Futures on Debt Securities

1
Futures on Debt Securities

• Types
• T-Bills (IMM)
• T-Bonds and Notes (CBT)
• Eurodollar Deposits (IMM)
• Municipal Bond Index (CBT)

2
T-Bill Futures

• T-Bill futures call for the delivery or purchase
  of a T-bill with a maturity of 91 days and a
  face value of 1M. Used for speculating on S-T
  rates and hedging.
• Prices on T-Bill futures are quoted in terms of
  the IMM index or discount yield (Rd)
• Formula to Convert

3
Eurodollar Futures

• Eurodollar Futures are similar to T-Bill
  futures. They call for delivery or purchase of
  Eurodollar deposits with a maturity of 90 days
  and F 1M. They are quoted in terms of the IMM
  index. They differ from T-Bill futures in that
  there is a cash settlement feature. The cash
  settlement is based on the LIBOR. Used for
  speculating on ST rates and for hedging bank
  positions ( correlated with CD rates).

4
T-Bond Futures

• T-Bond Futures contracts call for the delivery or
  purchase of a T-Bond with a face value of
  100,000. The contract allows for the delivery of
  a number of T-Bonds there is a conversion factor
  used to determine the actual price of the futures
  given the bond that is delivered.
• T-Bond futures are quoted in terms of a T-Bond
  with an 8 coupon, semiannual payments, maturity
  of 15 years, and face value of 100.

5
Long Hedging with Debt Futures

• Bond manager expecting an inflow of cash in the
  future which he plans to invest in T-Bills for
  90 days (or long term). To hedge the manager
  would go long in T-Bill futures (T-Bond Futures).

6
Short Hedging with Debt Futures

• Short Hedging Strategies
• Bond manager expecting to liquidate a bond
  portfolio in the future.
• A company planning to issue bonds or borrow.
• A bank or financial institution managing its
  maturity gap.
• A company wanting to fix a variable-rate loan.

7
Speculation

• Outright Positions
• Long Expect rates to decrease. ST Rates use
  T-Bills or Eurodollar futures LT use T-Bonds or
  Notes.
• Short Expect rates to increase. ST use T-Bills
  or Eurodollars LT use T-Bonds or Notes.
• Spread
• Intracommodity
• Intercommodity
• Expect Recession Short MBI, Long T-Bond or Short
  Eurodollar, long T-Bill.
• Expect Upward Twist of YC Short T-B0nd, Long
  T-Bill.

8
Cross Hedging

• Cross Hedging is hedging a position with a
  futures contract in which the asset underlying
  the futures is different than the asset to be
  hedged.
• Example Future CP sale hedged with T-Bill
  futures AA Bond portfolio hedged with T-Bond
  futures.
• For bond positions, the following formula can be
  used

9
Futures

• Pricing and Hedging with Debt
• Futures Contracts

10
Pricing T-Bill Futures

• Carrying Cost Model

11
Pricing T-Bill Futures

• Example
• If the rate on a 161-day spot T-Bill is 5.7 and
  the repo rate (or RF rate ) for 70 days is 6.38,
  then the price on a T-Bill futures contract with
  an expiration of 70 days would be 98.74875

12
Pricing T-Bill Futures

• The futures price is governed by arbitrage. If
  the market price is above f, arbitrageurs would
  short the futures and go long in the spot.
• Example Suppose Fm 99. An arbitrageur would go
  short in the futures, agreeing to sell a 91-day
  T-Bill for 99 seventy days later and would go
  long in the spot, borrowing 97.5844 at 6.38 for
  70 days to finance the purchase of the 161-day
  T-Bill that is trading at 97.5844. Seventy days
  later (expiration), the arbitrageur would sell
  the bill (which now would have a maturity of 91
  days) on the futures for 99 (fm) and pay off his
  financing debt of 98.74875 (f), realizing a cash
  flow of 2,513

13
Pricing T-Bill Futures

• Note at fm 99, a money market manager planning
  to invest for 70 days in a T-Bill at 6.38 could
  earn a greater return by buying a 161-day bill
  and going short in the 70-day T-Bill futures to
  lock in the selling price. For example, using
  the above numbers, if a money market manager were
  planning to invest 97.5844 for 70 days, she could
  buy a 161-day bill for that amount and go short
  in the futures at 99. Her return would be 7.8,
  compared to only 6.38 from the 70-day T-Bill.

