Portfolio Management - Chapter 23

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					                Chapter 23

    Removing Interest Rate Risk


Prof. Rushen Chahal


                      Prof. Rushen Chahal   1
The first mistake is usually the cheapest mistake.




                                          - A trader adage




                    Prof. Rushen Chahal                      2
                   Outline
• Introduction
• Interest rate futures contracts
• Concept of immunization




                     Prof. Rushen Chahal   3
                   Introduction
• A portfolio is interest rate sensitive if its value
  declines in response to interest rate increases
   – Especially pronounced:
      • For portfolios with income as their primary objective

      • For corporate and government bonds




                          Prof. Rushen Chahal                   4
              Interest Rate
            Futures Contracts
• Categories of interest rate futures contracts
• U.S. Treasury bills and their futures contracts
• Treasury bonds and their futures contracts




                     Prof. Rushen Chahal            5
Categories of Interest Rate Futures
            Contracts
• Short-term contracts
• Intermediate- and long-term contracts




                   Prof. Rushen Chahal    6
            Short-Term Contracts
• The two principal short-term futures contracts
  are:
  – Eurodollars
     •   U.S. dollars on deposit in a bank outside the U.S.
     •   The most popular form of short-term futures
     •   Not subject to reserve requirements
     •   Carry more risk than a domestic deposit
  – U.S. Treasury bills


                           Prof. Rushen Chahal                7
           Intermediate- and
          Long-Term Contracts
• Futures contract on U.S. Treasury notes is the
  only intermediate-term contract
• The principal long-term contract is the
  contract on U.S. Treasury bonds
• Special-purpose contracts:
  – Municipal bonds
  – U.S. dollar index


                        Prof. Rushen Chahal        8
         U.S. Treasury Bills and
        Their Futures Contracts
• Characteristics of U.S. Treasury bills
• Treasury bill futures contracts




                      Prof. Rushen Chahal   9
             Characteristics of
             U.S. Treasury Bills
• U.S. Treasury bills:
   – Are sold at a discount from par value

   – Are sold with 91-day and 182-day maturities at a
     weekly auction

   – Are calculated following a standard convention
     and on a bond equivalent basis


                         Prof. Rushen Chahal            10
            Characteristics of
       U.S. Treasury Bills (cont’d)
• Standard convention:


     T-bill price = Face value - Discount amount

                                    Days to maturity
Discount amount = Face value  (                     )  Ask discount
                                          360




                           Prof. Rushen Chahal                          11
           Characteristics of
      U.S. Treasury Bills (cont’d)
• The T-bill yield on a bond equivalent basis
  adjusts for:
  – The fact that there are 365 days in a year

  – The fact that the discount price is the required
    investment, not the face value




                       Prof. Rushen Chahal             12
           Characteristics of
      U.S. Treasury Bills (cont’d)
• The T-bill yield on a bond equivalent basis:


                             Discount amount       365
   Bond equivalent yield                    
                              Discount price Days to maturity




                             Prof. Rushen Chahal                13
             Characteristics of
        U.S. Treasury Bills (cont’d)
                            Example

A 182-day T-bill has an ask discount of 5.30 percent. The par
value is $10,000.

What is the price of the T-bill? What is the yield of this T-bill on
a bond equivalent basis?




                            Prof. Rushen Chahal                    14
            Characteristics of
       U.S. Treasury Bills (cont’d)
                      Example (cont’d)

Solution: We must first compute the discount amount to
determine the price of the T-bill:

                                      Days to maturity
 Discount amount = Face value  (                      )  Ask discount
                                            360
                                182
                  $10, 000  (     )  0.053
                                360
                  $267.94


                            Prof. Rushen Chahal                       15
             Characteristics of
        U.S. Treasury Bills (cont’d)
                      Example (cont’d)

Solution (cont’d): With a discount of $267.94, the price of this
T-bill is:



            T-bill price = Face value - Discount amount
                        $10,000  $267.94
                        $9,732.06



