Futures Hedging 

Hedging concepts

Lecture 5: Futures Hedging

01135531: Risk Management and Financial Instrument

Nattawut Jenwittayaroje, Ph.D., CFA Chulalongkorn Business School Chulalongkorn University

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Short and long hedges

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Factors involved when constructing a hedge

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Hedge ratios (e.g., number of futures contracts needed for hedging)

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Examples of bond and stock index futures hedges

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Hedging Concepts 

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Short Hedge and Long Hedge  Short (long) hedge implies a short (long) position in futures Short hedges can occur because the hedger owns an asset and plans to sell it later.  

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Hedging Concepts 

Some Risks of Hedging 

• Cross hedging involves an additional source of basis risk arising from the fact that the asset being hedged is not the same as the asset underlying the futures.

So short hedge means long spot, short futures. For example, a rice producer concerned about a decrease in rice price might consider hedging the price risk with a short position in rice futures.

Long hedges can occur because the hedger plans to purchase an asset later (i.e., an anticipatory hedge) or because having sold short an asset. So long hedge means short spot, long futures.  For example, a Thai importer planning to buy luxury British cars might buy British pound futures contracts to protect against an appreciation in British Pound against Thai baht. See Table 11.1 for hedging situations.

• One example of cross-hedging is the hedging of a corporate bond with a Treasury bond futures contract. That is, corporate and government bond prices tend to move together, but the relationship is weaker than that of two government bonds.

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Cross Hedging

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Spot and futures prices occasionally move opposite • Then a hedge will increase risk, i.e., produce either a profit or a loss on both the spot and the futures positions. • This is unlikely to occur if the correct futures contract is chosen.

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Hedging Concepts 

Hedging Concepts

Contract Choice 

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The choice of contract generally consists of four decisions: (1) which futures underlying asset, (2) which expiration month, (3) whether to be long or short, and (4) the number of contracts.

Contract Choice (continued) (3) Long or short?

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• A critical decision! No room for mistakes. Going long (short) when it should have been short (long), has doubled the risk!

(1) Which futures underlying asset?

• The decision of whether to go long or short futures can be made by determining whether a spot market move will help or hurt the spot position and how the futures market can used to offset that risk.

• The futures contract used for hedging should be liquid and should be on an asset that is highly correlated with the asset being hedged. • Favorably priced – a short (long) hedger should look for overpriced (underpriced) contracts or at least correctly priced. 

(2) Which expiration? • The hedger should choose a contract that expires as close as possible to but after the hedge termination date. • Concept of rolling the hedge forward – a futures contract with a short expiration is usually preferred due to its high liquidity. 5

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Determination of the Hedge Ratio 

Determination of the Bond Futures Hedge Ratio

Hedge ratio: The number of futures contracts to hedge a particular exposure in the spot market. 

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Price Sensitivity Hedge Ratio 

The hedge ratio is as follows:

The hedge ratio should be the one in which the futures profit or loss matches the spot loss or profit. Appropriate hedge ratio • The profit from a short (long) hedge is  = ΔS + ΔfNf ( = - ΔS + ΔfNf)

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• Set  = 0, then the appropriate hedge ratio would be

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Nf = - ∆S/∆f for a short hedge

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Nf = + ∆S/∆f for a long hedge

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• Note that this ratio must be estimated. 

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where MDB and MDf are the modified durations of the bond being hedged and the bond futures contract, respectively. B is the price of the bond held. f is the price of the bond futures contract. The price sensitivity hedge ratio gives the optimal number of futures to hedge against interest rate changes. Technically, the hedge ratio will change continuously and it will not capture the risk of large moves. 8

Intermediate and Long-Term Interest Rate Hedges 

The risk associated with intermediate- and long-term interest rates is typically faced by bond portfolio managers.

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The interest rate futures markets are usually used by bond portfolio managers to hedge the interest rate risk of current as well as anticipated bond positions.

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Let us look at some examples of CBOT T-note and bond contracts 

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Hedging a Long Position in a Government Bond Table 11.7 below is an example of hedging a long position in a government bond  short hedge.

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T-bond contract: must be a T-bond with at least 15 years to maturity  long-term interest rate futures contract. T-note contract: are based on three contracts (2-, 5-, and 10-year)  intermediate-term interest rate futures contract. Price is quoted in units and 32nds, relative to $100 par, e.g., 93 14/32 is $93.4375.

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Contract size is $100,000 face value, so price is $93,437.50

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Expiration months are March, June, September, and December. 9

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Hedging a Corporate Bond Issue

Determination of the Stock Index Futures Hedge Ratio

Table 11.9 shows an example of short hedge and cross-hedged 

Stock Index Futures Hedging 

Appropriate hedge ratio is

• where S is the beta from the CAPM and f is the beta of the futures, often assumed to be 1. • S is the value of the portfolio being hedged, and f the price of the stock index futures contract. 11

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Stock Portfolio Hedge (con’t)

Stock Portfolio Hedge

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Hedging a Long Position in a Government Bond 

Table 11.7 below is an example of hedging a long position in a government bond  short hedge.

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Hedging a Corporate Bond Issue Table 11.9 shows an example of short hedge and cross-hedged

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Stock Portfolio Hedge

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Stock Portfolio Hedge (con’t)

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