14
Pricing T-Bill Futures

• If the market price is below f, then
  arbitrageurs would go long in the futures and
  short in the spot.
• Example Suppose Fm 98. An arbitrageur would
  go long in the futures, agreeing to buy a 91-day
  T-Bill for 98 seventy days later and would go
  short in the spot, borrowing the 161-day T-Bill,
  selling it for 97.5844 and investing the proceeds
  at 6.38 for 70 days. Seventy days later
  (expiration), the arbitrageur would buy the bill
  (which now would have a maturity of 91 days) on
  the futures for 98 (fm), use the bill to close
  his short position, and collect 98.74875 (f)
  from his investment, realizing a cash flow of
  7487.

15
Pricing T-Bill Futures

• Note at fm 98, a money market manager with a
  161-day T-Bill could earn an arbitrage by selling
  the bill for 97.5844 and investing the proceed at
  6.38 for 70 days, then going long in the 70-day
  T-Bill futures. Seventy days later, the money
  market manager would receive 98.74875 from the
  investment and would pay 98 on the futures to
  reacquire the bill for a CF of .74875.

16
Pricing T-Bill Futures

• Implication If the carrying-cost model holds,
  then the spot rate on a 70-day bill (repo rate)
  will be equal to the synthetic rate (implied repo
  rate) formed by buying the 161-day bill and going
  short in the 70-day futures.

17
Pricing T-Bill Futures

• Implication If the carrying-cost model holds,
  then the YTM of the futures will be equal to the
  implied forward rate (F)

18
Hedging with T-Bill Futures

• Case 1 Money market manager is expecting a 5M
  CF in June which she plans to invest in a 91-day
  T-Bill. With June T-Bill futures trading at IMM
  of 91, the manager could lock in a 9.56 rate by
  going long in 5.115 June T-Bill futures.

19
Hedging with T-Bill Futures

• Hedge Relation

20
Hedging with T-Bill Futures

• Case 1 Suppose in June, the spot 91-day T-bill
  rate is at 8. The manager would find T-Bill
  prices higher at 980,995 but would realize a
  profit of 17,877 from closing the futures
  position. Combining the profit with the 5M CF,
  the manager would be able to buy 5.115 T-Bills
  and earn a rate off the 5M investment of 9.56.

21
Hedging with T-Bill Futures

• Case 1 Suppose in June, the spot 91-day T-bill
  rate is at 10. The manager would find T-Bill
  prices lower at 976,518 but would realize a loss
  of 5,025 from closing the futures position.
  After paying the CH 5,025, the manager would
  still be able to buy 5.115 T-Bills given the
  lower T-Bill prices, earning a a rate of return
  from the 5M investment of 9.56.

22
Hedging with T-Bill Futures

• Case 2 Money market manager is expecting a 5M
  CF in June which she plans to invest in a 182-day
  T-Bill. Since the T-Bill underlying a futures
  contract has a maturity of 91 days, the manager
  would need to go long in both a June T-Bill
  futures and a September T-Bill
• futures (note there is approximately 91 days
  between the contract) in order to lock in a
  return on a 182-day T-Bill investment. If June
  T-Bill futures were trading at IMM of 91 and
  September futures were trading at IMM of 91.4,
  then the manager could lock in a 9.3 rate on an
  investment in 182-day T-Bills by going long in
  5.115 June T-Bill futures and 5.11 September
  contracts

23
Hedging with T-Bill Futures

• Case 2 Suppose in June, the spot 91-day T-bill
  rate is at 8 and the spot 182-day T-Bill rate is
  at 8.25. At these rates, the price on the
  91-day spot T-Bill would be 980,995, the price
  on the 182-day spot would be 961,245, and if the
  carrying-cost model holds, the price on the
  September futures would be 979,865. At these
  prices, the manager would be able to earn a
  profit of 24,852 from closing both futures
  contract (which offsets the higher T-bill futures
  prices) and would be able to buy 5.227 182-day
  T-bills, yielding a rate of 9.3 from a 5M
  investment.

24
Hedging with T-Bill Futures

• Case 2 Suppose in June, the spot 91-day T-bill
  rate is at 10 and the spot 182- day T-Bill rate
  is at 10.25. At these rates, the price on the
  91-day spot T-Bill would be 976,518, the price
  on the 182-day spot would be 952,508, and if the
  carrying-cost model holds, the price on the
  September futures would be 975,413. At these
  prices, the manager would incur a loss of 20,798
  from closing both futures contracts. However,
  with lower T-bill futures prices, the manager
  would still be able to buy 5.227 182-day T-bills,
  yielding a rate of 9.3 from a 5M investment.

