CHAPTER 7 INTEREST RATE FUTURES

1
CHAPTER 7INTEREST RATE FUTURES

• In this chapter, we explore one of the most
  successful innovations in the history of futures
  markets that is, interest rate futures
  contracts. This chapter is organized into the
  following sections
• Interest Rate Futures Contracts
• Pricing Interest Rate Futures Contracts
• Speculating With Interest Rate Futures
  Contracts
• Hedging With Interest Rate Futures Contracts

2
Interest Rate Futures Introduction

• Interest rate futures contracts are one of the
  most successful innovations in futures trading.
• Pioneered in the United States, they have
  expanded internationally with strong presence in
  Great Britain and Singapore.
• The CBOT specializes in contracts with long-term
  maturity (e.g., 2-year, 5-year and 10-year
  T-notes, and 5-year LIBOR-based swaps).
• The CME International Monetary Market (IMM)
  specializes in contracts with short-term maturity
  (e.g., 1-month, and 3-month Eurodollar deposits).

3
Short-Term Interest Rates Contracts

• In this section, four short-term interest rate
  futures contracts will be examined
• Eurodollar Futures
• Euribor Futures
• TIEE 28 Futures
• Treasury Bill Futures

4
Eurodollar Futures Product Profile
5
Eurodollar Futures

• Eurodollar futures currently dominate the U.S.
  market for short-term futures contracts.
• Rates on Eurodollar deposits are usually based on
  LIBOR (London Interbank Offer Rate).
• LIBOR is the rate at which banks are willing to
  lend funds to other banks in the interbank
  market.
• Eurodollars are U.S. dollar denominated deposits
  held in a commercial bank outside the U.S.
• The Eurodollar contracts is for 1,000,000.
• A Eurodollar futures contract is based on a time
  deposit held in a commercial bank (e.g., 3-month
  Eurodollar)
• Eurodollar contracts are non-transferable.

6
Eurodollar Futures

• Eurodollar futures were the first contract to use
  cash settlement rather than delivery of an actual
  good for contract fulfillment.
• To establish the settlement rate at the close of
  trading, the IMM determines the three-month LIBOR
  rate.
• This settlement rate is then used to compute the
  amount of the cash payment that must be made.
• The yield on the Eurodollar contract is quoted on
  an add-on basis as follows

7
Eurodollar Add-on Yield

• In order to calculate the add-on yield, the price
  and discount must be computed as follows

Or equivalently
8
Eurodollar Add-on Yield

• Suppose you have a 90-day Eurodollar deposit with
  a discount yield of 8.32.
• Step 1 Compute the discount and the price.

9
Eurodollar Add-on Yield
Step 2 Compute the add-on yield using
A one basis point change in the Add-on Yield, on
a 3-month Eurodollar contract implies a 25
change in price. This amount can be compute
using
Eurodollar futures contract prices are quoted
using the IMM Index which is a function of the
3-month LIBOR rate IMM Index 100.00 -
3-Month LIBOR
10
Euribor Futures

• Euribors are Eurodollar time deposits.
• Swaps dealers use Euribor futures to hedge the
  risk resulting from their activities.
• Euribor futures are traded at
• Euronex.liffe
• Contracts are based on a 3-month time deposit
  with a 1,000,000 notional value.
• Contracts are cash settled at expiration .
• Eurex
• Contracts are based on a 3-month time deposit
  with a 3,000,000 notional value.
• Contracts are cash-settled at expiration.

11
Euribor Futures Product Profile
12
TIEE 28 Futures

• The TIEE 28 futures contract is based on the
  short-term (28-day) Mexican interest rate.
• The contract is traded on the Mexican Derivatives
  Exchange (Mercado Mexicano de Derivados, or
  MexDer)
• A 28-day TIIE futures contract has a face value
  of 100,000 Mexican pesos.
• The contract is cash settled based on the 28-day
  Interbank Equilibrium Interest Rate (TIIE),
  calculated by Banco de México.

