Question of Bond Markets, Analysis and Strategies by cob75748

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									            Pricing of Bonds
                           Zvi Wiener
             Based on Chapter 2 in Fabozzi
          Bond Markets, Analysis and Strategies
Fall-02        http://pluto.mscc.huji.ac.il/~mswiener/zvi.html   EMBAF
      Time value of money
      How to calculate price of a bond
      Why the price of a bond changes
      Relation between yield and price
      Relation between coupon and price
      Price changes when approaching maturity
      Floaters and inverse floaters
      Accrued interest and price quotes


Zvi Wiener                Fabozzi Ch 2          slide 2
                   Time Value of Money
        present value PV = CFt/(1+r)t

        Future value FV = CFt(1+r)t

        Net present value NPV = sum of all PV

             -PV    5         5    5         5    105
                          4
                                5        105
                   PV                
                        t 1 (1  r ) (1  r )5
                                     t



Zvi Wiener                        Fabozzi Ch 2          slide 3
                    Time Value
      You have $100 now and are going to deposit
      it for 5 years with 6% interest.
      What will be the final amount?
      It depends on calculation method!
      Yearly compounding: $100*1.065
      Semiannual compounding: $100*1.0312
      Monthly compounding: $100*1.00560


Zvi Wiener              Fabozzi Ch 2               slide 4
                        Periodic Rate
                Annual interest rateA
   r=                             =
      Number of periods in a year   n

                        Effective Rate
                                           n
                            A
             1  r 
                    n
                          1    1  R
                            n
Zvi Wiener                  Fabozzi Ch 2       slide 5
             Pricing of Bonds
                         T
                              Ct
                 PV  
                      t 1 (1  r )t


                                           100
      Zero coupon bond           price 
                                         (1  r ) t




Zvi Wiener             Fabozzi Ch 2                   slide 6
                 Pricing of Bonds
                             T
                                  Ct
                     PV  
                          t 1 (1  r )t


             Term structure of interest rates

                             T
                                  Ct
                     PV  
                          t 1 (1  rt ) t


Zvi Wiener                 Fabozzi Ch 2         slide 7
                               Yield
             Yield = IRR = Internal Rate of Return
                                     T
                                          Ct
                         Pr ice  
                                  t 1 (1  y ) t

              How do we know that there is a solution?




Zvi Wiener                      Fabozzi Ch 2             slide 8
                         Example
    Price calculation:

                  5    5     105
                        2
                               3  83.34
                1.10 1.11 1.12
    Yield calculation:

               5       5          105
                                          83 .34
             1  y (1  y ) 2
                                (1  y ) 3



                         y  11.9278%
Zvi Wiener                 Fabozzi Ch 2               slide 9
             Price-Yield Relationship
      Price and yield (of a straight bond) move in
      opposite directions.
price




                                        yield
Zvi Wiener               Fabozzi Ch 2                slide 10
                 General pricing formula
                            n
                                      Ct
                      P
                        t 1 (1  r ) v (1  r )t 1


                days between settlement and next coupon
             v
                       days in six months period




Zvi Wiener                        Fabozzi Ch 2            slide 11
                 Accrued Interest
      Accrued interest = interest due in full period*
      (number of days since last coupon)/
      (number of days in period between coupon
      payments)




Zvi Wiener                Fabozzi Ch 2                  slide 12
             Day Count Convention
      Actual/Actual - true number of days
      30/360 - assume that there are 30 days in each
      month and 360 days in a year.
      Actual/360




Zvi Wiener               Fabozzi Ch 2                  slide 13
                        Floater

      The coupon rate of a floater is equal to a
      reference rate plus a spread.

      For example LIBOR + 50 bp.

      Sometimes it has a cap or a floor.



Zvi Wiener                Fabozzi Ch 2             slide 14
                   Inverse Floater
      Is usually created from a fixed rate security.
      Floater coupon             = LIBOR + 1%
      Inverse Floater coupon = 10% - LIBOR
      Note that the sum is a fixed rate security.
      If LIBOR>10% there is typically a floor.



Zvi Wiener                Fabozzi Ch 2                 slide 15
       Price Quotes and Accrued Interest

      Assume that the par value of a bond is $1,000.
      Price quote is in % of par + accrued interest
      the accrued interest must compensate the
      seller for the next coupon.




Zvi Wiener                Fabozzi Ch 2                 slide 16
                 Home Assignment
                    Chapter 2

      Questions 2, 3, 7, 8, 11




Zvi Wiener                Fabozzi Ch 2   slide 17
                FRM-99, Question 17
      Assume a semi-annual compounded rate of
      8% per annum. What is the equivalent
      annually compounded rate?
      A. 9.2%
      B. 8.16%
      C. 7.45%
      D. 8%

Zvi Wiener              Fabozzi Ch 2            slide 18
              FRM-99, Question 17
      (1 + ys/2)2 = 1 + y
      (1 + 0.08/2)2 = 1.0816 ==> 8.16%




Zvi Wiener                  Fabozzi Ch 2   slide 19
              FRM-99, Question 28
      Assume a continuously compounded interest
      rate is 10% per annum. What is the equivalent
      semi-annual compounded rate?
      A. 10.25% per annum.
      B. 9.88% per annum.
      C. 9.76% per annum.
      D. 10.52% per annum.

Zvi Wiener               Fabozzi Ch 2                 slide 20
               FRM-99, Question 28
      (1 + ys/2)2 = ey
      (1 + ys/2)2 = e0.1
      1 + ys/2 = e0.05
      ys = 2 (e0.05 - 1) = 10.25%




Zvi Wiener                 Fabozzi Ch 2   slide 21
                       Mortgage example
      You take a mortgage $100,000 for 10 years
      with yearly payments and 7% interest.
      What is the size of each payment?
                          10
                                  x
             100 ,000  
                        t 1 (1  0.07 ) t

                            10
                                 1
             100 ,000  x          t              x  14.2378
                          t 1 1.07




Zvi Wiener                          Fabozzi Ch 2                 slide 22
                Mortgage example
      How much do you own bank after 3 first
      payments?
                   7
                       14 .2378
                   1.07 t  76 .7314
                  t 1

      What is the fair value of your debt if interest
      rates are 5%?
                   7
                       14 .2378
                   1.05 t  82 .3849
                  t 1


Zvi Wiener                Fabozzi Ch 2                  slide 23

								
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