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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 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 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 Exp Open High Low Settle Change Interest MAR 85.75**

Orange Juice futures (FCOJ) are traded on the NYBOT (New York Board of Trade) Contract = 15,000 Lbs. ; Price = cents/lb Exp Open High Low Settle Change Interest MAR 85.75 86.00 84.20 85.20 -1.25 18,849 MAY 88.20 88.40 86.60 87.70 -1.20 14,354 JUL 88.50 87.60 88.45 -1.15 1,889 NOV 91.50 90.00 89.95 -1.65 905 Every contract must have two participants (Long = Buy, Short = Sell)

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**Exp Open High Low Settle Change Interest MAR 85.75 86.00 84.20 85.20**

-1.25 18,849 MAY 88.20 88.40 86.60 87.70 -1.20 14,354 JUL 88.50 87.60 88.45 -1.15 1,889 NOV 91.50 90.00 89.95 -1.65 905 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 Now Mar Apr May June July Aug

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**Dealers pass orders along to the pit traders who create a contract.**

Short 3 May Contracts (15k * 3 = 45k 88 cents/lb.

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**The contracts are then passed along to the exchange who will become the middleman**

Note: the exchange is holding two contracts with a zero net position Short (3 contracts) Long (3 contracts) Long (3 Contracts) Short (3 Contracts)

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**Contract Completion (FCOJ)**

First Notice Date Last Delivery Date Last Trading Day First Delivery Date Last Notice Date May 1 May 8 May 10 May 23 May 31

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Contract Completion 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 He could take a long position on 3 May contracts at a price of .92/LB 3 Contracts .88/LB This would effectively “cancel out” the previous position at a loss of 3 cents/LB .03*45,000 = $1,350 Loss May 1 May 8 May 10 May 23 May 31

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

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**Types of Futures Currencies Agriculture Metals & Energy Financial**

British Pound Lumber Copper Treasuries Euro Milk Gold LIBOR Japanese Yen Cocoa Silver Municipal Index Canadian Dollar Coffee Platinum S&P 500 Mexican Peso Sugar Oil DJIA Cotton Natural Gas Nikkei Wheat Eurodollar Cattle Soybeans

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**Stock Index Futures Stock Index Futures have no underlying commodity**

S&P 500 NYSE Composite 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.**

Profits from price increases Long Position Short Position Profits from price decreases

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**Treasury Futures Profits from price increases**

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

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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 Last Trading Day (T-Bill Auction) First Trading Day Delivery Day Nov 16, 2004 Feb 14 Feb 18

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

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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. $100 - $98 360 DY = *100 = 8% $100 90 IMM = 100 – 8 = 92 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 Eurodollar refers to deposits denominated in a currency other than the bank’s home currency 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)

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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 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 $ ($25 per basis point)

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**Eurodollar Futures vs. T-Bill 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 We also have the current money rates (LIBOR) Term Yield 1 Month 5.18% 3 Months 5.3125 6 Months 5.6438 1 Year 5.8163 IMM = LIBOR This contract is paying an annualized (yield) of – = 5.445%

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**Term Yield 1 Month 5.18% 3 Months 5.3125 6 Months 5.6438 1 Year 5.8163**

The Eurodollar Future currently has an annual yield of 5.445% 5.445 = % 4 $1M ( ) = $1,013,613 Delivery of a $1M 90Day Eurodollar account Purchase/Sale of Eurodollar Future Receipt of $1,013,613 Now Day 47 Day 137 90 Days

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**Term Yield 1 Month 5.18% 3 Months 5.3125 6 Months 5.6438 1 Year 5.8163**

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

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**Term Yield 1 Month 5.18% 3 Months 5.3125 6 Months 5.6438 1 Year 5.8163**

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

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Term Yield S(47) .6811% S(137) 2.0875% The Eurodollar Future currently has an annual yield of 5.445% 5.445 = % 4 S(47) = .6811% S(137) = % Now Day 47 Day 137 = = % = F(47,90)

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**The Eurodollar Future currently has an annual yield of 5. 445% (1**

IMM = 100 – = The implied no-arbitrage interest rate between 47 and 137 days is 5.588% (1.3970%) IMM = 100 – = 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) Now Day 47 Day 137 Profit = – $1M = $357 Lend at the implied forward rate

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**How do you lend at the implied forward rate?**

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! Borrow Lend Now Day 47 Day 137

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**Go Short on a the futures contract at a price of 94.555**

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

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**On the 47th day, you get a net cash flow of $352**

On the 47th 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) Date Cash In Cash Out Now $992,855 47 Days $1,000,000 $999,648 137 Days $1,013,613

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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**

Contract Underlying Asset 20 Year T-Bond (FV = $100,000) 15-20 Year T-Bond with a 6% coupon 10 Year T-Note 6.5 – 10 Year T-Note with a 6% coupon 5 Year T-Note 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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**Requirements for Delivery **

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 The Face value of the delivered notes must sum to $100,000 (per contract) All the notes must have the same characteristics (term, coupon) It’s the short position’s option to deliver whatever has the lowest cost

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**Conversion Factors Maturity Coupon Bid Price May 2020 8.75% 149:16**

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: Maturity Coupon Bid Price May 2020 8.75% 149:16 August 2023 7.25% 134:21 August 2025 6.875% 132:21 The cheapest to deliver bond will always be the lowest coupon, longest maturity bond

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**Conversion Factors Maturity Coupon Conversion Factor May 2020 8.75%**

1.2695 August 2023 7.25% 1.1331 August 2025 6.875% 1.1017 The conversion factors are meant to make all deliverable bonds “equally attractive” Invoice Amount Contract Size Futures Price Conversion Factor Accrued Interest =

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**Requirements for Delivery **

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

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**Pricing T-Note/Bond Futures**

20 Year Treasury Delivered 20 Year Treasury Expires Now March March 2025 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! Expected Future Treasury Price Futures Price = + (Carry Costs – Carry Return) Arbitrage Costs

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Hedging 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 $25,000 $25,000 $25,000 $525,000 P + + + + = = $500,000 2 3 4 5 (1.05) (1.05) (1.05) (1.05) (1.05) 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 bond’s price by (.043)($500,000) = $21,500

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**Hedging with T-Bill Futures**

Profits from price decreases Profits from increasing interest rates Short Position (Futures) 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**

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

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**Hedging with T-Bill Futures**

Change in value of each contract Change in value of bond position Change in value of Value of Futures position # of Futures Contracts = = $2,500 $21,500 $21,500/$2,500 = 8.6 Contracts Dollar Duration of Bonds MD(B) FV(B) 4.3 $500K = Hedge Ratio = = MD(F) FV(F) .25 $1M Dollar Duration of Futures

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

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**Change in value of each contract**

Change in value of bond position Change in value of Value of Futures position # of Futures Contracts = = $2,500 $21,500 $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 90 Day Treasury Rate Change in 5 Year Rate = (.5) 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 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 Correlation between the interest rate affecting your bond portfolio and the interest rate influencing the futures price Impact of interest rate on CTD bond

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