hedge NO, we can not lock into Spot price as forward prices, in general, are different from the spot prices.

Perfect hedge may not lead to better outcome!Suppose the asset's price movements prove to be favourable to a hedger. A perfect hedge totally neutralizes the company's gain from these favourable price movements.An imperfect hedge, which only partially neutralizes the gains, might well give a better outcome.

3 reasons for not hedgingIf the competitors are not hedging, the treasurer might feel that the company will experience less risk if it does not hedge

The treasurer might feel that the company's shareholders have diversified their risk away.

If there is a loss on hedge and gain from company's exposure to the UA, the treasurer might find it difficult in justifying the hedging to other executives within the organization.

Hedging is too demanding!The hedger shall be able to identify the precise date in future when an asset would be bought / sold.Then he/she shall decide b/w Futures and option to remove almost all the risk arising from the price of the asset on that date. In practice, hedging is often not straightforward.The asset whose price is to be hedged (ATH) may not be exactly the same as the asset underlying (UA) the futures.Hedger may be uncertain as to the exact date when the asset will be bought or sold.Hedge termination date is not the same as the contract maturity in such cases (closing out the futures).

*Convergence of Futures to Spot(Hedge initiated at time t1 and closed out at time t2) TimeSpot PriceFuturesPricet1t2t1t2FuturesPriceSpot PriceBasis is negativeBasis is positiveBasis = Spot price of asset to be hedged Futures price of contract used

*Basis RiskBasis = 0 when both ATH and UA are same and the hedge is lifted on contract expiration day.Prior to expiration, the basis may be +ve or -ve.As time passes, spot prices and futures price does not change by same amount!Basis risk arises from hedgers uncertainty as to the basis at the hedge termination date (closed out)The hedge termination date is not the same as the contract maturity in such cases.Basis risk can lead to an improvement or a worsening of a hedger's position.Basis strengthening increase in basisBasis weakening decrease in basis

*Long Hedge and Short hedgeWe defineS1 : Initial Asset PriceS2 : Final Asset PriceF1 : Initial Futures PriceF2 : Final Futures Price

If you hedge the future purchase by entering into a long futures contract thenCost of Asset = S2 (F2 F1) = F1 + Basis2 If you hedge the future sale of an asset by entering into a short futures contract thenPrice Realized = S2+ (F1 F2) = F1 + Basis2

*Short HedgeTo minimize basis risk, S and F must be highly correlatedBasis is the amount by which the spot price exceeds the forward price.A short hedger is long the asset and short futures contracts. The value of his position hence improves as the basis increases. Similarly it worsens as the basis decreases.

Basis strengthens (increases) unexpectedly / suddenlyBasis weakens(decreases) unexpectedly / SuddenlyLong hedgehedger's position worsenshedger's position improves

Short hedgeHedgers position improveshedgers position worsens

2 issues in choosing a contractOne key factor affecting basis risk is the choice of the futures contract to be used. This contract choice has two components:The choice of the asset underlying the contractThe choice of the delivery month1. If ATH UA, carry out a careful analysis todetermine which of the available futures contracts has futures prices that are most closely correlated with the price of ATH

2 issues in choosing a contract2. A contract with a later delivery month is usually chosen for asset to be purchased in this monthThe futures prices are in some instances quite erratic during the delivery month. Moreover, a long hedger runs the risk of having to take delivery of the physical asset if the contract is held during the delivery month. Taking delivery can be expensive &inconvenient.

Determining the no. of contractsHedge ratio = size of the position in futures / size of ATH. If UA = ATH, it is natural to use a hedge ratio of 1.0.If UA = ATH, the hedger should choose a value for the hedge ratio that minimizes the variance of the value of the hedged position.

