Bond immunized when duration equal to investment horizon

" Bond immunized when duration equal to investment horizon " I don’t understand…

Why the bond will only be immunized when duration equal to investment horizon? How does it works? How to know the change in interest on interest exactly offsets the change in price when rates change? Anyone can explain to me?

Sorry for my poor english

One of the characteristics of Macaulay duration is that it gives you the period of indifference.


When interest rates change, the value of your bond changes, and your reinvestment rate changes. Suppose that interest rates increase by 50bp. Your bond decreases in value (because it has a 50bp higher YTM), but you earn (50bp) more interest when you reinvest your coupon payments. If the Macaulay duration of your bond is, say, 7 years, then after 7 years the value of your total portfolio (bond + coupon payments + interest on coupon payments) will be the same as it would have been had interest rates not changed by 50bp.

Thus, if your investment horizon (the length of time you plan to hold this bond before you sell it) is 7 years, then you don’t care if interest rates change or not: you end up with the same portfolio value either way.

Note that we’re assuming a parallel shift in the yield curve: _ all _ interest rates increase by 50bp.)