Derivatives

1
Derivatives

• A derivative is any instrument or contract that
  derives its value from another underlying asset,
  instrument, or contract.

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Managing Interest Rate Risk

• Derivatives Used to Manage Interest Rate Risk
• Financial Futures Contracts
• Forward Rate Agreements
• Interest Rate Swaps
• Options on Interest Rates
• Interest Rate Caps
• Interest Rate Floors

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Characteristics of Financial Futures

• Financial Futures Contracts
• A commitment, between a buyer and a seller, on
  the quantity of a standardized financial asset or
  index
• Futures Markets
• The organized exchanges where futures contracts
  are traded
• Interest Rate Futures
• When the underlying asset is an interest-bearing
  security

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Characteristics of Financial Futures

• Buyers
• A buyer of a futures contract is said to be long
  futures
• Agrees to pay the underlying futures price or
  take delivery of the underlying asset
• Buyers gain when futures prices rise and lose
  when futures prices fall

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Characteristics of Financial Futures

• Sellers
• A seller of a futures contract is said to be
  short futures
• Agrees to receive the underlying futures price or
  to deliver the underlying asset
• Sellers gain when futures prices fall and lose
  when futures prices rise

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Characteristics of Financial Futures

• Cash or Spot Market
• Market for any asset where the buyer tenders
  payment and takes possession of the asset when
  the price is set
• Forward Contract
• Contract for any asset where the buyer and seller
  agree on the assets price but defer the actual
  exchange until a specified future date

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Interest Rate Derivatives-Background

• Treasury futures
• Price quotes
• Treasury bill contracts and treasury bill futures
  are not quoted in the same units
• Treasury bill contracts are quoted in terms of a
  discount yield
• Treasury bill futures are quoted in terms of a
  price relative to 100
• To convert
• Cash price 100 yield(number of days in
  contract/360)
• Quoted price 100 yield
• The value of a T-bill future at maturity
• FV (yieldfvdays/360)

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Interest Rate Derivatives-Background

• Example Suppose that the yield on a 90-day
  T-bill future is 9.8, the value of delivery of
  the bill would be 1,000,000 -
  (.098)(1,000,000)(.25) 975,500.
• The minimum tick for treasury bill futures is a 1
  basis point change in the discount yield. This
  translates into a 25 per tick price movement in
  the final delivery value of the bill.
• To see this, assume the yield in the previous
  example were to increase to 9.81. The value of
  the bill at delivery would be
• 1,000,000 - (.0981)(1,000,000)(.25)
  975,475, or 25 less than the previous example.

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Interest Rate Derivatives-Background

• Example Suppose that we purchase a treasury
  bill futures contract with a discount yield of 6
  and that at the end of the life of the contract
  the discount yield on a 90 day T-bill is 6.3.
• We would have to pay 985,000 for a bill whose
  current cash price is 984,250 for a loss of
  750, or, 25 30 750.

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Hedging with Futures Contracts
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A Long Hedge

• A long hedge (buy futures) is appropriate for a
  participant who wants to reduce spot market risk
  associated with a decline in interest rates
• If spot rates decline, futures rates will
  typically also decline so that the value of the
  futures position will likely increase.
• Any loss in the cash market is at least partially
  offset by a gain in futures

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Long Hedge Example

• On March 10, 2005, your bank expects to receive a
  1 million payment on November 8, 2005, and
  anticipates investing the funds in 3-month
  Eurodollar time deposits
• The cash market risk exposure is that the bank
  will not have access to the funds for eight
  months.
• In March 2005, the market expected Eurodollar
  rates to increase sharply as evidenced by rising
  futures rates.

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Long Hedge Example

• In order to hedge, the bank should buy futures
  contracts
• The best futures contract will generally be the
  December 2005, 3-month Eurodollar futures
  contract, which is the first to expire after
  November 2005.
• The contract that expires immediately after the
  known cash transactions date is generally best
  because its futures price will show the highest
  correlation with the cash price.

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Long Hedge Example

• The time line of the banks hedging activities
  would look something like this

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Long Hedge Example
16
A Short Hedge

• A short hedge (sell futures) is appropriate for a
  participant who wants to reduce spot market risk
  associated with an increase in interest rates
• If spot rates increase, futures rates will
  typically also increase so that the value of the
  futures position will likely decrease.
• Any loss in the cash market is at least partially
  offset by a gain in the futures market

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Short Hedge Example

• On March 10, 2005, your bank expects to sell a
  six-month 1 million Eurodollar deposit on
  August 15, 2005
• The cash market risk exposure is that interest
  rates may rise and the value of the Eurodollar
  deposit will fall by August 2005
• In order to hedge, the bank should sell futures
  contracts

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Short Hedge Example

• The time line of the banks hedging activities
  would look something like this

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Short Hedge Example
20
Change in the Basis

