Why Bond Prices and Yields Move in Opposite Directions
A worked example of the most important relationship in fixed income, plus duration — the number that tells you how much a bond will move.
“Treasury yields rose sharply today” and “bond prices fell” describe the same event. To anyone new to fixed income this seesaw is confusing. A simple example makes it obvious.
A bond is a fixed set of payments
Suppose the government issues a 10-year bond with a face value of $1,000 and a 4% coupon. It promises to pay $40 a year for ten years and then return the $1,000. Those payments are fixed: whatever happens to interest rates, this bond will pay exactly $40 a year.
When it is issued, investors will pay about $1,000 for it, because 4% is the going rate for 10-year government debt.
Now rates rise
A year later, suppose newly issued bonds pay 5%. Why would anyone pay $1,000 for your bond paying $40 a year when a new $1,000 bond pays $50? They won’t. Your bond’s price must fall until its return to a new buyer matches the market rate.
How far? Price equals the present value of the remaining payments, discounted at the market yield. For a 10-year 4% bond (with annual coupons, for simplicity) priced at a 5% yield:
| Value | |
|---|---|
| Present value of ten $40 coupons at 5% | $308.87 |
| Present value of $1,000 in ten years at 5% | $613.91 |
| Price | $922.78 |
A one-percentage-point rise in yield cut the price by about 7.7%. The new buyer gets the $40 coupons plus a gain of about $77 at maturity, which together work out to a 5% annual return.
If yields had instead fallen to 3%, the bond would be worth more than $1,000, because its $40 coupons beat what new bonds pay.
That is the whole relationship: the payments are fixed, so the price must adjust to deliver the market yield. Higher yields mean lower prices; lower yields mean higher prices.
Duration: how sensitive is the price?
Not all bonds move by the same amount. The key measure is duration, which estimates the percentage price change for a one-point change in yield.
- A bond with a duration of 8 loses about 8% if yields rise one percentage point, and gains about 8% if they fall one point.
- Our 10-year 4% bond has a (modified) duration of roughly 8, which is why its price fell by around 8% — a bit less, in fact, because of a curvature effect called convexity.
Duration is higher for:
- Longer maturities. A 30-year bond can move two to three times as much as a 10-year bond for the same change in yields.
- Lower coupons. More of the value is paid far in the future, so it is more sensitive to discounting.
This is why long-term bond funds can fall sharply when rates rise, as many investors discovered in 2022, when a rapid rise in interest rates produced some of the worst bond-market losses in decades.
What it means for bond-fund investors
A bond fund has no maturity date, but it has an average duration, listed on its fact sheet. As a rough guide:
- If you will need the money in two years, a fund with a duration of 15 exposes you to large swings.
- If your horizon is longer than the fund’s duration, rising yields eventually help you: the fund reinvests maturing bonds at the higher rates, and the higher income gradually makes up the initial price drop.
Yield is a return, not just a rate
The “yield” quoted in the news for a Treasury bond is its yield to maturity: the annual return you would earn if you bought at today’s price and held to maturity, with all payments made as promised. That is why the yield moves every second the bond trades, even though the coupon never changes.
Once you see that prices and yields are two ways of expressing the same thing, bond-market headlines become simple: when you read that the 10-year yield jumped, you know that everyone holding 10-year bonds just lost money on paper — and that new buyers are being offered a better deal.