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Hedging Interest Rate Risk Treasury/Eurodollar Futures

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Derivative Securities Stocks and Bonds represent claims to specific future cash flows Stocks and Bonds represent claims to specific future cash flows Derivative securities on the other hand represent contracts that designate future transactions Derivative securities on the other hand represent contracts that designate future transactions Currently, there are approximately 300 million derivative contracts outstanding with a market value of around $50 Trillion Currently, there are approximately 300 million derivative contracts outstanding with a market value of around $50 Trillion While equity trading is centered in New York (NYSE, NASDAQ), derivative markets are centered in Chicago (CME, CBOT, CBOE) While equity trading is centered in New York (NYSE, NASDAQ), derivative markets are centered in Chicago (CME, CBOT, CBOE)

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Futures Contracts A futures contract describes a transaction (Commodity, Price, and Quantity) that will be made in the future. In Trading Places (1983), Eddie Murphy and Dan Ackroyd were trading Orange Juice Futures

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Futures Contracts Orange Juice futures (FCOJ) are traded on the NYBOT (New York Board of Trade) ExpOpenHighLowSettleChangeInterest MAR85.7586.0084.2085.20-1.2518,849 MAY88.2088.4086.6087.70-1.2014,354 JUL88.5088.5087.6088.45-1.151,889 NOV91.5091.5090.0089.95-1.65905 Contract = 15,000 Lbs. ; Price = cents/lb Every contract must have two participants (Long = Buy, Short = Sell)

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NowMarAprJuneMayJulyAug ExpOpenHighLowSettleChangeInterest MAR85.7586.0084.2085.20-1.2518,849 MAY88.2088.4086.6087.70-1.2014,354 JUL88.5088.5087.6088.45-1.151,889 NOV91.5091.5090.0089.95-1.65905 A long position in MAR FCOJ would require you to purchase FCOJ in March A short position in JUL FCOJ would require you to deliver FCOJ in March

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Dealers pass orders along to the pit traders who create a contract. LongShort 3 May Contracts (15k * 3 = 45k lbs.) @ 88 cents/lb.

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The contracts are then passed along to the exchange who will become the middleman Short (3 contracts)Long (3 contracts) Long (3 Contracts)Short (3 Contracts) Note: the exchange is holding two contracts with a zero net position

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Contract Completion (FCOJ) May 1May 8May 10 May 31May 23 First Notice Date First Delivery Date Last Trading Day Last Notice Date Last Delivery Date

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Contract Completion May 1May 8May 10 May 31May 23 Suppose that, on May 3, the short position decides that he wants out of the contract. The current May futures price is.92 per Lb 3 Contracts (Short) @.88/LB He could take a long position on 3 May contracts at a price of.92/LB This would effectively cancel out the previous position at a loss of 3 cents/LB.03*45,000 = $1,350 Loss

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Contract Completion May 1May 8May 10 May 31May 23 Suppose that, on May 12, the short position opts for delivery of the commodity. The current spot price is.84 per Lb 3 Contracts (Short) @.88/LB 3 Contracts (Long) @.88/LB The Exchange Pairs up Longs with Shorts Profit = (.88-.84)*45,000 = $1,800 Loss = (.88-.84)*45,000 = $1,800

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Types of Futures CurrenciesAgricultureMetals & Energy Financial British Pound LumberCopperTreasuries EuroMilkGoldLIBOR Japanese Yen CocoaSilver Municipal Index Canadian Dollar CoffeePlatinum S&P 500 Mexican Peso SugarOilDJIA Cotton Natural Gas Nikkei WheatEurodollar Cattle Soybeans

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Stock Index Futures Stock Index Futures have no underlying commodity Stock Index Futures have no underlying commodity S&P 500 S&P 500 NYSE Composite NYSE Composite Value Line Index Value Line Index These contracts are settled on a cash basis: Short Position Profits = (F – S)*500 Long Position Profits = (S – F)*500 F = Futures Price, S = Current Spot Price

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Regardless, futures positions are making bets on the price of the underlying commodity. Regardless, futures positions are making bets on the price of the underlying commodity. Long Position Short Position Profits from price increases Profits from price decreases

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Treasury Futures Treasury futures first began trading on the CME in 1976. The underlying commodity is a Treasury Bill, Note, or Bond. Remember, when interest rates rise, Treasury prices fall! Long Position Short Position Profits from price increases Profits from price decreases Profits from decreasing interest rates Profits from increasing interest rates

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T-Bill Futures With T-Bill Futures, the commodity is a $1M Treasury Bill with 3 months left until maturity Contracts exist for February, March, April, June, September, and December delivery Nov 16, 2004Feb 14Feb 18 First Trading Day Last Trading Day (T-Bill Auction) Delivery Day

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T-Bill Yields We have already calculated the Yield to Maturity for 90 Day Treasury Bills YTM = Face Value - Price Price 365 t Annualized Often, the yield referred to for Treasury Bills is the discount yield DY = Face Value - Price Face Value 360 t Interest As a percentage of Face Value rather than Price Annualized with a 360 day year Days left until maturity *100

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Pricing T-Bill Futures T-Bill futures are listed using the IMM (International Monetary Market) Index IMM = 100 – Discount Yield For example, if the Price of a $100, 90 Day Treasury were $98. DY = $100 - $98 $100 360 90 IMM = 100 – 8 = 92 *100 = 8% Every.005 increase in the IMM raises the value of a long T-Bill position by $12.50 ($25 per basis point).

