Question

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% |

17. Manager C plans to buy the security at beginning of year 2 (after 2 coupon payments) and hold it to maturity with YTM of 3.9%. What is the security’s convexity (in years squared) at the beginning of year 2? Round the final answer to nearest 3 decimals i.e. 1.234.

Answer #1

You have to find the convexity after 2 years or one years before maturity

Periodic coupon payment = 1000*0.05/2 = 25

Periodic YTM = 3.9/2 = 1.95%

Year | Period (t) | Coupon | Face Value | CF | DCF = CF/1.0195^t | w = DCF/PV | Macaulay Duration = t * w | Convexity w*t*(t+1)/(1+y)^2 |

0.5 | 1 | 25 | 25 | 24.522 | 0.024 | 0.024 | 0.047 | |

1 | 2 | 25 | 1000 | 1025 | 986.165 | 0.976 | 1.951 | 5.633 |

PV = | 1010.686 | 1.000 | 1.976 | 5.679 |

Semi-annual convexity = 5.679

Annual convexity = 5.679 / (2^2) = 1.420

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.

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