Why do bond prices fall when interest rates rise?

A bond pays a fixed set of amounts: regular interest payments (the coupon) and its face value back at the end. When interest rates rise, newly issued bonds pay more. Nobody will pay full price for an older bond paying less, so its price falls until its return matches what new bonds offer.

When rates fall, the opposite happens: the older bond's higher payments become attractive, and its price rises. This inverse relationship isn't a market habit. It follows from the arithmetic of valuing fixed payments.

The arithmetic behind it

A bond's price is the value today of all its future payments. To get that value, each payment is discounted at the current market interest rate: money arriving in the future is worth less than money now, and the higher the rate, the less it's worth today.

The payments are fixed, so the price is the only thing that can change. Higher rate, lower present value, lower price.

A worked example

Take a bond with a $1,000 face value, a 5% coupon (it pays $50 a year), and 10 years until it matures. While market rates are 5%, it's worth $1,000.

Now suppose rates rise to 6%. A new $1,000 bond pays $60 a year, so the old $50-a-year bond has to get cheaper:

Market rate	Price of the 5% bond
4%	about $1,081
5%	$1,000
6%	about $926

At about $926, a buyer gets $50 a year plus a $74 gain when the bond repays $1,000 at maturity. Together, those work out to roughly a 6% return per year, matching new bonds.

(Figures assume one coupon payment a year.)

Yield to maturity

The yield to maturity is the single rate that makes all of a bond's future payments add up to its current price. It's the full return you'd earn by buying at today's price and holding to the end, counting both the coupons and any gain or loss at maturity. When news reports quote a bond's "yield", this is usually what they mean.

Why long bonds move more

The further away a bond's payments are, the more a rate change affects their value today. Here's the same 5% bond when rates move to 6%, with different times left to maturity:

Years to maturity	Price at 6%
2	about $982
10	about $926
30	about $862

This sensitivity is measured by duration. Long maturities and low coupons mean high duration and bigger price swings; short maturities and high coupons mean smaller ones. When rates rose sharply in 2022, long-dated bonds took the biggest losses.

Does a price fall matter if you hold to maturity?

If you hold an individual bond until it matures, and the issuer pays as promised, you still get the face value back at the end. The price fall matters most if you need to sell before then, or if you hold a bond fund, whose value moves with the market prices of the bonds inside it.

Learn it properly

Finance Brain's The Price-Yield Relationship lesson, in the Bonds course, covers this inverse rule, yield to maturity and an introduction to duration, and ends with a short quiz. The course goes on to cover duration and interest rate risk in more depth.

Finance Brain is educational content, not financial advice.