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Chapter 20

Benching the Equity Players

Portfolio Construction, Management, & Protection, 4e, Robert A. StrongCopyright ©2006 by South-Western, a division of Thomson Business & Economics. All rights reserved.

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Using Futures Contracts Importance of Financial Futures Stock Index Futures Contracts S&P 500 Stock Index Futures Contract Hedging with Stock Index Futures Calculating a Hedge Ratio Hedging in Retrospect

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Importance of Financial Futures

Financial futures are the fastest-growing segment of the futures market

The number of underlying assets on which futures contracts are available grows every year

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Stock Index Futures Contracts Stock index futures contracts are similar to

the traditional agricultural contracts except for the matter of delivery

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S&P 500 Stock Index Futures Contract

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Hedging with Stock Index Futures

With the S&P 500 futures contract, a portfolio manager can attenuate the impact of a decline in the value of the portfolio components

S&P 500 futures can be used to hedge:• Endowment funds• Mutual funds• Other broad-based portfolios

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Hedging with Stock Index Futures (cont’d)

To hedge using S&P stock index futures:• Take a position opposite to the stock position

– e.g., if you are long in stock, short futures• Determine the number of contracts necessary to

counteract likely changes in the portfolio value using:– The value of the appropriate futures contract– The dollar value of the portfolio to be hedged– The beta of your portfolio

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Hedging with Stock Index Futures (cont’d)

Determine the value of the futures contract• The CME sets the size of an S&P 500 futures

contract at $250 times the value of the S&P 500 index

• The difference between a particular futures price and the current index is the basis

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Calculating A Hedge Ratio Computation The Market Falls The Market Rises The Market is Unchanged

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Computation A futures hedge ratio indicates the number

of contracts needed to mimic the behavior of a portfolio

The hedge ratio has two components:• The scale factor

– Deals with the dollar value of the portfolio relative to the dollar value of the futures contract

• The level of systematic risk– i.e., the beta of the portfolio

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Computation (cont’d) The futures hedge ratio is:

Dollar value of portfolio Beta

Dollar value of S&P contractHR

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Computation (cont’d)Example

You are managing a $90 million portfolio with a beta of 1.50. The portfolio is well-diversified and you want to short S&P 500 futures to hedge the portfolio. S&P 500 futures are currently trading for 353.00.

How many S&P 500 stock index futures should you short to hedge the portfolio?

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Computation (cont’d)Example (cont’d)

Solution: Calculate the hedge ratio:

75.529,1

50.1353250$

0$90,000,00

Betacontract P&S of ueDollar val

portfolio of ueDollar val

HR

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Computation (cont’d)Example (cont’d)

Solution: The hedge ratio indicates that you need 1,530 S&P 500 stock index futures contracts to hedge the portfolio.

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The Market Falls If the market falls:

• There is a loss in the stock portfolio

• There is a gain in the futures market

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The Market Falls (cont’d)Example

Consider the previous example. Assume that the S&P 500 index is currently at a level of 348.76. Over the next few months, the S&P 500 index falls to 325.00.

Show the gains and losses for the stock portfolio and the S&P 500 futures, assuming you close out your futures position when the S&P 500 index is at 325.00.

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The Market Falls (cont’d)Example (cont’d)

Solution: For the $90 million stock portfolio:

–6.81% × 1.50 × $90,000,000 = $9,193,500 loss

For the futures:

(353 – 325) × 1,530 × $250 = $10,710,000 gain

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The Market Rises If the market rises:

• There is a gain in the stock portfolio

• There is a loss in the futures market

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The Market Rises (cont’d)Example

Consider the previous example. Assume that the S&P 500 index is currently at a level of 348.76. Over the next few months, the S&P 500 index rises to to 365.00.

Show the gains and losses for the stock portfolio and the S&P 500 futures, assuming you close out your futures position when the S&P 500 index is at 365.00.

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The Market Rises (cont’d)Example (cont’d)

Solution: For the $90 million stock portfolio:

4.66% × 1.50 × $90,000,000 = $6,291,000 gain

For the futures:

(365 – 353) × 1,530 × $250 = $4,590,000 loss

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The Market Is Unchanged If the market remains unchanged:

• There is no gain or loss on the stock portfolio

• There is a gain in the futures market– The basis will deteriorate to 0 at expiration (basis

convergence)

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Hedging in Retrospect Futures hedging is never perfect in practice:

• It is usually not possible to hedge exactly– Index futures are available in integer quantities only

• Stock portfolio seldom behave exactly as their betas say they should

Short hedging reduces profits in a rising market