25
Managing the Maturity Gap

• Case In June, a bank makes a 1M loan for 180
  days which it plans to finance by selling a
  90-day CD now at the LIBOR of 8.258 and a
  90-day CD ninety days later (in September) at the
  LIBOR prevailing at that time. To minimize its
  exposure to market risk, the bank goes short in
  1.03951 September Eurodollar futures at 92.1
  (IMM). By doing this, the bank is able to lock
  in a rate on its CD financing for 180 days of
  8.17

26
Managing the Maturity Gap

• Case In September, the bank will sell a new
  90-day CD at the prevailing LIBOR to finance its
  1.019758M debt on the maturing CD plus (minus)
  any debt (profit) from closing its short
  September Eurodollar futures position. If the
  LIBOR rate is higher, the bank will have to pay
  greater interest on the new CD, but it will
  realize a profit on its futures which, in turn,
  will lower the amount of funds it needs to
  finance. On the other hand, if the LIBOR is
  lower, then the bank will have lower interest
  payment on its new CD, but it will also incur a
  loss on its futures position and therefore have
  more funds that need to be financed.
• As shown in the exhibit, at September LIBORs of
  7.5 or 8.7, the banks total debt at the end of
  the 180-day period will be 1,039,509 which
  equates to a rate of 8.17.
• Note This is true for any rate.

27
Managing the Maturity Gap

• Managing Maturity Gap Case

28
Fixing a Variable Rate Loan

• Case A construction company obtains a 1M,
  one-year variable rate loan to finance one of its
  projects. The loan starts on 9/20 with the rate
  at 11.25 the rate is then reset on 12/20, 3/20,
  and 6/20 at the prevailing LIBOR plus 150 BP.
  The company fixes the variable rate by going
  short in a series of Eurodollar futures
  (Eurodollar strip) with expirations of 12/20,
  3/20, and 6/20 and the following prices

29
Fixing a Variable Rate Loan

• By doing this, the company is able to lock in a
  fixed rate of 10.12

30
Fixing a Variable Rate Loan

• For example, if the LIBOR is at 9 on date 12/20,
  the company will have to pay 26,250 on its loan
  the next quarter but it will also have a profit
  on its 12/20 Eurodollar futures of 1,250 which
  it can use to defray part of the interest
  expenses, yielding an effective hedged rate of
  10.

31
Fixing a Variable Rate Loan

• If the LIBOR is at 6 on date 12/20, the company
  will have to pay only 18,750 on its loan the
  next quarter but it will also have to cover a
  loss on its 12/20 Eurodollar futures of 6,250.
  The payment of interest and the loss on the
  futures yields an effective hedged rate of 10.

32
Cross Hedge Price-Sensitivity Model

• Price-Sensitivity Model

33
Hedging A Future CP Issue with T-Bills Cross
Hedge

• Case A company plans to sell a 182-day CP issue
  with a 10M principal in June to finance its
  anticipated accounts receivable. The company
  would like to lock in the current CP rate of 6,
  ensuring it of funds from the CP sale of
  9.713635M. Using the price-sensitivity model,
  the company locks in a rate by going short in 20
  June T-bill futures contracts at IMM index 95.

34
Hedging A Future CP Issue with T-Bills Cross
Hedge
35
Hedging A Future CP Issue with T-Bills Cross
Hedge

• If CP sold at a discount yield that was 25 BP
  greater than the discount yield on T-Bills, then
  the company would be able to lock in a rate on
  its CP of 5.48.

36
Hedging A Future BondSale with T-Bond Futures
Cross Hedge

• Bond portfolio manager plans to sell AA bond
  portfolio in June. Currently, the fund is worth
  1.02M and has a YTM of 11.76 and duration of
  7.36 years.
• Using the price-sensitivity model to hedge the
  sale against a rate increase, the manager goes
  short in 15 June T-Bond contract trading at 72 -
  16.

37
Options on Treasury Securities

• Hedging with Options
• on T-Bills and T-Bonds

38
T-Bill Options

• Options on T-Bills give the holder the right to
  buy a T-Bill with a face value of 1M and
  maturity of 91 days.
• Exercise price is quoted in terms of the IMM
  index and the following formula can be used to
  determine X
• The option premium is quoted in terms of annual
  discount points (PT). The actual premium is

39
T- Bond Options

• Options on T-Bonds give the holder the right to
  buy a specified T-Bond with a face value of
  100,000.
• Exercise price is quoted as a percentage of par
  (e.g. IN 90). If the holder exercises, she
  pays the exercise price plus the accrued
  interest
• The option premium is quoted in terms of points
  (PT). The actual premium is

40
Hedging with T-Bill Options

• Hedging 5M CF in June with June T-Bill Call
• Call X IMM 90 X 975,000 C PT .5 C
  1250 Hedge nc 5M/975,000 5.128205
  Cost (5.128205)(1250) 6410.

