Question 6
For the short position, KTC should ask its brokers to find any other investor who would be willing to lend 4.25% bond to KTC. Afterwards, the borrowed bonds would be sold by KTC, and must post about cash received from the sales as collateral. From its own capital, it has to post additional 2%. In this dissertation, KTC has received 0.10% interest on the posted additional cash.
For the long position, only 98% of the purchased amount, the lender can lend 98% at 0.15% annual rate. The residual 2% haircut should come from the KTC capital. In addition to this, the brokers tend to require the purchased 10.625% bond in order to be posted as collateral.
Exhibit 1
| Term | Cash Flow | PV | Time Weight PV | Convexity |
| 0.5 | 53.125 | 51.84469138 | 25.92234569 | 25.92235 |
| 1 | 53.125 | 50.5952381 | 50.5952381 | 75.89286 |
| 1.5 | 53.125 | 49.37589655 | 74.06384482 | 148.1277 |
| 2 | 53.125 | 48.18594104 | 96.37188209 | 240.9297 |
| 2.5 | 53.125 | 47.02466338 | 117.5616584 | 352.685 |
| 3 | 53.125 | 45.89137242 | 137.6741173 | 481.8594 |
| 3.5 | 53.125 | 44.78539369 | 156.7488779 | 626.9955 |
| 4 | 53.125 | 43.70606897 | 174.8242759 | 786.7092 |
| 4.5 | 53.125 | 42.6527559 | 191.9374015 | 959.687 |
| 5 | 53.125 | 41.62482759 | 208.124138 | 1144.683 |
| 5.5 | 53.125 | 40.62167229 | 223.4191976 | 1340.515 |
| 6 | 53.125 | 39.64269295 | 237.8561577 | 1546.065 |
| 6.5 | 53.125 | 38.68730694 | 251.4674951 | 1760.272 |
| 7 | 1053.125 | 766.918967 | 5368.432769 | 40263.25 |
| SUM | 1351.557488 | 7314.999399 | 49753.59 | |
| Mac Duration | 5.41227396 | |||
| Convexity | 33.18051668 | |||
| Mod Duration | 5.371372389 |
Exhibit 2
| Term | Cash Flow | PV | Time Weight PV | Convexity |
| 0.5 | 21.25 | 20.73787655 | 10.36893828 | 10.36894 |
| 1 | 21.25 | 20.23809524 | 20.23809524 | 30.35714 |
| 1.5 | 21.25 | 19.75035862 | 29.62553793 | 59.25108 |
| 2 | 21.25 | 19.27437642 | 38.54875283 | 96.37188 |
| 2.5 | 21.25 | 18.80986535 | 47.02466338 | 141.074 |
| 3 | 21.25 | 18.35654897 | 55.06964691 | 192.7438 |
| 3.5 | 21.25 | 17.91415748 | 62.69955117 | 250.7982 |
| 4 | 21.25 | 17.48242759 | 69.92971036 | 314.6837 |
| 4.5 | 21.25 | 17.06110236 | 76.77496062 | 383.8748 |
| 5 | 21.25 | 16.64993104 | 83.24965519 | 457.8731 |
| 5.5 | 21.25 | 16.24866891 | 89.36767903 | 536.2061 |
| 6 | 21.25 | 15.85707718 | 95.14246307 | 618.426 |
| 6.5 | 21.25 | 15.47492278 | 100.586998 | 704.109 |
| 7 | 21.25 | 743.7065828 | 5205.94608 | 39044.6 |
| Sum | 977.5619913 | 5984.572732 | 42840.73 | |
| Mac Duration | 6.121936803 | |||
| Convexity | 37.81352829 | |||
| Mod Duration | 6.055716461 |
Exhibit 3
| Yield to Maturity | |||||
| 10.625% bond | 4.25% bond | ||||
| 53.125 | 21.25 | ||||
| 60.86312 | 84.6570922 | ||||
| 570.915 | 552.98 | ||||
| YTM | 11% | 15% | |||
Exhibit 4
| Potential Trade | ||||||
| Buy 1000 Face value bond at high yield | ||||||
| Price of bond | 1418.281 | |||||
| Accrual | 23.86986 | |||||
| Total price | 1442.151 | |||||
| Sell 1000 face value bond at low yield | 1185.6 | |||||
| Price of bond | 1256.366 | |||||
| Accrual | 11.32004 | |||||
| Total price | 1267.686 | |||||
| Borrow at short term overnight rate | 174.4647 | |||||
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