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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?

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One reason that you might roll to a higher coupon bond is that it will lower your duration, which is defined as the sensitivity to interest rate changes. Bonds with higher coupons have less sensitivity to interest changes (for boring mathematical reasons). If you keep the lower coupon bond and rates keep going up, the value of that bond will go down less than if you had rolled to a higher coupon bond. It would also change the timing of the cash flows, since you're paying a bit more upfront in exchange for higher coupon payments, which might be a better fit your cash flow needs. A pension fund, for example, might be taking in cash now and expect to pay it out in the future, so higher coupon bonds might be a good option to pay more upfront in exchange for higher interest payments later.

There might also be tax reasons (e.g. tax loss harvesting) that on would want to roll to a higher coupon bond.

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