Assuming there is no arbitrage, and say the Federal Reserve hiked rates from, say, 2% to 3%. I am holding a US treasury bond with a YTM of 2% (before the drop in price due to the rate hike).
If I am holding this 2% bond, I would assume then that the price of that bond would drop such that selling that 2% bond and buying a 3% bond with the same maturity date would result in the exact same payout. In other words that the YTM of my current bond would rise to be 3%. For this reasoning, I would see no reason to sell the bond early and "roll" my position to a higher yield bond.
In an efficient market, is this the case? Or am I thinking about this incorrectly and there are often cases where I would want to "convert" my position to this higher yield?