Director of FRM Operations
Effective duration approximates modified duration. Both express interest rate sensitivity: an effective (or modified) duration of 6.2 years tells us to expect a 0.620% price change if the yield changes by 10 basis points; i.e., 0.10% ∆y * 6.2 years = 0.620% ∆P. Effective duration is given by -1/P * [P(+∆y) - P(-∆y)]/(2*∆y) where ∆y is our selected, small yield shock. This video explain the intuition which is that we use effective duration when it's more realistic to retrieve to slope of a secant line, as an approximation to the exact slope of the nearby tangent line. Effective duration is appropriate when the price/yield relationship is non-trivial (e.g., embedded options cause negative convexity) and therefore doesn't lend itself to an easier, analytical modified duration.