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Chapter 24Appendix 1
More on Hedging with Financial
Derivatives
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Hedging withFinancial Futures
• Micro-hedge – hedge the interest-rate risk of a single asset.
• Macro-hedge – hedge the interest-rate risk of the overall portfolio, or firm.
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Micro Hedge Example
• First National Bank holds $10 million in 10% T-bonds, maturing in 2025.
• Will use exchange-traded futures contract to hedge risk.
• Short position. But how many contracts? No perfect match in futures market.
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Micro Hedge Example
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Micro Hedge Example
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Micro Hedge Example
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Micro Hedge Example (a)
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Micro Hedge Example (b)
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Micro Hedge Example (c)
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Micro Hedge Example (d)
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Macro Hedge Example
• First National Bank holds $100 million in assets with a duration gap of 1.72 years.
• Will use exchange-traded futures contract to hedge risk.
• Short position. But how many contracts? No perfect match in futures market.
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Macro Hedge Example
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Macro Hedge Example (a)
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Macro Hedge Example (b)
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Futures Options Hedge Example
• First National Bank has a $2 million, 7%, four year loan commitment that expires in two months
• Will use exchange-traded futures options contract to hedge risk.
• Long put option on T-note futures. But how many contracts? Not a perfect match.
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Futures Options Hedge Example
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Futures Options Hedge Example
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Futures Options Hedge Example
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Futures Options Hedge Example (a)
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Futures Options Hedge Example (b)
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Futures Options Hedge Example (c)
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Interest-Rate Swaps Hedge Example
• First National Bank holds $32 million and $49.5 million in rate-sensitive assets and liabilities, respectively.
• Use 10-year interest rate swap to hedge. ─ Receive 1% + 1-yr T-bill rate─ Pay fixed 7%
• What notional amount should be swapped?
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Interest-RateSwaps Hedge Example
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Interest-RateSwaps Hedge Example (a)
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Macro Hedge Example (b)
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Stock Index Futures
• Stock index futures can be used to hedge two situations:─ Reduce systematic risk─ Lock in stock prices
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Stock Index FuturesReducing Systematic Risk
• Systematic risk – sensitivity of portfolio to changes in entire market
• Measured with beta (β)─ β = 0.5 means portfolio will increase 1% when
the market increases 2%.
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Hedging with Stock Index Futures: Example
• Rock Solid stock portfolio of $100 million• β of portfolio is 1.0• Wants to reduce beta to zero using futures• Stock futures index contracts selling for
$1,000, contract size = $250,000
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Hedging with Stock Index Futures: Example
• Must sell $100 million worth of futures, or $100 million / $250,000 = 400 contracts
• Market down 10%?─ Portfolio falls to $90 million─ Futures price falls $25,000 / contract, or a gain to
Rock Solid of $25,000 x 400 = $10 million
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Hedging with Stock Index Futures
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Hedging with Stock Index Futures: Example (a)
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Hedging with Stock Index Futures: Example (b)
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Stock Index FuturesLocking in Stock Prices
• Can lock-in prices of market level today.• Useful in situations where cash to buy a
position is on the way.
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Stock Index FuturesLocking in Stock Prices: Example
• Today is January 1• Rock Solid expects to receive insurance
premiums of $20 million in March• March futures price is $1,000. Manger
forecasts price to rise 5% by March• Can lock-in price today!
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Stock Index FuturesLocking in Stock Prices: Example
• Long position on 80 contracts─ 80 = $20 million / $250,000
• Market up 5%─Gain of $12,500 per contract, or $1 million!