Homework SourseConsider the following step up security 1000 par with semian
Consider the following step up security ($1,000 par) with semi-annual coupons (all CFs are at the end of the semi-annual):
Year
1
2
3
Coupon rate
3%
4%
5%
16. Manager B plans to buy the security at middle of year 1 (after the 1st coupon payment) and hold it to maturity with YTM of 4.2%. What is the security’s Mod Duration (in years) at the middle of year 1? Round the final answer to nearest 3 decimals i.e. 1.234.
| Year | 1 | 2 | 3 |
| Coupon rate | 3% | 4% | 5% |
Solution
Mod Duration or Modified Duration refers to the Price Volatality and is given by :
Macaulays duration/Periodic Ytm factor
Now Macaulays duration is the average waiting time for the cash flows of the bond and is given by :
Sigma of PV of cash flows discounted by Ytm×time periods of receiving CF
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Sigma of PV of cash flows discounted at Ytm
Mod duration=2.561/1.021=2.508%
| Year(x) | cash flows | P.V.at Ytm(w) | Wx |
| 1 | 15(3/2=1.5%of1000) | 15/1.021=14.691 | 14.691 |
| 2 | 20 | 19.186 | 38.371 |
| 3 | 20 | 18.791 | 56.373 |
| 4 | 25 | 23.006 | 92.023 |
| 5 | 1025 | 923.837 | 4919.183 |
| Total | 1000 | 5120.641 | |
| Macaulays Duration | 5120.641/1000 | ||
| 5.121 half years | |||
| 5.121/2=2.561years |
