Question: Bond Duration and Bond Maturity are different. Macaulay Duration is a widely used measure of a bond's sensitivity to changes in bond yields, the equation

Bond Duration and Bond Maturity are different. Macaulay Duration is a widely used measure of a bond's sensitivity to changes in bond yields, the equation for which is: % in Bond Price =-Duration *YTM(1+YTM/2). Which, if any, of the following may be a logical explanation why the distinction between bond maturity and duration may be important:
a. Bonds have a legally contractual maturity date. However, most bonds are not held to maturity, but are sold (liquidated) at an earlier date, which changes the underlying assumptions of YTM calculations.
b. A well-managed bond portfolio will rebalance the bonds before maturity to optimize the timing of meeting long term (example) pension payment needs.
c. Given "a" and "b" above, the Duration becomes the practical and effective maturity of the bond for the investor, so dynamics such as "yield to duration" are more realistic than "yield to maturity."
d. All of the above.
e. None of the above.

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