I'll answer your question in more detail than MediumTex but less detail than Mkchiu.doodle wrote: I have a dumb question that I could probably figure out the answer to, but I am too lazy (and tired) to think on a Friday night.
Would LT bond price appreciation be the same if interest rates dropped in half from 8% to 4% as they would from 3% to 1.5%? In other words does the halving of the interest rates in both of these cases lead to the same bond price appreciation?
It's a fundamental principle that when interest rates rise, bond values fall, and when interest rates fall, bond values rise. The mathematical way to calculate this is a formula called Duration. Once you calculate the Duration of a specific bond (or calculate the weighted average duration of a group of bonds within a bond fund), you can estimate how bonds will move with respect to interest rates.
If the duration is calculated at 15 years, then a 1% movement in interest rates will cause a 15% change in the bond price, in the appropriate direction. i.e. 1% rise in rates causes a 15% drop in bond price.
Thus, it's not a matter of what percentage the interest rates move (i.e. in your example interest rates drop 50% from 8% to 4% or 3% to 1.5%), it's a matter of hard units of interest rate movement (i.e. 8% to 4% is a 4% drop; 3% to 1.5% is a 1.5% drop).
However, the formula to calculate Duration uses the current market interest rates. Thus, as interest rates shift, the duration shifts too because the algorithm to calculate duration uses the market interest rate. The duration of a specific bond is not going to remain the same as interest rates fluctuate wildly.
In other words, if you have a bond at 8% and the Duration is 10 years, then you can estimate that if the bond moves from 8% to 7%, the value will increase 10% based on the 10 years duration, however once the market interest rate is 7%, the duration calculation changes, so you need to continually re-calculate duration if you want to have an accurate picture.
All of this said, it's meaningless on a day-to-day basis for a PP investor because we are "blindly" moving assets into 4x25 alignment regardless of interest rates. It's useful to understand the underlying mechanisms of the bond market, but it's not essential to using the PP.