The inverse relationship between bond prices and yields is often stated and rarely explained. It follows directly from the fact that a conventional bond's payments are fixed at issue and cannot change afterwards.
The payments are fixed, so the price adjusts
A bond promises specified interest payments and a specified repayment at maturity. Those amounts are set when the bond is issued.
If newly issued bonds start offering higher interest, an older bond paying less is worth less to a buyer, and the only variable available to restore equivalence is the price.
The price falls until the return a buyer earns from holding it to maturity matches what is available elsewhere. That return is the yield.
Why yield and coupon are different numbers
The coupon is the fixed payment expressed against the bond's face value. It never changes for a conventional bond.
The yield is the return implied by the current price, and it incorporates both the coupon payments and any gain or loss between the purchase price and the face value repaid at maturity.
A bond bought below face value therefore yields more than its coupon, because the holder receives the coupons plus the difference at redemption.
Duration measures how much the price moves
The further away a bond's payments are, the more a change in rates affects their present value, because the discounting applies over more periods.
Duration expresses this sensitivity as an approximate percentage price change for a given change in yield, which allows bonds of different maturities to be compared directly.
This is why long-dated bonds can lose substantial value when rates rise even though they are considered low-risk in the sense of being repaid in full.
Credit risk moves prices independently
Government bonds in a country's own currency move mainly with interest rates. Corporate bonds also move with the market's view of whether the issuer will pay.
That view is expressed as a spread over comparable government bonds, and the spread widens when conditions deteriorate, pushing prices down separately from any rate change.
The two effects can offset or compound each other, which is why bond returns during stress depend heavily on what kind of bond is held.
Why holding to maturity changes the experience
An investor holding an individual bond to maturity receives the coupons and the face value regardless of what the price did along the way, provided the issuer pays.
Price movements in between are real but unrealised, and they represent the opportunity cost of holding an older rate rather than an actual loss of the promised amounts.
A bond fund has no maturity date, so its value reflects current prices continuously, which is the structural difference between owning bonds and owning a fund that holds them.