Bond prices and interest rates move in opposite directions, which surprises people who expect a fixed-income investment to be stable. The relationship follows directly from the coupon being fixed at issue.
The coupon cannot change, so the price must
A bond promises set payments on set dates and repayment of face value at maturity. Those terms are fixed in the contract when the bond is issued.
If new bonds are issued paying more, nobody will buy the older bond at its previous price when a better stream of payments is available for the same money.
The only variable left is price. It falls until the fixed payments, measured against the lower purchase price, produce a yield competitive with new issuance.
Yield and price are two views of one number
Yield to maturity expresses the return an investor receives if the bond is held to the end, accounting for coupons and any gain or loss against face value.
Quoting a bond by price and quoting it by yield convey identical information, which is why traders move between the two without ambiguity.
A rising yield therefore is a falling price, described from the other side, rather than two separate events happening together.
Duration measures how much the price moves
Duration expresses a bond's price sensitivity to a change in rates, and it rises with maturity and falls with the size of the coupon.
A long-dated bond has most of its value in payments far in the future, and those distant payments are revalued most heavily when the discount rate changes.
This is why long government bonds can move as sharply as equities during a rate shift, despite carrying no credit risk worth mentioning.
Holding to maturity changes the experience, not the value
An investor holding an individual bond to maturity receives the coupons and face value as contracted, regardless of what the price did in between.
What was lost is the opportunity to hold the higher-yielding alternative, which is a real cost even though it never appears as a realised loss.
Bond funds have no maturity date and continuously reinvest, so the price effect is visible in the unit value rather than being absorbed by a redemption at par.
Credit spreads move independently of the rate
Corporate bond yields combine a government rate with a spread compensating for default risk, and the two components do not move together.
A spread can widen while the underlying rate falls, which is common during periods when the economic outlook deteriorates.
That is why higher-yielding corporate debt often behaves more like equity than like government bonds when conditions turn, despite sitting in the same asset class.