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Eurodollar The term refers to deposits denominated in a currency other than the banks home currency The term Eurodollar refers to deposits denominated in a currency other than the banks home currency European banks offer Eurodollar time deposits (terms can range from overnight to several years) European banks offer Eurodollar time deposits (terms can range from overnight to several years) European banks will lend dollar reserves to each other at the LIBOR rate (London Inter- bank Offering Rate) European banks will lend dollar reserves to each other at the LIBOR rate (London Inter- bank Offering Rate)

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Eurodollar Futures (1981) The underlying commodity is a $1M 3 month Eurodollar time deposit. However, these deposits are not marketable. Therefore, Eurodollar futures are settled on a cash basis The underlying commodity is a $1M 3 month Eurodollar time deposit. However, these deposits are not marketable. Therefore, Eurodollar futures are settled on a cash basis Eurodollar futures can be treated like a T-Bill Future Eurodollar futures can be treated like a T-Bill Future IMM = 100 – LIBOR Every.005 increase in the IMM raises the value of the long position by $12.50. ($25 per basis point)

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Eurodollar Futures vs. T-Bill Futures T-Bill Futures Eurodollar Futures Volume (2001) 123($123M)730,000($730B) As the Eurodollar market grew, it became more liquid relative to the T-Bill market LIBOR is a risky rate. Therefore, it correlates better with other risks

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Pricing T-Bill/Eurodollar Futures Suppose that a march Eurodollar future (expires in 47 days) was currently selling for 94.555 TermYield 1 Month 5.18% 3 Months 5.3125 6 Months 5.6438 1 Year 5.8163 We also have the current money rates (LIBOR) IMM = 100 - LIBOR This contract is paying an annualized (yield) of 100 – 94.555 = 5.445%

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NowDay 47 Purchase/Sale of Eurodollar Future Day 137 90 Days Delivery of a $1M 90Day Eurodollar account The Eurodollar Future currently has an annual yield of 5.445% $1M (1.013613) = $1,013,613 5.445 4 = 1.3613% Receipt of $1,013,613 TermYield 1 Month 5.18% 3 Months 5.3125 6 Months 5.6438 1 Year 5.8163

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TermYield 1 Month 5.18% 3 Months 5.3125 6 Months 5.6438 1 Year 5.8163 Term Yield 1 Month3 Months 5.18% 5.3125% 47 Days 5.2175% Use a linear interpolation to get the 47 day spot rate 5.2175% 47 360 =.6811% 47 Day Return

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TermYield 1 Month 5.18% 3 Months 5.3125 6 Months 5.6438 1 Year 5.8163 Term Yield 3 Months6 Months 5.3125% 5.6438% 137 Days 5.4855% Use a linear interpolation to get the 137 day spot rate 5.4855% 137 360 = 2.0875% 137 Day Return

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TermYield S(47).6811% S(137)2.0875% NowDay 47Day 137 The Eurodollar Future currently has an annual yield of 5.445% 5.445 4 = 1.3613% S(47) =.6811% S(137) = 2.0875% F(47,90) 1.020875 1.006811 =1.01397 = 1.3970% =

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NowDay 47Day 137 The Eurodollar Future currently has an annual yield of 5.445% (1.3613%) IMM = 100 – 5.445 = 94.555 The implied no-arbitrage interest rate between 47 and 137 days is 5.588% (1.3970%) IMM = 100 – 5.588 = 94.412 The interest rate on the futures contract is to low!! or, alternatively The price of the futures contract is too high!!! Borrow at Futures Rate (Sell a Futures contract) Lend at the implied forward rate 1.013970 – 1.013613$1M = $357Profit =

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NowDay 47Day 137 How do you lend at the implied forward rate? Lend Borrow By lending for the entire 137 day period and borrowing for the first 47 days, your net position is as a lender for the last 90 day period!

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NowDay 47Day 137 Go Short on a the futures contract at a price of 94.555 Lend $992,885 for 137 days at the spot rate of 5.4855% (You will be paid $1,013,613 in 137 days) Borrow $992,885 for 47 days at the spot rate of 5.2175% Borrow $1,000,000 at the rate established by the futures contract (5.445%) Pay back the $992,885 Loan + interest ($999,643) Receive $1,013,613 from the original 137 day loan Pay $1,013,613 on the 90 day loan

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Date Cash In Cash Out Now$992,855$992,855 47 Days$1,000,000$999,648 137 Days $1,013,613$1,013,613 On the 47 th day, you get a net cash flow of $352. This is the present value of $357 dollars to be received in 90 Days (you get the profits on day 47 rather than day 137)

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The no arbitrage price of a price of a futures contract will reflect the forward rate implied by the yield curve. But remember, the forward rate is the expected future spot rate Futures Rate = Expected Future Spot Rate