Approaches to estimate the risk-minimizing hedge ratioPortfolio approach to a risk-minimizing hedge (MVHR)Dollar equivalency approach

MVHR - Portfolio approachAssume that hedger is long one unit of cash asset and is interested in risk minimization.Gain/loss on 1 unit is 1(S1 S0) = 1SRisk of unhedged position = Var(1S) = 12 Var(S)Suppose hedger sells h futures contractsGain/loss on portfolio = 1(S1 S0) h (F1 F0)Portfolio risk = Var [1(S1 S0) h (F1 F0) = 12 Var(S)+ h2 Var(F) 2(1)(h)Cov(S, F) = Var(S)+ h2 Var(F) 2h (S)(F) Corr(S, F)To minimize risk, take first derivative d/dx [risk(h)] = 02h F2 2h S F FS = 0h* = corr(S, F) (S) / (F)

If you ran the regression model S = a + b F using historical price data, then b = h* If you believe that past is not accurate portrayal of future, dont use regression approach; use dollar equivalency approach.

Hedge effectivenessThe hedge effectivenessthe proportion of the variance that is eliminated by hedging. This is the R2 from the regressionA hedger must be confident that a reliable relationship existsFor historical data, reliability is measured by R2Lower value imply greater basis riskIn deciding which of two possible contracts (with different UA), use futures contract with high R2If one contract has a higher R2 but lower liquidity, the hedger must evaluate how much liquidity she is willing to give up to obtain a more reliable hedgeIt is usually advisable to underhedge as your confidence in the future correlation b/w S and F declines

Dollar Equivalency methodThe goal of a hedge is to avoid losses in cash mkt resulting from adverse price changes.Alternative method of determining how many futures contracts to trade is to equate the anticipated loss in cash mkt if the price change by some amount to the likely gain in futures market that will occur concurrently with spot price changeThe goal of the hedger is to equate VS = h (VF)

VS = change in the value of spot positionVF = change in the value of futures positionh = no. of futures contracts

Why dollar equivalencyOne might prefer to use a subjective estimate of the relationship between the change in value of spot position and contemporaneous futures price change when spot data is not available to run regression (Sometimes)you might suspect that historical relationship will not exist in the future (Other times)MVHR and dollar equivalency can serve as checks on each other, increasing the likelihood that proper no. of futures contracts will be being traded

Caution!When employing dollar equivalency approach, the hedger must:Estimate the loss in the spot position that will occur if the spot changes by an arbitrary amountEstimate the change in the futures price that will occur if the spot price changes by that arbitrary amountCompute the change in the value of one futures contact given that change in the futures priceTrade the appropriate no.of futures contracts so as to realize a profit in the futures market equal to spot mkt lossDollar equivalency is used in IR futures market also

Tailing the HedgeA futures contract, when used for hedging, can give rise to cash flow problems due to M2M. Two way of determining the number of contracts to use for hedging areCompare the exposure to be hedged with the value of the assets underlying one futures contractCompare the exposure to be hedged with the value of one futures contract (=futures price time size of futures contractThe second approach incorporates an adjustment for the daily settlement of futures

Choosing the delivery month (A strip hedge vs. a stacked hedge)Selecting the delivery month requires proper analysis. You are expecting CF on 20-ug-15. June and Sep Contracts are traded in market.Use June futures alone, ________ risk is left during __________.Use June futures today, offset it just before the delivery date, and then (in June) use Sep futures to hedge. (Stacking hedge)Use Sep futures today and bear the ________ risk that exist when you offset the Sep futures on June 20. (Strip hedge)A firm faces series of dates (or periods) on which it faces price risk. Use a strip of futures contracts, each with a different delivery date.Use a stack hedge, in which the most nearby and liquid contract is used, and it is rolled over to the next-to-nearest contract as time passes viz. Rolling the hedge forward using a series of futures contracts to increase the life of a hedge

Factors to be consideredThe liquidity of nearby contracts relative to the liquidity of contracts with distant delivery datesNear-by contracts has far more liquidity and have a narrower bid-ask spreadsWhen liquidity is a factor, rolling hedge is goodTransaction costs will usually be lower when one is employing a strip hedgeRolling hedge may require double the contracts Is the contract with distant delivery more or less overpriced than nearby contract? Relative mispricingBasis risk for a rolling hedge is usually greater than that the basis risk existing in a strip hedge.