13
TIEE 28 Futures TIEE 28 Futures
14
Treasury Bill Futures

• A T-bill is the U.S. government borrowing money
  for a short period of time.
• Treasury bills have original maturities of 13
  weeks and 26 weeks.
• The Treasury bill futures contract calls for the
  delivery of T-bills having a face value of
  1,000,000 and a time to maturity of 90 days at
  the expiration of the futures contract.
• 91-day and 92 day T-bills may also be delivered
  with a price adjustment.
• The contracts have delivery dates in March, June,
  September, and December.
• The delivery dates are chosen to make newly
  issued 13 week T-bills immediately deliverable
  against the futures contract.

15
Treasury Bill Futures

• Price quotations for T-bill futures use the
  International Monetary Market Index (IMM).
• IMM Index 100 - DY
• Where
• DY Discount Yield
• Example
• A discount Yield of 7.1 implies an IMM Index
  of
• IMM Index 100 - 7.1
• IMM Index 92.9

16
Treasury Bill Futures

• Recall that a bill with 90 days to maturity and a
  8.32 discount yield, has a price of 979,200 and
  a discount of 20,800. For a futures contract
  with a discount yield of 8.32, the price to be
  paid for the T-bill at delivery would be
  979,200.
• A one basis point shift implies a 25 change on a
  1,000,000, 3-month futures contract.
• If the futures yield rose to 8.35, the delivery
  price would be 979,125.

17
Other Short-Term Interest Rate Futures

• Insert Figure 7.1 here

18
Longer-Maturity Interest Rate Futures

• Longer-maturity interest rate futures are based
  on coupon-bearing debt instruments as the
  underlying good.
• These instruments require the delivery of an
  actual bond.
• In this section, long-term interest rate futures
  contracts will be examined, including
• Treasury Bond Futures
• Treasury Note Futures
• Non-US Longer Maturity Interest Rate Futures

19
Treasury Bond Futures

• Traded at the CBOT, the Treasury bond futures
  contract is one of the most successful futures
  contracts.
• Requires the delivery of T-bonds with a 100,000
  face value and with at least 15 years remaining
  until maturity or until their first permissible
  call date.
• T-bond contracts trade for delivery in March,
  June, September, and December.
• Delivery against the T-bond contract is a several
  day process that the short trader can trigger to
  cause delivery on any business day of the
  delivery month.
• First Position Day
• First permissible day for the short to declare
  his/her intentions to make delivery, with
  delivery taking place 2 business days later.
• Position Day
• Short declares his/her intentions to make
  delivery. This may occur on the first position
  day or some other later day.
• Delivery Day
• Clearinghouse matches the short and long traders
  and requires them to fulfill their
  responsibilities.

20
Treasury Bond FuturesPrice Quotation for Major
Interest Rate Futures Contracts

• Insert Figure 7.1 Here

21
Treasury Bond Futures Delivery Process

• Insert Figure 7.2 here

22
Treasury Bond Futures Product Profile
23
Treasury Bond Futures Conversion Factor

• The T-bond contract does not specify exactly
  which bond must be delivered to fulfill the
  futures contract. Rather, a number of different
  bonds can be delivered to fulfill the futures
  contract.
• Because the short trader chooses whether to make
  delivery, and which bond to deliver, the short
  trader will want to deliver the bond that is
  least expensive for him/her to obtain. This bond
  is called the cheapest-to-deliver bond.
• To address this issue, a conversion factor is
  computed to equate the bonds.

24
Treasury Bond Futures Conversion Factor

• Where
• DSP Decimal Settlement Price
• (The decimal equivalent of the quoted price)
• CF Conversion Factor
• (the conversion factor as provided by the
  CBOT)
• AI Accrued Interest
• (Interest that has accrued since the last
  coupon payment onthe bond)
• This system is effective as long as the term
  structure of interest rates is flat and the bond
  yield is 6. However, if the term structure of
  interest rates is not flat, or if bond yields are
  not 6, some bonds will still be less expensive
  to deliver against the futures contract than
  others.

25
T-Bond and T-Notes Delivery Sequence

• Table 7.1 shows key dates in the delivery process
  for T-bond and T-note futures contracts in 1997.