41
Managing the Maturity Gap with T-Bill Put

• Case In June, a bank makes a 1M loan for 180
  days which it plans to finance by selling a
  90-day CD now at the LIBOR of 8.258 and a
  90-day CD ninety days later (in September) at the
  LIBOR prevailing at that time. To minimize its
  exposure to market risk, the bank buys a T-Bill
  put at X IMM 90 for 1250.

42
Maturity Gap Hedged with T-Bill Puts
43
Hedging future T-Bond Sale With T-Bond Puts

• Case Three months from the present (.25 of
  year), a bond manager plans to sell a T-Bond with
  maturity of 15.25 years, F 100,000, and coupon
  rate 10.
• Manager hedges the sale against interest rate
  increases by buying one put option on a T-Bond
  with a current maturity of 15.25 years and face
  value of 100,000. The put has an expiration of
  T .25 years, exercise price of X IN 95 or
  X 95,000, and is trading at P 1 - 5 or P
  1.15625/100(100,000) 1156.

44
Hedging future T-Bond Sale With T-Bond Puts

• Hedge T-Bond Sale

45
Hedging Future Bond PortfolioSale With T-Bond
Puts

• Case Three months from the present (.25 of
  year), a bond manager plans to liquidate a bond
  portfolio consisting of AAA, AA, and A bonds. The
  portfolio currently has a WAM of 15.25 years, F
  10M, WAC 10, and has tended to yield a rate
  1 above T-Bond rates.
• Manager hedges the sale against interest rate
  increases by buying put options on a T-Bond with
  a current maturity of 15.25 years and face value
  of 100,000. The put has an expiration of T
  .25 years, exercise price of X IN 95 or X
  95,000, and is trading at P 1 - 5 or P
  1.15625/100(100,000) 1156.
• To hedge, the manager buys 105.26316 T-Bond puts
  for 121,684

46
Hedging Future Bond PortfolioSale With T-Bond
Puts

• Hedge Bond Portfolio Sale

47
Futures Options onTreasury Securities

• Futures options give the holder the right to take
  a futures position
• Futures Call Option gives the holder the right to
  go long. When the holder exercises, she obtains
  a long position in the futures at the current
  price, ft, and the assigned writer takes the
  short position and pays the holder ft - X.
• Futures Put Option gives the holder the right to
  go short. When the holder exercises, she obtains
  a short position at the current futures price,
  ft, and the assigned writer takes the long
  position and pays put holder X - ft.
• Futures option on Treasuries Options on T-Bill
  Futures, T-Bond Futures, and T-Note Futures.

48
Futures Options onTreasury Securities

• Call on T-Bill Futures
• X IMM 90 or X 975,000
• PT .5 or C 1,250
• Futures and options futures have same expiration.

49
Futures Options onTreasury Securities

• Put on T-Bill Futures
• X IMM 90 or X 975,000
• PT .5 or P 1,250
• Futures and options futures have same expiration.

50
Futures Options onTreasury Securities

• Notes
• If the futures and the options on the futures
  expire at the same time and the carrying cost
  model holds, then the options on the spot and the
  options on the futures are equivalent.
• Futures options are more liquid than spot
  options, making them more popular.
• Hedging with Treasury futures options are similar
  to hedging with Treasury spot options.

51
Interest Rate Options
52
Interest Rate Options

• Interest rate call option gives the holder the
  right to a payoff if an interest rate (e.g.,
  LIBOR) exceeds a specified exercise rate
  interest rate put option gives the holder the
  right to a payoff if an interest rate is less
  than the exercise rate.
• Interest rate options are written by commercial
  banks in conjunction with a future loan or CD
  investment.

53
Interest Rate Call Option

• Case
• A company plans to borrow 10M in sixty days
  from Sun Bank. The loan is for 90 days with the
  rate equal to LIBOR in 60 days plus 100 BP.
• Worried that rates could increase in the next 60
  days, the company buys an interest rate call from
  the bank for 20,000.
• Terms Exercise Rate 7 call premium plus
  interest will be paid at the maturity of the
  loan any interest rate payoff will be paid at
  the loans maturity.
• See JG, pp 522.

