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ytm_sheet_closed_formula

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  • pg 1
									                     Scenario Summary
                     Current Values:  shift_up      shift down
Changing Cells:
              $C$12            0.065        0.065           0.055
Result Cells:
              $D$12           6.50%        6.50%           5.50%
              $C$13           0.0325       0.0325          0.0275
Notes: Current Values column represents values of changing cells at
time Scenario Summary Report was created. Changing cells for each
scenario are highlighted in gray.
                                                                                                         Bond Yield
Payment frequency:                                                             2
Years to maturity:                                                            30                         AKA:
*Settlement date to first coupon date is a full period
                                                                                                         - Yield to Maturity
Total number of periods:                                                      60
                                                                                                         - Required Yield
                                                                                                         - Prevailing interest Rate
Coupon (annual percentage)                                                     0                         - Prevailing annual rate
Coupon (annual percentage) period adjusted                                     0

                                                                                                         Bond Price
Yield - ENTER YIELD IN DECIMAL                                             0.06        6.00%
                                                                                                         aka:
Yield period adjusted                                                       0.03
                                                                                                         - present value, net prese
PV factor (for both coupon and principal)                            0.16973309                          - present value of interes
Coupon factor                                                       27.67556367
                                                                                                         -   principal is amount inve
Coupon term                                                                    0                         -   minimum bond amount
Principal term                                                         16.973309                         -   price is quoted in 00's s
                                                                                                         -   YTM is entered as decim
                  Sum of coupon and principal terms is Price      16.9733090

                                                                                                dv01
                                            Zero coupon price      16.973309        16.973309 16.9239 -0.04936




Example senstivity calculation:
For a 10 year 6% bond:                                                              price delta 2yr 2%

              1 bp change to yield up (to .0601) gives price:        99.9256470     0.0743530            99.9805
           1 bp change to yield down (to .0599) gives price:        100.0744218     0.0744218             100.02

                                                         "DV01" (avg of up/down):   0.0743874
               Quick and dirty pricing function (linear now)
                if we change yield by +50bp price delta is:                 3.719369297
                                                  New price:                 96.2806307

                                                                                                 Price calculated using
price error due to assuming away curvature of ytm function:                  -0.0845328
                                                               96.3651635
                                                                                                 DV01 approximation
                                                                                                 "greeks based" or "taylo
                                                                                                 series" approach



                                                                                          Error in price due to
                                     Price calculated using full                          assuming away curvature
                                     YTM pricing function                                 of YTM function and using
                                                                                          only first derivative
Bond Yield


 Yield to Maturity
 Required Yield
 Prevailing interest Rate
 Prevailing annual rate


Bond Price

 present value, net present value
 present value of interest + principal

 principal is amount invested (loaned to issuer)
 minimum bond amount "face" is conventionally $1000
 price is quoted in 00's so 100 means 100% or $1000
 YTM is entered as decimal and quoted as an annual percentage




                                  10 yr 6% bond yield     price
                                                                      up 1 bp     down 1 bp   up delta
                                                   0.05   107.7945811   107.712992 107.8762465 0.081589183
                    5yr 3%                        0.051   106.9821035
                                                  0.052   106.1771641
         0.019507 0.046098711                     0.053   105.3796863
         0.019512                                 0.054   104.5895943
                                                  0.055    103.806813 103.7289341 103.8847643 0.077878896
         0.019510                                 0.056   103.0312684
                                 0.57   102.2628869
                                0.058   101.5015961
                                0.059   100.7473242
                               0.0599   100.0744218
                                 0.06           100
                               0.0601     99.925647
   Price calculated using
                                0.061   99.25955338
   DV01 approximation -         0.062   98.52591481
   "greeks based" or "taylor    0.063   97.79901552
   series" approach             0.064    97.0787875
                                0.065   96.36516346
                                0.066   95.65807686
                                0.067   94.95746183
r in price due to               0.068   94.26325325
 ming away curvature            0.069   93.57538667
TM function and using            0.07   92.89379835 92.82598239 92.96167646 0.067815962
 first derivative



                                                 4           6          0.5           5
                                                 6          12
down delta  dv01
 0.081665339 0.081627261




0.077951261 0.077915079
              0.0743874




0.067878113 0.067847038

								
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