SummaryMost concepts about using forwards will apply when hedging with futuresTransaction costs, liquidity, accounting rules and basis risk will determine which contact is preferredLiquidity risk and basis risk are important considerations when one is comparing forwards with futures for RMUsing futures to manage price risk introducesBasis risk futures are standardized. The UA, delivery location, quantity and delivery date may differ from ATHIf the UA is sufficiently different from the asset being hedged, it is important to determine the degree to which price changes of the two assets are correlated.If date of the hedging horizon lies beyond the date of most nearby futures contract, the hedge must be rolled forwardBecause futures are M2M daily, futures hedges must be tailed.

SummaryHedging is a way of reducing risk. As such, it should be welcomed by most executives. On a theoretical level, we can argue that shareholders, by holding well-diversified portfolios, can eliminate many of the risks faced by a company. In reality, there are a number of theoretical and practical reasons why companies do not hedge. They do not require the company to hedge these risks. On a practical level, a company may find that it is increasing rather than decreasing risk by hedging if none of its competitors does so. Also, a treasurer may fear criticism from other executives if the company makes a gain from movements in the price of the underlying asset and a loss on the hedge.

SummaryThe hedger should first identify the net exposure to risk this determines whether futures should be bought or soldFutures price changes should be highly correlated with price changes of the asset being hedged, and the futures contract should be as liquid as possibleAn important concept in hedging is basis risk. The basis is the difference between the spot price of an asset and its futures price. Basis risk arises from uncertainty as to what the basis will be at maturity of the hedge.

SummaryThe hedge ratio is the ratio of the size of the position taken in futures contracts to the size of the exposure. Hedge ratio determines the number of futures contracts that will lead to a risk-minimizing hedge, and some hedgers may not wish to have such a position.It is not always optimal to use a hedge ratio of 1.0. If the hedger wishes to minimize the variance of a position, a hedge ratio different from 1.0 may be appropriate. The hedge ratio can be estimated using either the regression (portfolio) approach or the dollar equivalency approachThe optimal hedge ratio is the slope of the best-fit line obtained when changes in the spot price are regressed against changes in futures price.Hedges should be tailed when interest rates are high and/or hedging horizons are long.

SummaryStack and roll is appropriate When there is no liquid futures contract that matures later than the expiration of the hedge. This involves entering into a sequence of futures contracts. When the first futures contract is near expiration, it is closed out and the hedger enters into a second contract with a later delivery month.When the second contract is close to expiration, it is closed out and the hedger enters into a third contract with a later delivery month; and so on. The result of all this is the creation of a long-dated futures contract by trading a series of short-dated contracts.Finally, hedges should be actively monitored and evaluated.

The issue is whether you base the number of contracts used for hedging the futures price of the asset underlying a futures contract or the spot price of these assets. Tailing the hedge is a way of addressing for the marking to market of futures contracts.9All these specific issues would be covered in chapter 2.4 issues: decide the date; whether to use forward / futures / options; whether to use crude oil futures or heating oil futures; whether to use August futures or October futures to hedge September; Whether to hedge in full or partially*In both the figures, the basis is weakening (in absolute terms).First market is contago while the second market is in backwardation.Spot price may follow zig zag pattern as observed in practice. Futures price closely follows the spot.For most assets, basis weakens with time (there is no surprise!)Basis is negative in gold market and financial futures marketNote that the process of selecting which futures contract and the number of futures contracts to trade is frequently described as an art.There is no substitute for gathering as much information as possible and carefully analyzing the data to establish a predicted relationship b/w UA and ATHNaive use of any any one approach will lead to costly errors.A hedger transforms price risk into basis risk when futures were used while forwards transforms it into counterparty risk