26
Treasury Bond Futures Conversion Factor
27
Treasury Note Futures

• Treasury note futures are a shorter maturity
  version of a Treasury bond.
• T-note Futures are very similar to Treasury
  bond futures.
• T-note futures contracts are available for
  2-year, 5-year, and 10-year maturities.
• Contract Size
• 2-year contract 200,000
• 5-year 10 year contract 100,000
• Deliverable Maturities
• 2-year contract 21 -24 month
• 5-year contract 4 yrs 3 mos. to 5 yrs 3 mos.
• 10-year contract 6 yrs 6 mos. to 10 years

28
CBOTs 10-Year Treasury Note FuturesProduct
Profile
29
Non-US Long Maturity Interest Rate Futures
30
Pricing Interest Rate Futures Contracts

• Because, interest rate futures trade in a full
  carry market, the foundation for pricing interest
  rate futures is the Cost-of-Carry-Model that we
  discussed in Chapter 3.
• This section introduces a review of the
  Cost-of-Carry Model as discussed in Chapter 3,
  including
• Cost-of-Carry Rule 3
• Cost-of-Carry Rule 6
• Features that Promote Full Carry
• Repo Rates
• Cost-of-Carry Model in Perfect Market
• Cash-and-Carry Arbitrage for Interest Rate
  Futures

31
Cost-of-Carry Rule 3

• Recall the cost-of-carry rule 3 says

Where S0 The current spot price F0,t The
current futures price for delivery of the
product at time t C0,t The percentage
cost required to store (or carry)
the commodity from today until time t
32
Cost-of-Carry Rule 6

• Recall the cost-of-carry rule 6 says

F0,d the futures price at t0 for the the
distant delivery contract maturing at td Fo,n
the futures price at t0 for the nearby delivery
contract maturing at tn Cn,d the percentage
cost of carrying the good from tn to td
33
Full Carry Features

• Recall from Chapter 3 that there are five
  features that promote full carry
• Ease of Short Selling
• Large Supply
• Non-Seasonal Production
• Non-Seasonal Consumption
• High Storability
• Interest rates futures have each of these
  features and thus conform well to the
  Cost-of-Carry Model.

34
Repo Rate

• Recall from Chapter 3 that if we assume that the
  only carrying cost is the financing cost, we can
  compute the implied repo rate as

or
Interest rate futures conform almost perfectly to
the Cost-of-Carry Model. However, we must take
into account some of the peculiar aspects of debt
instruments.
35
Cost-of-Carry Model in Perfect Market

• Assumptions
• Markets are perfect.
• The financing cost is the only cost of carrying
  charge.
• Ignore the options that the seller may possess
  such as the option to deliver differing
  securities.
• Ignore the differences between forward and
  futures prices.

36
Cash-and-Carry Arbitrage for Interest Rate Futures

• Recall from Chapter 3 that in order to earn an
  arbitrage profit, a trader might want to try a
  cash-and-carry arbitrage.
• Recall further that a cash-and-carry arbitrage
  involves selling a futures contract, buying the
  commodity and storing it until the futures
  delivery date. Then you would deliver the
  commodity against the futures contract.
• Applying the cash-and-carry arbitrage to interest
  rate futures requires careful selection of the
  commoditys interest rate (T-bill, T-bond etc)
  that will be purchased.
• Each of the interest rate futures contracts
  specifies the maturity of the interest rate
  instrument to be delivered. The interest rate
  instrument must have this maturity on the
  delivery date.

37
Cash-and-Carry Arbitrage for Interest Rate Futures

• Example, a T-bill futures contract requires the
  delivery of a T-bill with 90 days to maturity on
  the delivery date.
• So, if you sell a T-bill futures contract that
  calls for delivery in 77 days, we must purchase a
  T-bill that will have 90 days to maturity, 77
  days from today, in order to meet your
  obligations. That is, you must purchase a T-bill
  that has 167 days to maturity today.

Table 7.2 and 7.3 further develop this example.
38
Cash-and-Carry Arbitrage for Interest Rate Futures

• Assume that markets are perfect including the
  assumption of borrowing and lending at a
  risk-less rate represented by the T-bill yields.
  Suppose that you have gathered the information in
  Table 7.2 and wish to determine if an arbitrage
  opportunity is present.

