Can someone please help explain why the return on a bond over one year is always equal to the one-year risk-free rate if spot rates develop as predicted by today’s forward curve?
So say for example the 1-year spot rate is 4%.
Why is it that no matter what bond I’m holding–a 2-year, a 5-year, or even a 30-year–after one year, each of those bonds will have earned the 1-year spot of 4%?
I understand that the math works out but I can’t seem to understand the intuition. Any help would be greatly appreciated.
Thanks so much!