Hedging Strategies Using Hedging Strategies Using FuturesFuturesChapter 3

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HEDGERSHEDGERS

PROBLEM: TO OPEN

A LONG HEDGE

OR

A SHORT HEDGE?

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Long & Short HedgesLong & Short Hedges

A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price

A short futures hedge is appropriate when you know you will sell an asset in the future and want to lock in the price

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Short HedgesShort HedgesAssume that it is May 15 today and that an oil producer has just negotiated a contract to sell 1 million barrels of crude oil. It has been agreed that the price that will apply in the contract is the market price on August 15.Suppose that on May 15 the spot price is $80 per barrel and the crude oil futures price for August delivery is $79 per barrel.

Each futures contract is for the delivery of 1,000 barrels

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Long HedgesLong HedgesSuppose that it is now January 15. A copper fabricator knows it will require 100,000 pounds of copper on May 15 to meet a certain contract. The spot price of copper is 340 cents per pound, and the futures price for May delivery is 320 cents per pound.

Each contract is for the delivery of 25,000 pounds of copperSuppose that the spot price of copper on May 15 proves to be 325 cents per pound

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Arguments in Favor of HedgingArguments 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

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Arguments against HedgingArguments against HedgingShareholders 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

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Convergence of Futures to SpotConvergence of Futures to Spot(Hedge initiated at time (Hedge initiated at time tt11 and closed out at time and closed out at time tt22))

Time

Spot Price

FuturesPrice

t1 t2

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Basis RiskBasis Risk

Basis is the difference between the spot and futures price

Basis risk arises because of the uncertainty about the basis when the hedge is closed out

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Basis RiskBasis Risk

1. The asset whose price is to be hedged may not be exactly the same as the asset underlying the futures contract.

2. The hedger may be uncertain as to the exact date when the asset will be bought or sold.

3. The hedge may require the futures contract to be closed out before its delivery month.

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Long Hedge Long Hedge

We defineF1 : Initial Futures PriceF2 : Final Futures PriceS2 : Final Asset Price

If you hedge the future purchase of an asset by entering into a long futures contract then

Cost of Asset=S2 – (F2 – F1) = F1 + Basis

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Short HedgeShort HedgeAgain we define

F1 : Initial Futures Price

F2 : Final Futures Price

S2 : Final Asset PriceIf you hedge the future sale of an asset by

entering into a short futures contract thenPrice Realized=S2+ (F1 – F2) = F1 + Basis

ExampleExampleIt is March 1. A US company expects to receive 50 million Japanese yen at the end of July. Yen futures contracts on the CME Group have delivery months of March, June, September, and December. One contract is for the delivery of 12.5 million yen. The company therefore _____ four September yen futures contracts on March 1. When the yen are received at the end of July, the company closes out its position. We suppose that the futures price on March 1 in cents per yen is 0.7800 and that the spot and futures prices when the contract is closed out are 0.7200 and 0.7250, respectively.

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ExampleExampleIt is June 8 and a company knows that it will need to purchase 20,000 barrels of crude oil at some time in October or November. Oil futures contracts are currently traded for delivery every month on the NYMEX. The futures price on June 8 is $68.00 per barrel. The company finds that it is ready to purchase the crude oil on November 10. The spot price and futures price on November 10 are $70.00 per barrel and $69.10 per barrel.

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Choice of ContractChoice of ContractChoose a delivery month that is as close as

possible to, but later than, the end of the life of the hedge

When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as cross hedging.

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Optimal Hedge RatioOptimal Hedge Ratio

Proportion of the exposure that should optimally be hedged is

where S is the standard deviation of S, the change in

the spot price during the hedging period, F is the standard deviation of F, the change in the futures price during the hedging period is the coefficient of correlation between S and F.

F

S

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Optimal Number of Contracts Optimal Number of Contracts

N* = h* Qa / Qf

Where,Q a = Size of position to be hedged (units)Q f = Size of one future contract (units) N* = Optimal number of future contracts for hedging

Example- Calculating the optimal Example- Calculating the optimal # of contracts.# of contracts.

An airline expects to purchase 2 million gallons of jet fuel in 1 month and decides to use heating oil futures for hedging. the usual formulas for calculating standard deviations and correlations give standard deviation of future price =0.0313, standard deviation of spot price =0.0263, and correlation of 0.928. Each heating oil contract is on 42,000 gallons of heating oil.

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Tailing the HedgeTailing the HedgeTwo way of determining the number of

contracts to use for hedging are◦Compare the exposure to be hedged with the

value of the assets underlying one futures contract

◦Compare the exposure to be hedged with the value of one futures contract (=futures price time size of futures contract

The second approach incorporates an adjustment for the daily settlement of futures

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Hedging Using Index FuturesHedging Using Index Futures

To hedge the risk in a portfolio the number of contracts that should be shorted is

where P is the value of the portfolio, is its beta, and F is the value of one futures contract

FP

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ExampleExampleS&P 500 index is 1,000S&P 500 future price (250 times) is 1,010Value of Portfolio is 5,050,000 millionBeta of portfolio is 1.5

What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?

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Changing BetaChanging Beta

What position is necessary to reduce the beta of the portfolio to 0.75?

What position is necessary to increase the beta of the portfolio to 2.0?

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Hedging Price of an Individual Hedging Price of an Individual StockStock

Similar to hedging a portfolioDoes not work as well because only the

systematic risk is hedgedThe unsystematic risk that is unique to the

stock is not hedged

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Why Hedge Equity ReturnsWhy Hedge Equity ReturnsMay want to be out of the market for a

while. Hedging avoids the costs of selling and repurchasing the portfolio

Suppose stocks in your portfolio have an average beta of 1.0, but you feel they have been chosen well and will outperform the market in both good and bad times. Hedging ensures that the return you earn is the risk-free return plus the excess return of your portfolio over the market.

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Rolling The Hedge ForwardRolling The Hedge Forward

We can use a series of futures contracts to increase the life of a hedge

Each time we switch from one futures contract to another we incur a type of basis risk

QuestionsQuestionsA company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on the S&P 500 to hedge its risk. The index futures price is currently standing at 1080, and each contract is for delivery of $250 times the index. What is the hedge that minimizes risk? What should the company do if it wants to reduce the beta of the portfolio to 0.6?

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