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Posted on Jul 14, 2024

Question: Calculate the Macaulay duration, Macaulay convexity and dispersion of a 10 year bond with semiannual coupons paid at 6% per year earning an annual

Question: Calculate the Macaulay duration, Macaulay convexity and dispersion of a 10 year bond with semiannual coupons paid at 6% per year earning an annual effective yield of 11%. I don't know how to find the dispersion since I have to use excel. The answer should be 11.84. I have included a picture of my work. The duration and convexity is correct. Thank you! image text in transcribed

30 Effective annual Yield 11% Semiannual yield 0.0536 Face Value 1000 Number of periods 20 Annual Coupon rate 0.06 Semiannual Coupon rat 0.03 Periods Cash Flows Discount PV of Cash Flows Duration PV"(t^2+t) 0.5 0.949158 28.47473987 14.23737 21.3560549 1 30 0.9009009 27.02702703 27.02703 54.0540541 1.5 30 0.8550973 25.6529188 38.47938 96.1984455 2 30 0.8116224 24.348673 48.69735 146.092038 2.5 30 0.7703579 23.11073766 57.77684 202.218955 3 30 0.7311914 21.93574144 65.80722 263.228897 3.5 30 0.6940161 20.82048438 72.8717 327.922629 4 30 0.658731 19.76192922 79.04772 395.238584 4.5 30 0.6252398 18.75719313 84.40737 464.24053 30 0.5934513 17.80353984 89.0177 534.106195 5.5 30 0.5632791 16.89837219 92.94105 604.116806 6 30 0.5346408 16.03922508 96.23535 673.647453 6.5 30 0.5074586 15.22375873 98.95443 742.158238 7 30 0.4816584 14.44975233 101.1483 809.18613 7.5 30 0.4571699 13.71509796 102.8632 874.337495 8 30 0.4339265 13.01779489 104.1424 937.281232 8.5 30 0.4118648 12.35594411 105.0255 997.742487 9 30 0.3909248 11.72774314 105.5497 1055.49688 9.5 30 0.3710494 11.13148118 105.7491 1110.36525 1030 0.3521845 362.7500131 3627.5 39902.5014 Sums 715.0021671 5117.479 50211.4898 Duration 7.157291 Convexity 63.06836 Dispersion 10 30 Effective annual Yield 11% Semiannual yield 0.0536 Face Value 1000 Number of periods 20 Annual Coupon rate 0.06 Semiannual Coupon rat 0.03 Periods Cash Flows Discount PV of Cash Flows Duration PV"(t^2+t) 0.5 0.949158 28.47473987 14.23737 21.3560549 1 30 0.9009009 27.02702703 27.02703 54.0540541 1.5 30 0.8550973 25.6529188 38.47938 96.1984455 2 30 0.8116224 24.348673 48.69735 146.092038 2.5 30 0.7703579 23.11073766 57.77684 202.218955 3 30 0.7311914 21.93574144 65.80722 263.228897 3.5 30 0.6940161 20.82048438 72.8717 327.922629 4 30 0.658731 19.76192922 79.04772 395.238584 4.5 30 0.6252398 18.75719313 84.40737 464.24053 30 0.5934513 17.80353984 89.0177 534.106195 5.5 30 0.5632791 16.89837219 92.94105 604.116806 6 30 0.5346408 16.03922508 96.23535 673.647453 6.5 30 0.5074586 15.22375873 98.95443 742.158238 7 30 0.4816584 14.44975233 101.1483 809.18613 7.5 30 0.4571699 13.71509796 102.8632 874.337495 8 30 0.4339265 13.01779489 104.1424 937.281232 8.5 30 0.4118648 12.35594411 105.0255 997.742487 9 30 0.3909248 11.72774314 105.5497 1055.49688 9.5 30 0.3710494 11.13148118 105.7491 1110.36525 1030 0.3521845 362.7500131 3627.5 39902.5014 Sums 715.0021671 5117.479 50211.4898 Duration 7.157291 Convexity 63.06836 Dispersion 10