How was the bill price of 987,167 from Table 7.2
calculated?
39
Cash-and-Carry Arbitrage for Interest Rate Futures

• The bill prices were calculated as follows

For the March Futures Contract
For the March 167-day T-bill
For the 77-day T-bill with 1,000,000 face value
40
Cash-and-Carry Arbitrage for Interest Rate Futures

• The transactions necessary to earn an arbitrage
  profit are given in Table 7.3.

How was the 966,008 from Table 7.3 calculated?
41
Cash-and-Carry Arbitrage for Interest Rate Futures

• The 966,008 is the face value of a 77-day T-bill
  with a current price of 953,611. To calculate
  this value, rearrange the bill price formula

Rearranging the equation results
42
Cash-and-Carry Arbitrage to Interest Rate Futures

• When delivery is due on the futures contract on
  March 22, you deliver the T-bill (which now has
  90 days to maturity) against the futures contract.

Combined, these transactions appear as follows on
a timeline
43
Reverse Cash-and-Carry Arbitrage to Interest
Rate Futures

• Using the same values as shown in Table 7.2, now
  assume that the rate on the 77-day T-bill is 8.
• Given this new information and Table 7.2 prices,
  a reverse cash-and-carry arbitrage opportunity is
  present. Table 7.4 shows the result.
• To calculate the values in Table 7.4 follow the
  steps shown for the previous cash-and-carry
  example.

44
Reverse Cash-and-Carry Arbitrage to Interest
Rate Futures

• Combined, these transactions appear as follows on
  a timeline

45
Interest Rate Futures Rate Relationships

• Rate relationship that must exist between
  interest rates to avoid arbitrage
• Consider two methods of holding a T-bill for 167
  days.
• Method 1
• Buy a 167 day T-bill
• Method 2
• Buy a 77 day T-bill.
• Buy a futures contract for delivery of a 90 day
  T-bill in 77 days.
• Use the futures contract to buy a 90-day T-bill.
• These investment appear as follows on a timeline.

46
Interest Rate Futures Rate Relationships
Method 1

• Method 2

Either of these two methods of investing in
T-bills has exactly the same investment and
exactly the same risk. Since both investment have
exactly the same risk and exactly the same
investment, they must have exactly the same yield
to avoid arbitrage.
47
Financing Cost and Implied Repo Rate

• Calculate the rate that must exist on the 77-day
  T-bill to avoid the arbitrage as follows

Use the no arbitrage equation to determine the
appropriate yield on the 77-day T-bill by, using
the following equation
Where NA Yield the no arbitrage Yield DTMFC
days to maturity of the futures contract
48
Financing Cost and Implied Repo Rate
So in order for there to be no arbitrage
opportunities available, the yield on the 77 day
T-bill must be 7.3063. If the yield on the 77
day T-bill is greater than 7.3063, then engage
in a reverse cash-and-carry arbitrage. If the
yield on the 77 day T-bill is less than 7.3063,
engage in a cash-and-carry arbitrage.
49
Financing Cost and Implied Repo Rate

• We can also calculate the implied repo rate as
  follows

In our case the spot price is the price of the
167-day to maturity T-bill, so
The implied repo rate (C) is 1.5875
The implied repo rate is the cost of holding the
commodity for 77 days, between today and the time
that the futures contract matures, assuming this
is the only financing cost, it is also the cost
of carry.
50
Financing Cost and Implied Repo Rate

• If the implied repo rate exceeds the financing
  cost, then exploit a cash-and-carry arbitrage
  opportunity

2. If the implied repo rate is less than the
financing cost, then exploit a reverse
cash-and-carry arbitrage.
51
Cost-of-Carry Model for T-Bond Futures

• The cost of carry concepts for T-bill futures
  that we have just examined also apply to T-bond
  futures. However, the computation must be
  adjusted to reflect the coupon payment and
  accrued interests.