                            Prof. Rushen Chahal                    16
             Characteristics of
        U.S. Treasury Bills (cont’d)
                      Example (cont’d)

Solution (cont’d): The bond equivalent yield is 5.52%:


                           Discount amount        365
   Bond equivalent yield                  
                             Discount price Days to maturity
                            $267.94 365
                                    
                           $9, 732.06 182
                          5.52%

                           Prof. Rushen Chahal                 17
               Treasury Bill
             Futures Contracts
• T-bill futures contracts:
  – Call for the delivery of $1 million par value

  – Of 90-day T-bills

  – On the delivery date of the futures contract




                        Prof. Rushen Chahal         18
              Treasury Bill
        Futures Contracts (cont’d)
                            Example

Listed below is information regarding a T-bill futures contract.
What would you pay for this futures contract today?


                                                    Discount
Open    High     Low     Settle      Change Settle      Change Open
                                                               Interest
92.43   92.43    92.41   92.42       -.01        7.52   +.01    250


                           Prof. Rushen Chahal                        19
              Treasury Bill
        Futures Contracts (cont’d)
                        Example (cont’d)

Solution: First, determine the yield for the life of the T-bill:
                      7.52% x 90/360 = 1.88%

Next, discount the contract value by the yield:

               $1,000,000/(1.0188) = $981,546.92



                             Prof. Rushen Chahal                   20
Treasury Bonds and Their Futures
           Contracts
• Characteristics of U.S. Treasury bonds
• Treasury bond futures contracts




                    Prof. Rushen Chahal    21
  Characteristics of U.S. Treasury
              Bonds
• U.S. Treasury bonds:
  – Pay semiannual interest

  – Have a maturity of up to 30 years

  – Trade readily in the capital markets




                      Prof. Rushen Chahal   22
  Characteristics of U.S. Treasury
         Bonds (cont’d)
• U.S. Treasury bonds differ from U.S. Treasury
  notes:
  – T-notes have a life of less than ten year

  – T-bonds are callable fifteen years after they are
    issued




                       Prof. Rushen Chahal              23
              Treasury Bond
             Futures Contracts
• U.S. Treasury bond futures:
  – Call for the delivery of $100,000 face value of U.S.
    T-bonds
  – With a minimum of fifteen years until maturity
    (fifteen years of call protection for callable bonds)

• Bonds that meet these criteria are deliverable
  bonds


                       Prof. Rushen Chahal              24
           Treasury Bond
      Futures Contracts (cont’d)
• A conversion factor is used to standardize
  deliverable bonds:
  – The conversion is to bonds yielding 6 percent

  – Published by the Chicago Board of Trade

  – Is used to determine the invoice price



                      Prof. Rushen Chahal           25
     Sample
Conversion Factors




    Prof. Rushen Chahal   26
             Treasury Bond
        Futures Contracts (cont’d)
• The invoice price is the amount that the
  deliverer of the bond receives when a
  particular bond is delivered against a futures
  contract:

  Invoice price = (Settlement price on position day  Conversion factor)
                  + Accrued interest




                               Prof. Rushen Chahal                         27
           Treasury Bond
      Futures Contracts (cont’d)
• Position day is the day the bondholder
  notifies the clearinghouse of an intent to
  delivery bonds against a futures position
  – Two business days prior to the delivery date

  – Delivery occurs by wire transfer between accounts




                      Prof. Rushen Chahal           28
           Treasury Bond
      Futures Contracts (cont’d)
• At any given time, several bonds may be
  eligible for delivery
  – Only one bond is cheapest to delivery
     • Normally the eligible bond with the longest duration

     • The bond with the lowest ratio of the bond’s market
       price to the conversion factor is the cheapest to deliver




                         Prof. Rushen Chahal                   29
    Cheapest to
Deliver Calculation




     Prof. Rushen Chahal   30
        Concept of Immunization
•   Definition
•   Duration matching
•   Immunizing with interest rate futures
•   Immunizing with interest rate swaps
•   Disadvantages of immunizing




