So Modified Duration is defined to be the log derivative of bond price with respect to the yield on that bond. That creates by definition that for an infinitesimal change in the yield of that bond the change in price relative to the price will be the duration multiplied by the change in yield. Predicting the new price is basically a first order Taylor series expansion of the price function of yield around a point. Since the duration continues to be a function of yield and a second derivative exists one should also consider higher order approximation, meaning to consider convexity. Etc., etc. For large changes in interest rates approximations become less and less accurate.
Note by definition the price/yield relationship is instant. How various yields follow or anticipate other interest rates is a different question.
For a bond fund you can calculate weighted averages of all this stuff keeping in mind that the yield is different for different bonds in the portfolio. The concept of the yield curve was mentioned, meaning that different bonds of different maturities have their own yield and their own changes in yield.
The concept that the yield for any given bond and Federal rate cuts are two different things has been made.
Note by definition the price/yield relationship is instant. How various yields follow or anticipate other interest rates is a different question.
For a bond fund you can calculate weighted averages of all this stuff keeping in mind that the yield is different for different bonds in the portfolio. The concept of the yield curve was mentioned, meaning that different bonds of different maturities have their own yield and their own changes in yield.
The concept that the yield for any given bond and Federal rate cuts are two different things has been made.
Statistics: Posted by dbr — Sun Jun 23, 2024 7:16 am — Replies 10 — Views 960