Question

In: Finance

A three-year old 10-year 8% semi-annual coupon bond is selling at $1,200 today. If the yield...

A three-year old 10-year 8% semi-annual coupon bond is selling at $1,200 today. If the yield increases by 25 basis points, how much of the price change is due to

convexity of the bond? (Face Value = $1,000)

Solutions

Expert Solution

                  K = Nx2
Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2
                   k=1
                  K =10x2
1200 =∑ [(8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2
                   k=1
YTM% = 5.39

Period Cash Flow Discounting factor PV Cash Flow Duration Calc Convexity Calc
0 ($1,200.00) =(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             40.00                                                             1.03                    38.95                  38.95                  73.87
2             40.00                                                             1.05                    37.93                  75.86                215.78
3             40.00                                                             1.08                    36.93                110.80                420.24
4             40.00                                                             1.11                    35.96                143.85                682.02
5             40.00                                                             1.14                    35.02                175.10                996.18
6             40.00                                                             1.17                    34.10                204.60              1,358.05
7             40.00                                                             1.20                    33.21                232.44              1,763.21
8             40.00                                                             1.24                    32.33                258.68              2,207.49
9             40.00                                                             1.27                    31.49                283.37              2,686.95
10             40.00                                                             1.30                    30.66                306.60              3,197.87
11             40.00                                                             1.34                    29.86                328.41              3,736.74
12             40.00                                                             1.38                    29.07                348.86              4,300.26
13             40.00                                                             1.41                    28.31                368.01              4,885.31
14             40.00                                                             1.45                    27.57                385.92              5,488.97
15             40.00                                                             1.49                    26.84                402.64              6,108.48
16             40.00                                                             1.53                    26.14                418.21              6,741.27
17             40.00                                                             1.57                    25.45                432.68              7,384.90
18             40.00                                                             1.61                    24.78                446.11              8,037.11
19             40.00                                                             1.66                    24.13                458.54              8,695.78
20       1,040.00                                                             1.70                  611.01            12,220.17          243,331.34
      Total            17,639.80          312,311.80
Convexity =(∑ convexity calc)/(bond price*number of coupon per year^2)
=312311.8/(1200*2^2)
=65.06
Using convexity adjustment
Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price
0.5*65.06*0.0025^2*1200
=0.24

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