Modified duration is used to determine the percentage change in the bond's prices for a 100 basis point (1%) change in the yield. The underlying assumption is that the bond's expected cash flows would not change when yield changes. It means that to calculate the value of V- and V+ in equation (1) the same cash flows used for calculating V0 are used.
The assumption that cash flow would not change when yield changes is not true for all types of bonds. It is true in case of option-free bond but it is not applicable in case of putable and callable bonds. For example, the payments made by the Treasury Department to the holders of its obligations do not change when interest rates change. However, the same is not true for bond with embedded options. The expected cash flows may change significantly with the change in the yield.
Effective duration is a duration calculation for bonds with embedded options. Effective duration takes into account both the discounting at different interest rates and how the expected cash flow may change. Effective duration can be estimated using modified duration if the bond with embedded options behaves like an option-free bond. This behavior occurs when exercise of the embedded option would offer the investor no benefit. As such, the security's cash flows cannot be expected to change given a change in yield. There can be huge difference between the modified duration and effective duration. For example, the modified duration for a callable bond could be 7, whereas the effective duration could be 5. Sometimes it may be the other way round, i.e for certain mortgage obligations the effective duration may be more than the modified duration. Therefore, we can conclude that the effective duration is a more appropriate measure in case of bonds with embedded options.