There's another way to look at this...
Because... this is a bit simplified (mainly because it does not take bond liquidity and potentially mismatched maturity dates into account), but essentially...
The investment value of a bond I currently own doesn't actually decrease when new bond yields go up... the value stays the same irrespective of how new bond yields move (up or down)!
For instance...
If I'm holding a bond that matures in 5 years (regardless of its original term or when I bought it) and new issue 5-year bonds are available at a higher yield, then if I want to sell my existing bond, I will have to do so a discount (lower price).
Now if I go and buy the new issue higher yield 5-year bond with the proceeds from the sale I just made, I will end up with a little bit less face amount than I had before, because I sold at a discount... but the new bond lower face amount and higher yield would theoretically offset each other and net to the value of the bond I had sold!
In other words, in 5 years I'll have the same bucks I would have had whether I kept the original bond or sold it and bought the new one.
Likewise, if I sell a bond at a premium (higher price) because current rates for the same maturity as my bond are lower, I will end up buying more face amount at lower yield when reinvesting... but net the same amount (value) at maturity.
My main point here is that bond "value" and "price" are not the same... notice if I ask Google, "do bond values go down if new yields go up?", the answer is "Yes, bond values (prices)" [are the same]...
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Yet, if I ask Google, "are bond value and price the same?", the answer is "No, bond value and price are not the same"...
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Tell me if I'm nuts!