Duration

Study guide: Exam FM-2

Duration measures the weighted-average time of a bond's (or portfolio's) cash flows, and quantifies its sensitivity to interest rate changes. Two main types:

• Macaulay Duration D_{Mac}: weighted-average time of cash flows, weighted by present value
• Modified Duration D_{Mod}: approximate percentage decrease in price per unit increase in yield

On Exam FM, "duration" means Macaulay duration unless the question says otherwise.

D_{Mod} = \frac{D_{Mac}}{1+j} = -\frac{1}{P}\frac{dP}{dj}

• where j is the Yield Rate per period; a longer duration means higher interest rate sensitivity
• Duration is the foundation for Immunization and Duration Matching

Duration and Price Change A bond has modified duration of 6 years. Yields rise by 0.5%. Estimate the percentage change in price.

Answer \frac{\Delta P}{P} \approx -D_{Mod} \cdot \Delta j = -6 \times 0.005 = -0.03 = -3\% The bond price falls approximately 3%.