                      Prof. Rushen Chahal   31
                  Definition
• Immunization means protecting a bond
  portfolio from damage due to fluctuations in
  market interest rates

• It is rarely possible to eliminate interest rate
  risk completely



                      Prof. Rushen Chahal            32
             Duration Matching
•   An independent portfolio
•   Bullet immunization example
•   Expectation of changing interest rates
•   An asset portfolio with a corresponding
    liability portfolio




                      Prof. Rushen Chahal     33
      An Independent Portfolio
• Bullet immunization is one method of
  reducing interest rate risk associated with an
  independent portfolio
  – Seeks to ensure that a set sum of money will be
    available at a specific point in the future

  – The effects of interest rate risk and reinvestment
    rate risk cancel each other out


                      Prof. Rushen Chahal                34
   Bullet Immunization Example
• Assume:
  – You are required to invest $936
  – You are to ensure that the investment will grow at
    a 10 percent compound rate over the next 6 years
     • $936 x (1.10)6 = $1,658.18
  – The funds are withdrawn after 6 years




                         Prof. Rushen Chahal         35
          Bullet Immunization
           Example (cont’d)
• If interest rates increase over the next 6 years:
  – Reinvested coupons will earn more interest

  – The value of any bonds we buy will decrease
     • Our portfolio may end up below the target value




                        Prof. Rushen Chahal              36
          Bullet Immunization
           Example (cont’d)
• Reduce the interest rate risk by investing in a
  bond with a duration of 6 years

• One possibility is the 8.8 percent coupon bond
  shown on the next two slides:
  – Interest is paid annually
  – Market interest rates change only once, at the end
    of the third year

                      Prof. Rushen Chahal            37
Prof. Rushen Chahal   38
Prof. Rushen Chahal   39
 Expectation of Changing Interest
              Rates
• The higher the duration, the higher the
  interest rate risk

• To reduce interest rate risk, reduce the
  duration of the portfolio when interest rates
  are expected to increase
  – Duration declines with shorter maturities and
    higher coupons


                      Prof. Rushen Chahal           40
        An Asset Portfolio With
          A Liability Portfolio
• A bank immunization case occurs when there
  are simultaneously interest-sensitive assets
  and interest-sensitive liabilities

• A bank’s funds gap is its rate-sensitive assets
  (RSA) minus its rate-sensitive liabilities (RSL)



                     Prof. Rushen Chahal             41
       An Asset Portfolio With
     A Liability Portfolio (cont’d)
• A bank can immunize itself from interest rate
  fluctuations by restructuring its balance sheet
  so that:

          $ A  DA  $ L  DL
       where $ A, L  dollar value of rate-sensitive
                        assets and liabilities
             DA , L    dollar-weighted average duration
                        of assets and liabilities

                             Prof. Rushen Chahal           42
       An Asset Portfolio With
     A Liability Portfolio (cont’d)
• If the dollar-duration value of the asset side
  exceeds the dollar-duration of the liability
  side:
  – The value of RSA will fall to a greater extent than
    the value of RSL

  – The net worth of the bank will decline



                       Prof. Rushen Chahal                43
       An Asset Portfolio With
     A Liability Portfolio (cont’d)
• To immunize if RSA are more sensitive than
  RSL:
  – Get rid of some RSA
  – Reduce the duration of the RSA
  – Issue more RSL or
  – Raise the duration of the RSL




                     Prof. Rushen Chahal       44
            Immunizing With
          Interest Rate Futures
• Financial institutions use futures to hedge
  interest rate risk

• If interest rate are expected to rise, go short T-
  bond futures contracts




                      Prof. Rushen Chahal          45
          Immunizing With
    Interest Rate Futures (cont’d)
• To hedge, first calculate the hedge ratio:

                  Pb  Db
     HR  CFctd 
                  Pf  D f
where Pb  price of bond portfolio as a percentage of par
      Db  duration of bond portfolio
      Pf  price of futures contract as a percentage
     D f  duration of cheapest-to-deliver bond eligible for delivery
   CFctd  conversion factor for the cheapest-to-deliver bond