52
Cost-of-Carry Model in Imperfect Markets

• In this section, the borrowing and lending
  assumptions are relaxed, and the Cost-of-Carry
  Model is explored under the following assumption
• The borrowing rate exceeds the lending rate.
• The financing cost is the only carrying charge.
• Ignore the options that the seller may possess.
• Ignore the differences between forward and
  futures prices.
• Recall that allowing the borrowing and lending
  rates to differ leads to an arbitrage band around
  the futures price. Now assume that the borrowing
  rate is 25 basis points, or one-fourth of a
  percentage point, higher than the lending rate.
  Continuing to use our T-bill example.

53
Cash-and-Carry Strategy
Notice that the entire arbitrage profit
disappears when these differential borrowing and
lending rates are considered.
54
Reserve Cash-and-Carry Transaction
Again notice that the entire arbitrage profit
disappears when these different borrowing and
lending rates are considered.
55
A Practical Survey of Interest Rate Futures
Pricing

• Recall from Chapter 3 that transaction costs lead
  to a no-arbitrage band of possible futures
  prices. In essence, transaction costs increase
  the no-arbitrage band just as unequal borrowing
  and lending rates do.
• Impediments to short selling as a market
  imperfection would frustrate the reverse
  cash-and-carry arbitrage strategy.
• From a practical perspective, restrictions on
  short selling are unimportant in interest rate
  futures pricing because
• Supplies of deliverable Treasury securities are
  plentiful and government securities have little
  (or zero) convenience yield.
• Treasury securities are so widely held, many
  traders can simulate short selling by selling
  T-bills, T-notes, or T-bonds from inventory.
  Therefore, restrictions on short selling are
  unlikely to have any pricing effect.

56
Speculating with Interest Rate Futures

• There are several ways that you can speculate
  with interest rate futures
• Outright Position.
• Intra-Commodity T-Bill Spread
• A T-bill/Eurodollar (TED) Spread
• Notes over Bonds (NOB)

57
Speculating with Outright Position

• Two ways to speculate with outright positions
  are
• Purchase an interest rate futures contract a
  bet that interest rates will go down.
• Sell an interest rate futures contract a bet
  that interest rates will go up.
• Suppose you think that interest rates will go up.
• The transactions necessary to bet on your hunch
  are outlined in Table 7.80.

58
Speculating with Outright Position

• Interest rates have gone up as you predicted.
  Your profit (based on 25 per basis point
  contract) is
• Profit (Sell Rate Buy Rate)(25)
• Profit (90.30 90.12) 0.18
• 0.18 is 18 basis points, each of which implies a
  25 change in contract value so
• Profit (Basis Points)(Value per Basis Point)
• Profit (18)(25) 450

59
Intra-Commodity T-Bill Spread

• If you dont know if rates will rise or fall, but
  do think that the shape of the yield curve will
  change, (that is the relationship between short
  term interest rates and long term interest rates
  will change) you might engage in an
  Intra-commodity T-bill spread.
• If you think that the spread will narrow (the
  yield curve will become flatter) you would buy
  the longer term contract and sell the shorter
  term contract.
• If you think that the spread will widen (the
  yield curve will become steeper), you would buy
  the shorter term contract and sell the longer
  term contract.

60
Intra-Commodity T-Bill Spread

• Suppose you have the following information (Table
  7.9) regarding T-bills and T-bill futures
  contracts for March 20. The left 2 columns are
  T-bills, and the right 3 columns are futures
  contracts. You think that the yield curve will
  flatten and wish to trade to make a profit.

61
Intra-Commodity T-Bill Spread

• Notice that the T-bills exhibit an upward sloping
  yield curve.
• Notice that the futures contract yields also
  exhibit and upward sloping yield curve.
• If the yield curve flattens, the yield spread
  between subsequent maturing futures contracts
  must narrow. That is, the difference between the
  yield on the December contract and on the
  September contract must narrow.
• Since you think that the spread will narrow (the
  yield curve will become flatter) you would buy
  the longer term contract and sell the shorter
  term contract, as it is demonstrated in Table
  7.10.

