Applied Portfolio Management

Applied Portfolio Management

Bond Portfolio Management II

This tutorial session examined the concepts duration and convexity. The task was divided into four different scenarios.

Duration is the average maturity of bonds, and modified duration measure the bonds interest rate sensitivity. Convexity capture the curvature of the present value profile, and not only the slope. In combination with duration convexity give a better estimate of sensitivity to interest rate changes.

Scenario 1

In this first task we calculated the duration, modified duration and convexity for 10, 15 and 20 year bonds by using formulas in the spreadsheet. We got the coupon, YTM and cash-flows for every six months for the three different bonds. Since the bonds here paid coupon twice a year, we divided (i) by two in the formulas. When calculating the duration we used this formula:

D = 0.5tCF/(1+i/2)^(t+1). The modified duration was found by dividing duration with the price. Convexity was calculated by using the following formula;

C = 0,25(t+1)CF/(1+i/2)^(t+2)

SUMMARY | MOD. DURATION | CONVEXITY | PV CF |

10 year bond | 8,072571915 | 77,37983784 | 93,32742502 |

15 year bond | 10,62683677 | 142,7000642 | 99,46969724 |

20 year bond | 13,15276988 | 226,6472329 | 94,45452064 |

Weight in 15 yr bond | 0,456373478 |

Weight in 20 yr bond | 0,543626522 |

SUM | 1 |

| |

Duration of portfolio | 12,000001 |

Target duration | 12 |

REQUIRED INVESTMENT IN PORTFOLIO £m |

15 YEAR BOND | 150,6032478 |

20 YEAR BOND | 179,3967522 |

Total (£m) | 330 |

We also computed the modified duration by using the Excel-function MDURATION. The modified duration from the formula based calculations and from the Excel-function seemed to be quite similar, but using the Excel-function was less time consuming. In this MDURATION formula we also used the date-function for the settlement- and maturity-part. Settlement is referring to the date of purchase of the bond.

After calculating...