Mac duration 和 Modified duration问题

嗨，爱思考的PZer你好：

不客气，预祝考试顺利~

----------------------------------------------
加油吧，让我们一起遇见更好的自己！

嗨，从没放弃的小努力你好：

是这样的。在三级CME学科中，教材之论述了两个DURATION比大小的结论，并无相关的解释。

以下是原版书的完整论述。

Assuming cash flows are received in full and on time, there are two main reasons why realized return may not equal the initial yield to maturity.

First, if the investment horizon is shorter than the amount of time until the bond’s maturity, any change in interest rate (i.e., the bond’s YTM) will generate a capital gain or loss at the horizon.

Second, the cash flows may be reinvested at rates above or below the initial YTM. The longer the horizon, the more sensitive the realized return will be to reinvestment rates.

These two issues work in opposite directions: Rising (falling) rates induce capital losses (gains) but increase (decrease) reinvestment income.

If the investment horizon equals the (Macaulay) duration of the bond or portfolio, the capital gain/loss and reinvestment effects will roughly offset, leaving the realized return close to the original YTM.

 This relationship is exact if (a) the yield curve is flat and (b) the change in rates occurs immediately in a single step.

In practice, the relationship is only an approximation. Nonetheless, it provides an important insight:

 Over horizons shorter than the duration, the capital gain/loss impact will tend to dominate such that rising (declining) rates imply lower (higher) return,

whereas over horizons longer than the duration, the reinvestment impact will tend to dominate such that rising (declining) rates imply higher (lower) return.

至于同学你问的基本的原理性问题不会出现在CME考题里。这部分是一二级固定收益学科的内容，如果你想搞清楚，请就文字部分重新提问下，然后标记固收学科的标记，会有负责这个学科的老师为你解释，谢谢理解~

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！