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Treasury Note/Bond Futures ContractUnderlying Asset 20 Year T-Bond (FV = $100,000) 15-20 Year T-Bond with a 6% coupon 10 Year T-Note (FV = $100,000) 6.5 – 10 Year T-Note with a 6% coupon 5 Year T-Note (FV = $100,000) 4.25 – 5 Year T-Note with 6% coupon 2 Year T-Note (FV = $200,000) 1.75 – 2 Year T-Note with 6% coupon

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The commodity for T-Note/Bond futures is a Treasury with a 6% annual coupon. What if there are no 6% bonds available? Treasury Note/Bond futures are based on cheapest to deliver (CTD) basis. Requirements for Delivery 1.The Face value of the delivered notes must sum to $100,000 (per contract) 2.All the notes must have the same characteristics (term, coupon) Its the short positions option to deliver whatever has the lowest cost

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Conversion Factors Suppose that you have a short position on a a Treasury bond future that expires this month (any bond with an expiration date between 2020 and 2030 would be acceptable for delivery: MaturityCouponBid Price May 2020 8.75%149:16 August 2023 7.25%134:21 August 20256.875%132:21 The cheapest to deliver bond will always be the lowest coupon, longest maturity bond

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Conversion Factors The conversion factors are meant to make all deliverable bonds equally attractive MaturityCouponConversion Factor May 2020 8.75%1.2695 August 2023 7.25%1.1331 August 20256.875%1.1017 Invoice Amount = Contract Size Futures Price Conversion Factor Accrued Interest

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Requirements for Delivery 1.The Face value of the delivered notes must sum to $100,000 (per contract) 2.All the notes must have the same characteristics (term, coupon) Its the short positions option to deliver whatever has the lowest cost To Find the cheapest to deliver bond/note - Spot Price Current Futures Price Conversion Factor Maximize Note: This will always be negative

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Pricing T-Note/Bond Futures NowMarchMarch 2025 20 Year Treasury Delivered 20 Year Treasury Expires The Logic behind pricing treasury note/bond futures is the same as with T-Bill futures. The price should reflect expectation of future spot rates. However, note that expectations of future spot rates are already incorporated in bond prices! Futures Price = Expected Future Treasury Price + (Carry Costs – Carry Return) Arbitrage Costs

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Hedging $25,000 = ++++ (1.05) 2345 P = $500,000 Lets return to the 5 year Treasury Note example. Interest rates are currently 5% and are expected to stay at 5% (the yield curve is flat). A 5 year treasury note with $500,000 of face value and a 5% annual coupon. $25,000 $525,000 We already calculated the Modified Duration for this bond MD = 4.3 That is, a 100 basis point increase in the interest rate lowers this bonds price by (.043)($500,000) = $21,500

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Hedging with T-Bill Futures Short Position (Futures) Profits from price decreases Profits from increasing interest rates If you are long in bonds, you are worried about rising interest rates (rising interest rates lower the value of your bond). Therefore, you could hedge this risk by holding short positions in T-Bill futures (Short positions make money when interest rates drop)

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Hedging with T-Bill Futures Short Position (Futures) Profits from price decreases Profits from increasing interest rates A perfect hedge eliminates all your interest rate risk Change in value of Value of Futures position = # of Futures Contracts Change in value of each contract = Change in value of bond position $21,500$2,500 $21,500/$2,500 = 8.6 Contracts

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Hedging with T-Bill Futures Change in value of Value of Futures position = # of Futures Contracts Change in value of each contract = Change in value of bond position $21,500$2,500 $21,500/$2,500 = 8.6 Contracts Hedge Ratio = Dollar Duration of Bonds Dollar Duration of Futures MD(B) MD(F) = FV(B) FV(F) 4.3.25 $500K $1M =

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Here we have the 5 year Treasury key durations. Note that this bonds price is most sensitive to the 5 Year spot rate. The futures value is based on the 90 day treasury rate X 100 One Problem…..

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Change in value of Value of Futures position = # of Futures Contracts Change in value of each contract = Change in value of bond position $21,500$2,500 $21,500/$2,500 = 8.6 Contracts We assumed that the 90 Day T-Bill rate and the 5 Year Rate were perfectly correlated. Suppose, instead, that we have Change in 5 Year Rate = (.5) Change in 90 Day Treasury Rate The hedge ratio drops to 4.3!

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Hedging with T-Note/Bond Futures The strategy would be the same. If you are worried about increasing interest rates, take a short position in futures contracts. The hedge ratio for T-Note/Bond futures depends on The strategy would be the same. If you are worried about increasing interest rates, take a short position in futures contracts. The hedge ratio for T-Note/Bond futures depends on Size of bond position relative to the size of a futures contract Size of bond position relative to the size of a futures contract Duration of your bond position relative to the duration of the underlying asset in the futures contract Duration of your bond position relative to the duration of the underlying asset in the futures contract Correlation between the interest rate affecting your bond portfolio and the interest rate influencing the futures price Correlation between the interest rate affecting your bond portfolio and the interest rate influencing the futures price Impact of interest rate on CTD bond Impact of interest rate on CTD bond

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