• Long and short hedges work well if the futures
  rate moves in line with the spot rate
• The actual risk assumed by a trader in both
  hedges is that the basis might change between the
  time the hedge is initiated and closed
• In the long hedge position above, the spot rate
  increased by 0.93 while the futures rate fell by
  0.06. This caused the basis to fall by 0.99
  (The basis fell from 1.09 to 0.10, or by 0.99)

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Change in the Basis

• Effective Return from a Hedge
• Total income from the combined cash and futures
  positions relative to the investment amount
• Effective return
• Initial Cash Rate - Change in Basis
• In the long hedge example
• 3.00 - (-0.99) 3.99

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Basis Risk and Cross Hedging

• Cross Hedge
• Where a trader uses a futures contract based on
  one security that differs from the security being
  hedged in the cash market
• Example
• Using Eurodollar futures to hedge changes in the
  commercial paper rate
• Basis risk increases with a cross hedge because
  the futures and spot interest rates may not move
  closely together

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Example

• Your bank is a regular borrower in the Eurodollar
  market. You are planning to issue 10 million of
  Eurodollar debt in three months. The current
  Eurodollar rate is 4.71. The corresponding
  futures rate for a three-month Eurodollar futures
  contract is 4.83.

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Example

• 1. Should the bank be long or short in
  Eurodollar futures in order to hedge their risk?
• 2. Suppose that in three months the cash market
  Eurodollar rate is 4.95. What is your gain/loss
  on the futures position?
• 3. What is your total gain/loss?

27
Lengthening a T-Bill

• To lengthen the time to maturity of an existing
  T-bill investment an investor can go long in a
  T-bill futures contract with expiration occurring
  at the same time as the expiration of the
  existing T-bill investment.
• Suppose that we hold 100,000,000 in T-bills that
  mature in 30 days. For what ever reason, we feel
  that interest rates will fall and that the
  current 30 day T-bill futures contract with a
  yield of 9.8 does not already reflect that
  expectation. We would like to extend our
  investment in T-bills.

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Lengthening a T-Bill

• First, we know in 30 days we will have
  100,000,000 to reinvest. The yield on the
  T-bill futures contract of 9.8 implies a
  delivery price of 975,000. Hence, we could
  purchase 100,000,000/975,000 102.51 T-bills at
  the delivery price of 975,000. Thus, today we
  could purchase 102 T-bill futures contracts for
  delivery in 30 days. When the contract expires
  we will pay 99,501,000 for T-bill maturing in 30
  days that have a face value of 102,000,000.
  This allows us to extend the life of our existing
  T-bill investment.

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Converting a floating rate loan to a fixed rate
loan

• The basic idea behind this strategy is to use a
  sell futures contract to protect against an
  increase in interest rates over the floating legs
  of the loan. This creates a certain interest
  payment over the life of the loan.

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Converting a floating rate loan to a fixed rate
loan

• Suppose that we need to borrow 100,000,000 for
  six months. Our bank offers us a floating rate
  loan, with quarterly reset, at 200 basis points
  above the 90 day LIBOR rate. The current LIBOR
  rate is 7.0. We would like to protect ourselves
  against increases in the LIBOR rate. The current
  discount on a 90 day Eurodollar futures contract
  is 7.3. Since Eurodollar futures contracts are
  based on LIBOR, we can use the contracts to hedge
  against increases in interest rates.

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Converting a floating rate loan to a fixed rate
loan

• Solution Sell the LIBOR futures contract to
  protect against increases in interest rates. In
  this example, we will assume that LIBOR did
  increase to 7.8 after 90 days.

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Converting a floating rate loan to a fixed rate
loan

• Solution Using the contract, we guaranteed that
  we would pay, 9.0 in the first quarter and 9.3
  in the second quarter, or 9.15 over the life of
  the loan.

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Converting a fixed rate loan to a floating rate
loan

• In this situation, we will consider the above
  situation from the bank's perspective. We will
  assume that the bank will lend 100,000,000 to
  the investor at a fixed rate of 9.15 for six
  months. This is the average of the current LIBOR
  rate (7.0) and the LIBOR futures rate (7.3),
  with a 200 basis point profit for the bank.

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Converting a fixed rate loan to a floating rate
loan

• The bank, however, faces the potential for "gap
  risk." The bank's costs of funds, its
  liabilities (deposits) that fund the assests
  (loans), are short-term, floating rate,
  obligations on which the bank must pay LIBOR.
  Thus, if short term LIBOR rates increase, the
  fixed rate loan may not cover the bank's floating
  rate liability or, more likely, the bank will not
  earn a 200 basis point profit on the fixed rate
  loan.

36
Converting a fixed rate loan to a floating rate
loan

• Solution Assume that the bank finances the loan
  from 100,000,000 in deposits that have a term of
  90 days and are paid the LIBOR rate. Also,
  assume that LIBOR rates increase to 7.8 after 90
  days.

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Converting a fixed rate loan to a floating rate
loan

• The total cash flows of the bank are
• - 3,700,000 interest payments to
  depositors
• 4,575,000 from loan
• 125,000 from futures contract
• ________
• 1,000,000