Bond prices fall when interest rates rise and rise when rates fall. The relationship follows directly from the fact that a bond's payments are fixed at issue.
The payments cannot change, so the price must
A conventional bond promises defined interest payments and a defined repayment at maturity. Those amounts are set when it is issued and do not respond to conditions afterwards.
If newly issued bonds offer higher rates, an older bond paying less is only attractive at a lower price. The discount brings its effective return into line.
The mechanism is arithmetic rather than sentiment. Nothing about the issuer has changed; the alternatives have.
Yield and price are two views of the same thing
Yield expresses the return implied by the current price and the remaining payments. Quoting one determines the other, which is why they always move inversely.
A rising yield is therefore not additional income to an existing holder. It reflects a fall in the value of what they already own.
Confusing the two is common, and it makes rising rates look unambiguously good for bondholders when the immediate effect is the opposite.
Duration measures the sensitivity
The longer the remaining term, the more payments are affected by a change in rates, and the larger the price movement for a given shift.
Duration summarises this into a single figure describing approximate price sensitivity. A longer duration means more movement in both directions.
This is why long-dated bonds are more volatile than short-dated ones despite both being fixed income.
Credit risk moves separately
Alongside rate sensitivity, prices reflect the perceived likelihood of the issuer paying. Deterioration in that assessment lowers the price independently of prevailing rates.
Government and high-quality corporate bonds are dominated by rate movements, while lower-quality debt is influenced more by credit conditions.
The two can move in opposite directions, which is why bonds do not behave as a single uniform category.
Holding to maturity changes the exposure
An investor holding an individual bond to maturity receives the stated payments regardless of price movements along the way, assuming the issuer pays.
The loss from rising rates is then an opportunity cost rather than a realised one, since the money is committed at the older rate.
Funds holding many bonds do not have a single maturity date, so price movements pass through into the value of the holding continuously.