62
Intra-Commodity T-Bill Spread

• Gain in Basis Points
• Change in December Contract 1.64Change in
  September Contract -1.52
• Net Change in Positions 12 basis points
• Each Basis Point is worth 25
• Profit
• Net Change in Positions 12Basis Point
  Value 25Profit 300

63
T-Bill/Eurodollar (TED) Spread

• The TED spread is the spread between Treasury
  bill contracts and Eurodollar contracts.
• In theory, Treasury bills should always have a
  lower yield than Eurodollar deposits.
• T-bills are backed by the full taxing
  authority of the U.S. government.
• Eurodollar deposits are generally not backed by
  the respective governments.
• Thus, T-bills are a safer investment and as such,
  should pay a lower interest rate. Eurodollars
  are riskier and should pay a higher rate of
  interest.
• How much lower/higher?
• The amount of the difference depends upon world
  events. To the extent that the world situation
  is considered safe, the difference should be low.
  To the extent that the world situation is
  unsafe, the difference should be high.
• Table 7.11 shows the transactions necessary to
  engage in a TED spread when you wish to bet that
  the spread will widen.

64
T-Bill/Eurodollar (TED) Spread
Notice that the spread widened as the trader
expected, allowing him/her to earn a 675 profit.
65
Notes over Bonds (NOB)

• The NOB is a speculative strategy for trading
  T-note futures against T-bond futures.
• NOB spreads exploit the fact that T-bonds
  underlying the T-bond futures contract have a
  longer duration than the T-notes underlying the
  T-note futures contract. A given change in yields
  will cause a greater price reaction for the
  T-bond futures contract.
• Thus, the NOB spread is an attempt to take
  advantage of either changing levels of yields or
  a changing yield curve by using an inter-market
  spread.

66
Hedging with Interest Rate Futures

• There are several ways that you can hedge with
  interest rate futures, including
• Long Hedges
• Short Hedges
• Cross-Hedges

67
Hedging with Interest Rate Futures

• Recall that the goal of a hedger is to reduce
  risk, not to generate profits.
• Using interest rate futures to hedge involves
  taking a futures position that will generate a
  gain to offset a potential loss in the cash
  market.
• This also implies that a hedger takes a futures
  position that will generate a loss to offset a
  potential gain in the cash market.

68
Long Hedges

• On December 15, a portfolio manager learns that
  he will have 970,000 to invest in 90-day T-bills
  six months from now, on June 15. Current yields
  on T-bills stand at 12 and the yield curve is
  flat, so forward rates are all 12 as well. The
  manager finds the 12 rate attractive and decides
  to lock it in by going long in a T-bill futures
  contract maturing on June 15, exactly when the
  funds come available for investment as Table 7.12
  shows

69
Long Hedges

• With current and forward yields on T-bills at 12
  percent, the portfolio manager expects to be able
  to buy 1,000,000 face -value of T-bills for
  970,000 because

On June 15, the 90-day T-bill yield has fallen to
10. Thus, the price of a 90 day T-bill is
Thus, if the manager were to purchase the T-bill
in the market, he would be 5,000 short.
70
Long Hedges

• The futures profit exactly offsets the cash
  market loss for a zero change in wealth. With the
  receipt of the 970,000 that was to be invested,
  plus the 5,000 futures profit, the original plan
  may be executed, and the portfolio manager
  purchases 1,000,000 face value in 90-day T-bills.

• Insert Figure 7.7 here
• The idealized yield Curve Shit for the long Hedge.

71
Short Hedge
Banks may wish to hedge their interest rate
positions to lock in profits. Table 7.13
demonstrates how a bank that makes a one million
dollar fixed rate loan for 9 months, and can only
finance the loan with 6-month CDs, can hedged its
position.
Because the bank hedged, its profits were not
affected by a change in interest rates.
72
Cross-Hedge

• Recall that a cross-hedge occurs when the hedged
  and hedging instruments differ with respect to
• Risk level
• Coupon
• Maturity
• Or the time span covered by the instrument
  being hedged and the instrument deliverable
  against the futures contract.
• To illustrate how a cross-hedge is conducted,
  assume that a large furniture manufacturer has
  decided to issue one billion 90-day commercial
  paper in 3 months. Table 7.14 illustrate the
  cross-hedge.

73
Cross-Hedge