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QUESTION 28 For a 25-year, 5% annual pay bond currently trading at 6%, calculate the approximate convexity...

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Finance

QUESTION 28

  1. For a 25-year, 5% annual pay bond currently trading at 6%,calculate the approximate convexity based on a change in yield of100 basis points.

a.

200.15

b.

130.05

c.

259.07

Answer & Explanation Solved by verified expert
4.3 Ratings (762 Votes)

                  K = N
Bond Price =? [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N
                   k=1
                  K =25
Bond Price =? [(5*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^25
                   k=1
Bond Price = 872.17
Period Cash Flow Discounting factor PV Cash Flow Duration Calc Convexity Calc
0 ($872.17) =(1+YTM/number of coupon payments in the year)^period =cashflow/discounting factor =PV cashflow*period =duration calc*(1+period)/(1+YTM/N)^2
1             50.00                                                             1.06                    47.17                  47.17                  83.96
2             50.00                                                             1.12                    44.50                  89.00                237.63
3             50.00                                                             1.19                    41.98                125.94                448.35
4             50.00                                                             1.26                    39.60                158.42                704.96
5             50.00                                                             1.34                    37.36                186.81                997.59
6             50.00                                                             1.42                    35.25                211.49              1,317.57
7             50.00                                                             1.50                    33.25                232.77              1,657.32
8             50.00                                                             1.59                    31.37                250.96              2,010.22
9             50.00                                                             1.69                    29.59                266.35              2,370.54
10             50.00                                                             1.79                    27.92                279.20              2,733.33
11             50.00                                                             1.90                    26.34                289.73              3,094.34
12             50.00                                                             2.01                    24.85                298.18              3,449.95
13             50.00                                                             2.13                    23.44                304.75              3,797.11
14             50.00                                                             2.26                    22.12                309.61              4,133.29
15             50.00                                                             2.40                    20.86                312.95              4,456.37
16             50.00                                                             2.54                    19.68                314.92              4,764.68
17             50.00                                                             2.69                    18.57                315.66              5,056.85
18             50.00                                                             2.85                    17.52                315.31              5,331.86
19             50.00                                                             3.03                    16.53                313.99              5,588.95
20             50.00                                                             3.21                    15.59                311.80              5,827.61
21             50.00                                                             3.40                    14.71                308.86              6,047.52
22             50.00                                                             3.60                    13.88                305.26              6,248.56
23             50.00                                                             3.82                    13.09                301.07              6,430.76
24             50.00                                                             4.05                    12.35                296.37              6,594.30
25       1,050.00                                                             4.29                  244.65              6,116.21          141,528.63
      Total            12,262.79          224,912.23
Convexity =(? convexity calc)/(bond price*number of coupon per year^2)
=224912.23/(872.17*1^2)
=257.88 = 259.07

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Transcribed Image Text

QUESTION 28For a 25-year, 5% annual pay bond currently trading at 6%,calculate the approximate convexity based on a change in yield of100 basis points.a.200.15b.130.05c.259.07

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