That’s true only if the bond has an “infinite” term. Meaning it pays interest forever but you never get your initial principal back

If a bond has say a one-year term then it won’t lose 50% of its value if interest rates double from 1 to 2 percent because you still get your original full investment back after one year. It’s value instead drops by about 1%.

For a longer term example, a bond purchased for $1,000 and 1% interest rate with 30 years left is worth $776 if interest rates rise to 2%

Source: https://m.free-online-calculator-use.com/bond-value-calculat...

This is true in limited cases. Changes in bond values in relation to interest rate changes is much more involved than this. The first derivative is known as "duration" while the second derivative is known as "convexity". The size and timing of payments will vary from bond to bond, which heavily affects interest rate risk:

Duration: https://en.wikipedia.org/wiki/Bond_duration Convexity: https://en.wikipedia.org/wiki/Bond_convexity

The potato paradox disappears entirely with the right illustration [1]. Something similar (though not quite so clear as paradox's grid) for bonds: [2].

[1] https://en.wikipedia.org/wiki/File:Potato_paradox.svg

[2] https://bogleheads.org/w/images/thumb/8/84/Bond_-_Premium_-_...

That's not how bond yields work.

Let's say I have a bond that has a face value of $100, yields 1%, and matures in 1 year. It's value today is $99. Now interest rates go to 2%. That bond is now worth $98, because 1 year from now, at 2% interest, it will be worth $100.

But for longer term bonds (30 years, say), what you said can be true.