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Modified Duration 修正存续期间
A formula that expresses the measurable change in the value of a security in response to a change in interest rates. Calculated as:
Where:
n = number of coupon periods per year
YTM = the bond's yield to maturity
Modified duration follows the concept that interest rates and bond prices move in opposite directions. This formula is used to determine the effect that a 100-basis-point (1%) change in interest rates will have on the price of a bond.
修正存续期间(Modified duration)是其中一种常见的量度债券因利率变动而波动的估计幅度的计算方法。修正存续期间等于Macaulay duration除以(1+YTM/年配息次数)。
譬如说某债券的Macaulay duration为8年,债券的到期殖利率(YTM)为8%,一年配息两次。
那么它的修正存续期间为:
Modified duration = 8 / (1+ 0.08/2)= 8/ 1.04 = 7.69
修正存续期间的用法是,譬如某债券的修正存续期间是6年,这样当面对0.5%的利率上涨时,这张债券的价格会下跌约6 *0.5%=3%。债券价格变化幅度可以这样估算出来。不过值得注意的是,这是”约”,不是实际的变化程度,面对愈大的利率变动,用修正存续期间来估算债券价格的变化,会愈不准确。
假如你有一个由多张债券组成的投资组合,那么这个债券组合的整体修正存续期间就等于各别债券的修正存续期间以市值加权后的平均。
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