Question

In: Finance

Use the following information to determine duration and convexity, and then use those metrics to predict...

Use the following information to determine duration and convexity, and then use those metrics to predict a percentage change in the price of the bond assuming a 130 basis-point increase in yield. Time-to-maturity = 7 years, Coupon rate = 4%, paid semi-annually, Current bond-equivalent yield-to-maturity = 6.0%.

Solutions

Expert Solution

We use excel to find the duration and convexity

We first chalk out the cash-flows

Bond pays (4%/2) 2% coupon every 6 months and has a face value of $1000

Duration = Time weighted PV / PV

Convexity = Time^2 weighted PV / (PV*(1+ytm/2)^2)

Term Period Cash-flow Present value Time weighted PV Time^2 weighted PV
0.5 1 20 19.41747573 9.708737864 9.708737864
1 2 20 18.85191818 18.85191818 28.27787727
1.5 3 20 18.30283319 27.45424978 54.90849956
2 4 20 17.76974096 35.53948192 88.84870479
2.5 5 20 17.25217569 43.13043922 129.3913177
3 6 20 16.74968513 50.2490554 175.8716939
3.5 7 20 16.26183023 56.91640579 227.6656232
4 8 20 15.78818469 63.15273875 284.1873244
4.5 9 20 15.32833465 68.97750591 344.8875296
5 10 20 14.8818783 74.40939149 409.2516532
5.5 11 20 14.44842553 79.46634043 476.7980426
6 12 20 14.0275976 84.16558562 547.0763066
6.5 13 20 13.6190268 88.5236742 619.6657194
7 14 1020 674.3401619 4720.381134 35402.8585
887.0392686 5420.926658 38799.39753
Duration 6.111258937
Convexity 41.22946377

We get  

Duration 6.111258937
Convexity 41.22946377

Percentage change in price of the bond = -Duration*Change in yield + 0.5*Convexity*(Change in yield)^2

For a 130 basis-point increase in yield

Percentage change in price of the bond = -6.111258937*0.013+0.5*41.22946377*(0.013*0.013)

Percentage change in price of the bond = -0.0759 = -7.59%


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