54
Interest Rate Put Option

• Case
• A company plans to invest 10M in sixty days in a
  Sun Bank 90-day CD. The CD will pay the LIBBER.
• Worried that rates could decrease in the next 60
  days, the company buys an interest rate put from
  the bank for 15,000.
• Terms Exercise Rate 7 put premium plus
  interest will be paid at the maturity of the CD
  any interest rate payoff will be paid at the CDs
  maturity.
• See JG, pp 522.

55
Caps Series of Interest Rate Call Options

• A Cap is a series of interest rate calls that
  expire at or near the interest rate payment dates
  on a loan. They are written by financial
  institutions in conjunction with a variable rate
  loan.
• Case
• A company borrow 50M from Commerce Bank to
  finance its yearly construction projects. The
  loan starts on March 1 at 8 and is reset every
  three months at the prevailing LIBOR.
• Cap In order to obtain a maximum rate while
  still being able to obtain lower rates if the
  LIBOR falls, the company buys a Cap from the bank
  for 100,000 with exercise Rate 8.
• See JG, pp 524.

56
Floor Series of Interest Rate Put Options

• A floor is a series of interest rate puts that
  expire at or near the payment dates on a loan.
  They are purchased by financial institutions in
  conjunction with a variable rate loan they are
  providing.
• Case
• Commerce Bank purchases a floor with an exercise
  rate of 8 for 70,000 from another institution
  to protect the variable rate loan it made.
• See JG, pp 524.

57
Interest Rate Swaps
58
Interest Rate Swaps

• An interest rate swap is an exchange of CFs.
• Generic Interest Rate Swap involves the exchange
  of fixed-rate payments for floating-rate payments.

59
Interest Rate Swaps

• Terms
• Parties to a swap are called counterparties.
  There are two parties
• Fixed-Rate Payer
• Floating-Rate Payer
• Rates
• Fixed rate is usually a T-Note rate plus BP
• Floating rate is usually the LIBOR.

60
Interest Rate Swaps

• Terms
• Interest is usually made semiannually.
• Principal Most interest rate swaps do not
  exchange principal.
• Notional Principal Interest is applied to a
  notional principal.
• Maturity ranges between 3 and 5 years.
• Dates
• Effective Date is the date interest begins to
  accrue
• Payment Date is the date interest payments are
  made.
• Only the interest differential is paid.

61
Interest Rate Swaps

• Example
• Fixed-rate payer pays 9.5 every six months.
• Floating-rate payer pays LIBOR every six months,
• Notional Principal 10M.
• Effective Dates are 3/23 and 9/23 for the next
  three years.

62
Interest Rate Swaps

• Swap

63
Interest Rate Swaps

• Points
• If LIBOR gt 9.5, then fixed payer receives the
  interest differential.
• If LIBOR lt 9.5, then floating payer receives the
  interest differential.
• Fixed payers position is similar to a short
  position in Eurodollar strip.
• Floating payers position is similar to a long
  position in a Eurodollar strip. See JG 511-512.

64
Interest Rate Swaps

• A synthetic fixed-rate loan is formed by
  combining a variable rate loan with a fixed-rate
  payers position.
• Example A three-year, 10M variable rate loan
  with rates set equal to the LIBOR on 3/23 and
  9/23 combined with a fixed-rate payers position
  on the swap just analyzed.

65
Interest Rate Swaps

• Synthetic Fixed-Rate Loan

66
Interest Rate Swaps

• A synthetic variable-rate loan is formed by
  combining a fixed-rate loan with a floating-rate
  payers position.
• Example A three-year, 10M, 9 fixed-rate loan
  combined with the floating-rate payers position
  on the swap just analyzed.

67
Interest Rate Swaps

• Synthetic Fixed-Rate Loan

68
Interest Rate Swaps

• Points
• Swap Banks The market for swaps is organized
  through a group of brokers and dealers
  collectively referred to as swap banks.
• As brokers, swap banks try to match
  counterparties.
• As dealers, swap banks temporary positions as
  fixed or floating players often hedging their
  positions with positions in Eurodollar futures
  contracts.

69
Interest Rate Swaps

• Points
• Closing Unlike futures positions, closing a swap
  position prior to maturity can be difficult.
• Alternatives
• Sell Swap.
• Enter offsetting swap position.
• Hedge with Eurodollar futures.