1 chapter 20 benching the equity players portfolio construction, management, & protection, 4e,...
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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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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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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)