                             Prof. Rushen Chahal                  46
         Immunizing With
   Interest Rate Futures (cont’d)
• Next, calculate the number of contracts
  necessary given the hedge ratio:


                         Portfolio value
   Number of contracts                   HR
                           $100, 000




                    Prof. Rushen Chahal         47
           Immunizing With
     Interest Rate Futures (cont’d)
                          Example
A bank portfolio manager holds $20 million par value in
government bonds that have a current market price of $18.9
million. The weighted average duration of this portfolio is 7
years. Cheapest-to-deliver bonds are 8.125s28 T-bonds with a
duration of 10.92 years and a conversion factor of 1.2786.

What is the hedge ratio? How many futures contracts does the
bank manager have to short to immunize the bond portfolio,
assuming the last settlement price of the futures contract was
94 15/32?

                          Prof. Rushen Chahal                    48
           Immunizing With
     Interest Rate Futures (cont’d)
                            Example

Solution: First calculate the hedge ratio:


                               Pb  Db
                HR  CFctd 
                               Pf  D f
                                   0.945  7
                     1.2786 
                               0.9446875 10.92
                     0.8199


                            Prof. Rushen Chahal   49
          Immunizing With
    Interest Rate Futures (cont’d)
                          Example

Solution: Based on the hedge ratio, the bank manager needs to
short 155 contracts to immunize the portfolio:



                            $18,900,000
      Number of contracts               0.8199
                             $100, 000
                           154.96

                         Prof. Rushen Chahal                50
           Immunizing With
          Interest Rate Swaps
• Interest rate swaps are popular tools for
  managers who need to manage interest rate
  risk

• A swap enables a manager to alter the level of
  risk without disrupting the underlying
  portfolio


                    Prof. Rushen Chahal        51
          Immunizing With
    Interest Rate Swaps (cont’d)
• A basic interest rate swap involves:
  – A party receiving variable-rate payments
     • Believes interest rates will decrease
  – A party receiving fixed-rate payments
     • Believes interest rates will rise


• The two parties swap fixed-for-variable
  payments


                          Prof. Rushen Chahal   52
          Immunizing With
    Interest Rate Swaps (cont’d)
• The size of the swap is the notional amount
  – The reference point for determining how much
    interest is paid


• The price of the swap is the fixed rate to which
  the two parties agree




                     Prof. Rushen Chahal           53
          Immunizing With
    Interest Rate Swaps (cont’d)
• Interest rate swaps introduce counterparty
  risk:
  – No institution guarantees the trade

  – One party to the swap pay not honor its
    agreement




                      Prof. Rushen Chahal      54
     Disadvantages of Immunizing
•   Opportunity cost of being wrong
•   Lower yield
•   Transaction costs
•   Immunization is instantaneous only




                     Prof. Rushen Chahal   55
            Opportunity Cost
             of Being Wrong
• With an incorrect forecast of interest rate
  movements, immunized portfolios can suffer
  an opportunity loss

• For example, if a bank has more RSA than RSL,
  it would benefit from a decline in interest
  rates
  – Immunizing would have reduced the benefit


                    Prof. Rushen Chahal         56
                 Lower Yield
• The yield curve is usually upward sloping

• Immunizing may reduce the duration of a
  portfolio and shift fund characteristics to the
  left on the yield curve




                     Prof. Rushen Chahal            57
             Transaction Costs
• Buying and selling bonds requires brokerage
  commissions
  – Sales may also result in tax liabilities

• Commissions with the futures market are
  lower
  – The futures market is the method of choice for
    immunizing strategies


                        Prof. Rushen Chahal          58
             Immunization Is
           Instantaneous Only
• A portfolio is theoretically only immunized for
  an instant
  – Each day, durations, yields to maturity, and market
    interest rates change
• It is not practical to make daily adjustments
  for changing immunization needs
  – Make adjustments when conditions have changed
    enough to make revision cost effective


                      Prof. Rushen Chahal             59

				
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