Interest rate Futures and Swaps
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Interest-rate futures contracts
Currently traded interest-rate futures contracts
Pricing Interest-rate futures
Bond portfolio management applications
Interest rate Swap
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Basics of Futures
• Definition
• Opening position
• Liquidating a position
– Liquidation before settlement
– delivery
– Cash settlement
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Basics of Futures
• Role of Clearinghouse
– When an investor takes a position in the futures market, the clearinghouse takes
the opposite position and agrees to satisfy the terms set forth in the contract.
– Give instruction of delivery in the day of settlement
• Margin requirement
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Initial margin
Maintenance margin
Variation margin
Leverage is involved when taking position in futures
• Marking to market
– As futures price changes, the proceeds accrue to the trader’s margin account
immediately.
• Difference from Forwards
– More standardized and low default risk
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Treasury Bill Futures
• Based on 13-week treasury bill with a face
value of $1 million
– Seller needs to deliver to the buyer at the
settlement date a Treasury with 13 weeks
remaining to maturity
– Index price = 100 – (yd*100)
• Where yd = D/F*(360/t)
– A change of one basis point will change the dollar
discount, and the invoice price, by
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Example
• The index price for a Treasury bill futures
contract is 92.52. Then
– Yd
–D
– Invoice price
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Eurodollar CD Futures
• Traded on
– International Monetary Market of Chicago
Mercantile Exchange
– London International Financial Futures Exchanges
• Underlying asset: 3-month Eurodollar CD
• Face value is &1 million, price quoted as: 100
– annualized futures LIBOR
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Treasury Bond Futures
• Underlying asset is $100,000 par value of a
hypothetical 20-year 6% coupon bond
• CBOT allows the seller to deliver one of several
Treasury bonds that the CBOT declares is acceptable
for delivery.
• Conversion factor:
• Invoice price (example see page 523)
– Invoice price = contract size*futures contract settlement
price*conversion factor + accrued Interest
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Pricing Interest Rate Futures
• A 20-year 100-par-value bond with a coupon
rate of 12% is selling at par.
• The bond is the deliverable for a futures
contract that settles in three months.
• Current 3-month interest rate is 8% per year
• What should be the price of the futures
contract?
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What will you get from the futures contract?
• If you take long position in the futures
– After 3 months, pay futures price
– Get the bond
– Pay accrued interest (page 31)
• If you take short position in the futures
– Deliver the bond after 3 month
– Get futures price and accrued interest
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Cash-and-carry trade
• You decide to hold the hold the bond and take
a short position in futures
– Sell futures at P
– Get accrued interest
– Purchase bond by borrowing money
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Reverse cash-and-carry trade
• Buy the futures contract at P
• Sell the bond for ?
• Invest the proceed for 3 months at 8% per year
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Theoretical Futures Price
• F=P[1+t(r-c)]
– Where r is financing rate, c is current yield, P is
cash market price, and F is futures price and t is
time, in years to the futures delivery date
– R-c is the net financing cost
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Bond Portfolio Management Applications
• Speculating on the movement of interest rate
• Controlling the interest rate risk of a portfolio
• Creating synthetic securities for yield
enhancement
• Hedging
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Creating Synthetic Securities for Yield Enhancement
• Consider an investor who owns a 20-year treasury
bond and sells treasury futures that call for the
delivery of that particular bond 3 months from now.
• Synthetic 3-month T bill.
• Yield on the synthetic 3-month t-bill and yield on the
cash market treasury bill.
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Hedging
• Hedging: taking a futures position as a temporary
substitute for transactions to be made in the cash
market at a later date.
• The outcome of a hedge will depend on the
relationship between the cash price and the futures
price
• The difference between cash price and futures price is
basis
• The risk that the basis will change in an unpredictable
way is basis risk
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Hedging
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Cross hedging
Short hedge
Long hedge
Hedge ratio
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Allocating Funds between Stocks and Bonds
• An alternative way to reallocate assets is to
buy and sell interest rate futures and stock
index futures
• Benefits
– Transaction costs are lower
– Market impact costs are avoided
– Activities of the money managers employed by the
pension sponsor are not disrupted
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Interest rate Swap Basics
• Two parties agree to exchange periodical
interest payments. The dollar amount fo the
interest payments exchanged is based on a
predetermined dollar principal, notional
principal amount. (example: page 590)
• Fixed-rate payer
• Floating-rate payer
• Viewed as a package of forward contracts
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Exercise
• Chapter 543, Problem 4, 11.
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