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