1. Hedging Interest Rate Risk
Treasury/Eurodollar Futures

2. 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)

3. 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

4. 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)

5. 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

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

7. 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)

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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).

18. 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)

19. 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)

20. 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

21. 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%

22. 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

23. 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

24. 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

25. 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)

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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 =

35. 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

36. 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

37. 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

38. 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)

39. 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

40. 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

41. 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

42. 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!

43. 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