Hedging Through Futures

8/9/2019 Hedging Through Futures

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Hedging Through Futures

Prof Mahesh Kumar

Amity Business School

[email protected]


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Hedging- Some Facts Hedging is aimed to reduce risk relating to

price of oil, a foreign exchange rate, the levelof stock market or some other variable.

A hedge tends to make unfavorable outcomesless unfavorable and favorable outcomes lessfavorable.

A perfect hedge is the one that completely

eliminates the risk.


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Short Hedge A short hedge is a hedge that involve a short

position in futures contract.

A short hedge is appropriate when hedger

already own an asset and expect to sell it atsometime in future e.g. a trader, a farmer.

A short hedge can also be used when the assetis not owned right now but will be owned at

sometime in the future e.g. an exporter who isto receive a remittance in foreign currency.


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Long Hedge

Hedges that involve taking a long position in afutures contract are known as long hedges.

A long hedge is appropriate when a company

knows it will have to purchase a certain assetin future and wants to lock in a price now. e.g.rice mill owner.


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Hedge Ratio The ratio of the size of a position in a hedging

instrument to the size of the position beinghedged.

The hedge ratio of 1 implies that for Rs.10 lacposition in cash market, the position takenfutures market should also be 10 lac.


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Optimal Hedge Ratio

Proportion of the exposure that shouldoptimally be hedged is

where

WS

is the standard deviation of(S, the changein the spot price during the hedging period,

WF

is the standard deviation of(F, the change

in the futures price during the hedging periodF is the coefficient of correlation between (Sand (F.

If F ! and WS= W

Fthen hedge ratio is 1

F

Sh

W

WF!


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Optimal Number of Contracts

NA: Size of position being hedged.

QF: Size of one futures contract.

N: Optimal number of future contract for hedging.

Then optimal number of futures contract is given by

N=h* NA

/ QF


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Problem:A refinery expects to purchase two million gallonsof crude oil in one month and decides to usefutures for hedging. Each crude oil contract

trades on NYMEX is of 42000 gallons. The datafor change in spot and future prices of crude oilare given in the table. Calculate the optimalnumber of contracts.


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Hedge ratio for Stock Index Futures Example: A portfolio worth Rs.1000000.00

mirrors BSE 30 stocks. The current value ofindex is 1000 and each futures contract is on

Rs.250 times the index. Find the number offuture contracts that need to be shorted.

Here P=1000000 A=250*1000=250000

N=1000000/250000=4


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Hedge ratio for Stock Index Futures When the portfolio does not mirrors the index

then F is used to determine the hedge ratio. F isthe slope of the best line obtained when excess

return of the portfolio over the risk free rate isregressed against excess return of the marketover the risk free rate.

When F=1, the return on the portfolio tends tomirror the return on the market.

When F=2, the return on the portfolio tend tobe twice as great as the excess return on themarket.

When F=0.5, it tends to be half as great.


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Hedge ratio for Stock Index FuturesTo hedge the risk in a portfolio the number of

contracts that should be shorted is

where P is the value of the portfolio, F is its beta,and F is the current value of one futures (=futures

price times contract size)

F

PF


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Reasons for Hedging an Equity Portfolio Desire to be out of the market for a short period

of time. (Hedging may be cheaper than sellingthe portfolio and buying it back.)

Desire to hedge systematic risk (Appropriatewhen you feel that you have picked stocks thatwill outperform the market.)


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Changing Beta To change the beta of the portfolio from F to

F*, where F"F*, a short position in (FF*)P/Acontracts is required.

When FF*, a long position in (F*FP/Acontracts is required.


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Problem On January 1,2003 an investor has a portfolio of 5 shares as given

below:Security Price No of Shares BetaA 59.50 5000 1.05B 81.85 8000 0.35

C 101.10 10000 0.80D 125.15 15000 0.85E 140.50 1500 0.75The cost of capital to the investor is 12.5% p.a.You are required to:a. Calculate the beta of this portfoliob. Calculate the theoretical value of Nifty futures for February

c. If its current value is 1005 and NIFTY futures have a minimum tradelot requirement of 200 units, obtain the number of contracts to Niftyhe needs to sell in order to get a full hedge until February for hisportfolio. Assume that futures are trading at their fair value.

d. Calculate the number of futures contract the investor should trade if hedesires to reduce the beta of his portfolio to 0.7


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Hedge ratio for StocksThe number of index futures contracts that hedgershould short is given by

where P is the total value of the shares, F is the

beta of the stock, and A is the current value of thestocks underlying one index futures contract.

A

P

F


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Hedge ratio for Stocks Hedge ratio for stocks with stock index futures

is not a perfect hedge as it provides protectiononly against the risk arising from the market

movements, and this risk is relatively small inproportion of the total risk in the pricemovements of individual stocks.

This hedge is appropriate when an investor feelsthe stock will outperform the market but isunsure about the performance of the market.


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Hedge ratio for Stocks-Problem Consider an investor who in June holds 20000 IDBI

shares each worth Rs.100. The investor feels that themarket will be very volatile over next month but IDBI hasgood chance to outperform the market. The investor uses

August future contract on BSE index to hedge hisposition. The current level of index is 900 and the currentfuture price for August contract on BSE index is 908. Eachcontract is for delivery of Rs.250 times the Index. F ofIDBI is 1.1 Suppose IDBI share rise to Rs.125 and BSE

index rises to 1080 after a month when the investordecided to sell his shares. Discuss the gain strategy of theinvestor.


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Hedge ratio for Stocks-ProblemStrategy:

Here P= 20000*100=2000000 A=900*250=225000

The number of contracts that should be shorted is

2000000/225000=9.781. Rounding off, hedger shorts 10 contracts on BSE 30

2. Closes out the position one month later when his cashflows are as follows:

With the increase in the price of IDBI investor gains

20000*(125-100)=Rs.500000By hedging he loses

10*250*(1080-908)=Rs.430000


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Rolling Forward of a Hedge Sometimes, the horizon of hedging may extend

beyond the delivery dates of all the futurescontract that may be used. In such a eventhedger must roll the hedge forward.

This implies closing out one future contract andtaking the same position in a futures contractwith a later delivery date. The process iscontinued until the hedging span is reached.

This strategy has number of basis risk i.e.uncertainty about the difference between thefuture prices for the contract being closed andfor the contract being entered into.

Hedging Through Futures

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