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1 Chapter 20 Benching the Equity Players Portfolio Construction, Management, & Protection, 4e, Robert A. Strong Copyright ©2006 by South-Western, a division of Thomson Business & Economics. All rights reserved.

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

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3 Importance of Financial Futures u Financial futures are the fastest-growing segment of the futures market u The number of underlying assets on which futures contracts are available grows every year

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4 Stock Index Futures Contracts u Stock index futures contracts are similar to the traditional agricultural contracts except for the matter of delivery

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5 S&P 500 Stock Index Futures Contract

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6 Hedging with Stock Index Futures u With the S&P 500 futures contract, a portfolio manager can attenuate the impact of a decline in the value of the portfolio components u S&P 500 futures can be used to hedge: Endowment funds Mutual funds Other broad-based portfolios

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7 Hedging with Stock Index Futures (cont’d) u 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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8 Hedging with Stock Index Futures (cont’d) u 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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9 Calculating A Hedge Ratio u Computation u The Market Falls u The Market Rises u The Market is Unchanged

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10 Computation u A futures hedge ratio indicates the number of contracts needed to mimic the behavior of a portfolio u 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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11 Computation (cont’d) u The futures hedge ratio is:

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12 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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13 Computation (cont’d) Example (cont’d) Solution: Calculate the hedge ratio:

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14 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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15 The Market Falls u If the market falls: There is a loss in the stock portfolio There is a gain in the futures market

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16 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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17 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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18 The Market Rises u If the market rises: There is a gain in the stock portfolio There is a loss in the futures market

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19 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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20 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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21 The Market Is Unchanged u 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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22 Hedging in Retrospect u 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 u Short hedging reduces profits in a rising market

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