R Programming for Actuarial Science

9 Duration – A Measure of Interest Rate Sensitivity

Peter McQuire

library(lifecontingencies)

9.1 Introduction

The concept of duration is important to actuaries in understanding the sensitivity of the present value of a series of cashflows to changes in interest rates. For example, an analyst should understand by how much the value of a bond portfolio may fall if bond yields increase by 1%. The cashflows could be income (e.g. from a bond portfolio) or outgo (e.g. pension scheme liabilities).

This short chapter introduces the concept of duration, which will be developed in a number of later chapters in the book. As we will see, knowing the duration of our liabilities can go some way in helping us remove interest rate risk by ensuring the duration of our assets is similar to that of our liabilities. Indeed, it is usual for bond fund managers to publish the duration of their funds such that potential investors can choose appropriate funds to minimise interest rate risk.

9.2 Duration – Definitions and Interpretation

Before we proceed it is worth noting that there are a number of similar expressions related to duration which can lead to confusion. We will be discussing “Macaulay duration” (also known as “discounted mean term”), but similar expressions commonly used include “duration” itself (very confusingly), effective duration, modified duration, and volatility. We are also aware of some authors interchanging these terms, leading to further confusion. Care should therefore be ...