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Duration and convexity for two types of bonds Example 1: Yield to maturity is 9%, and the coupon rate is set from zero to 15%. Type II bond Maturity: 20 years Duration Convexity (years) (years) CONV = 1B Coupon ) D=- 0 1 2 3 4 5 Type I bond Maturity: 10 years Duration Convexity (years) (years) D=- tide CONV = 1 PB 10.00 92.58 9.31 84.34 8.79 78.02 8.37 73.02 8.03 68.96 7.75 65.60 7.52 62.79 7.32 60.38 7.15 58.31 6.99 56.50 6.86 54.90 6.76 53.49 6.64 52.23 6.55 51.10 6.50 50.58 6.46 50.08 6.38 49.16 7 8 9 10 11 20.00 15.90 13.81 12.59 11.78 11.21 10.77 10.44 10.17 9.95 9.76 9.61 9.48 9.36 9.31 9.29 9.18 353.50 251.50 215.98 188.85 170.80 158.00 148.40 140.94 134.98 130.10 126.04 122.61 119.70 117.12 115.97 114.89 112.93 12 13 13.5 14 15 . Increasing the coupon rate decrease both the duration and convexity. Sac Duration and convexity for two types of bonds Example 1: Yield to maturity is 9%, and the coupon rate is set from zero to 15%. Type II bond Maturity: 20 years Duration Convexity (years) (years) CONV = 1B Coupon ) D=- 0 1 2 3 4 5 Type I bond Maturity: 10 years Duration Convexity (years) (years) D=- tide CONV = 1 PB 10.00 92.58 9.31 84.34 8.79 78.02 8.37 73.02 8.03 68.96 7.75 65.60 7.52 62.79 7.32 60.38 7.15 58.31 6.99 56.50 6.86 54.90 6.76 53.49 6.64 52.23 6.55 51.10 6.50 50.58 6.46 50.08 6.38 49.16 7 8 9 10 11 20.00 15.90 13.81 12.59 11.78 11.21 10.77 10.44 10.17 9.95 9.76 9.61 9.48 9.36 9.31 9.29 9.18 353.50 251.50 215.98 188.85 170.80 158.00 148.40 140.94 134.98 130.10 126.04 122.61 119.70 117.12 115.97 114.89 112.93 12 13 13.5 14 15 . Increasing the coupon rate decrease both the duration and convexity. Sac