Bond Convexity Price Sensitivity Including Convexity

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Bond Convexity Price Sensitivity Including Convexity

  1. 1. BOND CONVEXITY Price Sensitivity Including Convexity Annual Percentage Rate Inputs Price Sensitivity Including Convexity Rate Convention: 1 = EAR, 0 = APR 0 5000% Annual Coupon Rate (CR) 5.0% Actual Per- Yield to Maturity (Annualized) (y) 9.0% 0% cent Change Number of Payments / Year (NOP) 2 -5000% in Price Percent Change in Price Number of Periods to Maturity (T) 8 Duration -10000% Face Value (FV) $1,000 Approxima- -15000% Duration and Outputs -20000% Convexity Discount Rate / Period (RATE) 4.5% -25000% Approx. Coupon Payment (PMT) $25 -30000% -35000% -40000% -45000% -15.0% -10.0% -5.0% 0.0% 5.0% 10.0% 15.0% Change in Yield To Maturity Chart Outputs Yield to Maturity (Annualized) 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% Discount Rate / Period 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% Change in Yield to Maturity -8.0% -7.0% -6.0% -5.0% -4.0% -3.0% -2.0% Actual Bond Price $1,156 $1,115 $1,075 $1,037 $1,000 $965 $931 Current Bond Price $868 $868 $868 $868 $868 $868 $868 Actual Percent Change in Price 33.2% 28.4% 23.8% 19.4% 15.2% 11.2% 7.3% Modified Duration 3.49 3.49 3.49 3.49 3.49 3.49 3.49 Duration Approximation 27.9% 24.4% 20.9% 17.4% 14.0% 10.5% 7.0% Convexity 16.23 16.23 16.23 16.23 16.23 16.23 16.23 Duration and Convexity Approx. 33.1% 28.4% 23.9% 19.5% 15.3% 11.2% 7.3%
  2. 2. Convexity Actual Per- cent Change in Price Duration Approxima- Duration and Convexity Approx. 5.0% 10.0% 15.0% Maturity 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 16.0% 17.0% 18.0% 19.0% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0% $899 $868 $838 $810 $783 $756 $731 $707 $684 $662 $640 $620 $868 $868 $868 $868 $868 $868 $868 $868 $868 $868 $868 $868 3.6% 0.0% -3.4% -6.7% -9.8% -12.9% -15.8% -18.5% -21.2% -23.8% -26.2% -28.6% 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.5% 0.0% -3.5% -7.0% -10.5% -14.0% -17.4% -20.9% -24.4% -27.9% -31.4% -34.9% 16.23 16.23 16.23 16.23 16.23 16.23 16.23 16.23 16.23 16.23 16.23 16.23 3.6% 0.0% -3.4% -6.7% -9.7% -12.7% -15.4% -18.0% -20.4% -22.7% -24.8% -26.8%
  3. 3. 20.0% 10.0% 11.0% $600 $868 -30.9% 3.49 -38.4% 16.23 -28.6%

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