Bonds with embedded options and mortgage backed securities do not have a well-defined YTM. These securities may be prepaid well before the maturity date. Hence, yield duration statistics are not suitable for these instruments. For such instruments, the best measure of interest rate sensitivity is the effective duration which measures the sensitivity of the bond’s price to a change in a benchmark yield curve (instead of its own YTM).
Effective Duration =
Difference between approx. modified duration and effective duration:
The denominator for approx. modified duration has the bond’s own yield-to-maturity. It measures the bond’s price change to changes in its own YTM. But, the denominator for effective duration has the change in the benchmark yield curve. It measures the interest rate risk in terms of change in benchmark yield curve.
Example 10: Calculating the effective duration
A Pakistani defined-benefit pension scheme seeks to measure the sensitivity of its retirement obligations to market interest rate changes. The pension scheme manager hires an actuarial consultant to model the present value of its liabilities under three interest rate scenarios
The following chart shows the results of the analysis:
|Interest Rate Assumption||Present Value of Liabilities|
|9.5%||PKR 10.5 million|
|PKR 10 million
PKR 9 million
Compute the effective duration of pension liabilities. PV0 = 10, PV+ = 9, PV– = 10.5, and Δ curve = 0.005. The effective duration of the pension liabilities is 15.
This effective duration statistic for the pension scheme’s liabilities might be used in asset allocation decisions to decide the mix of equity, fixed income, and alternative assets.