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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
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%
Answer:
T(Term) | DF @ 11% /2=5.5% | Cash Flow 1000*6% semi annually | PV | Duration | PV*T*(T+1) |
0.5 | 0.947867 | 60.00 | 56.87 | 28.44 | 42.65402844 |
1 | 0.898452 | 60.00 | 53.91 | 53.91 | 107.8142899 |
1.5 | 0.851614 | 60.00 | 51.10 | 76.65 | 191.6130744 |
2 | 0.807217 | 60.00 | 48.43 | 96.87 | 290.5980276 |
2.5 | 0.765134 | 60.00 | 45.91 | 114.77 | 401.6955358 |
3 | 0.725246 | 60.00 | 43.51 | 130.54 | 522.1769998 |
3.5 | 0.687437 | 60.00 | 41.25 | 144.36 | 649.6277841 |
4 | 0.651599 | 60.00 | 39.10 | 156.38 | 781.9186448 |
4.5 | 0.617629 | 60.00 | 37.06 | 166.76 | 917.179453 |
5 | 0.585431 | 60.00 | 35.13 | 175.63 | 1053.775043 |
5.5 | 0.554911 | 60.00 | 33.29 | 183.12 | 1190.283026 |
6 | 0.525982 | 60.00 | 31.56 | 189.35 | 1325.473426 |
6.5 | 0.498561 | 60.00 | 29.91 | 194.44 | 1458.289992 |
7 | 0.472569 | 60.00 | 28.35 | 198.48 | 1587.833069 |
7.5 | 0.447933 | 60.00 | 26.88 | 201.57 | 1713.343909 |
8 | 0.424581 | 60.00 | 25.47 | 203.80 | 1834.190301 |
8.5 | 0.402447 | 60.00 | 24.15 | 205.25 | 1949.853434 |
9 | 0.381466 | 60.00 | 22.89 | 205.99 | 2059.915884 |
9.5 | 0.361579 | 60.00 | 21.69 | 206.10 | 2164.050652 |
10 | 0.342729 | 1,060.00 | 363.29 | 3,632.93 | 39962.19712 |
1,059.75 | 6,565.33 | 60,204.48 | |||
Duration of the bond | 6565.33/1059.75 | 6.20 | |||
Convexity | 60204.483697857/1060 | ||||
56.80 QUESTION: What are the exact calculations to how these answers are formed?
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