Why bond prices fall when yields rise

Bond prices and bond yields move in opposite directions: when yields rise, prices fall, and when yields fall, prices rise. This is not a market quirk. It follows directly from the arithmetic of fixed payments. Once you see why, headlines about rising Treasury yields, and their effect on stocks, make much more sense.

The core idea

A bond pays a fixed set of cash flows: regular coupons and the face value at maturity (see how bonds work). Once the bond is issued, those payments do not change. What changes is the return that investors demand from similar bonds in the market today.

Suppose you hold a bond paying 5% coupons, and newly issued bonds of the same type and risk now pay 6%. Nobody will pay full price for your 5% bond when a 6% bond is available. To attract a buyer, your bond's price must drop until its yield for a new buyer is about 6%. The lower price makes up for the lower coupon. The reverse also holds: if new bonds pay only 4%, your 5% bond becomes more attractive and its price rises.

Three yield measures

• Coupon rate. The fixed interest rate on the face value. It never changes.
• Current yield. Annual coupon divided by the current price.
• Yield to maturity (YTM). The single annual return that equates the bond's price today with all of its remaining payments, assuming it is held to maturity, no default occurs and coupons are reinvested at the same rate. When people say "yield" without qualification, they usually mean YTM.

A bond's price is the sum of its future cash flows, each discounted at the yield:

Price = sum of [ coupon / (1 + y)^t ] + face value / (1 + y)^n

Here y is the yield, t is each year and n is the number of years to maturity. A higher y shrinks every term, so the price falls.

Example (illustrative numbers)

Take a 10-year bond with a $1,000 face value and a 5% annual coupon ($50 a year). The table shows its price at different market yields, computed with the formula above.

When the yield equals the coupon (5%), the bond sells at par. At 6%, the bond is worth $926.40. A buyer paying that price collects $50 a year and gets $1,000 back, and the combination yields 6%. At 4%, the same bond is worth $1,081.11.

Note that the changes are not symmetrical. A one-point drop in yield raises the price by 8.1%, and a one-point rise cuts it by 7.4%. This curvature is called convexity.

If you hold this bond to maturity and the issuer pays, you still receive $1,000 at the end, so a price drop along the way is a paper loss unless you sell. But the fall is real in the sense that selling early locks it in, and new money could have earned more.

Maturity and duration: how sensitive is the price?

Not all bonds react equally. Two features drive sensitivity:

• Longer maturity. More distant cash flows are discounted over more years, so they are more affected by a change in yield.
• Lower coupon. More of the value is in the final payment, which is far in the future.

Duration summarizes this in one number, expressed in years. As a rough rule of thumb, a bond's price changes by about its modified duration, times the change in yield, with the sign reversed. A bond with a modified duration of 8 would fall about 8% if yields rose by one percentage point, and rise about 8% if they fell by one point.

Using the same 5% annual coupon, here are modified durations at a 5% yield, computed from the formula:

Consistent with that, the 10-year bond above fell 7.4% when yields rose one point. A 30-year bond with the same coupon would have fallen about 13.8% from par, from $1,000 to $862.35 at a 6% yield. A 2-year bond would have dropped only 1.8%, to $981.67. Duration is an approximation that works best for small changes in yield.

Why it matters for stocks

• Discount rates. The value of a stock is the present value of its future cash flows. When long-term yields rise, the rate used to discount those cash flows tends to rise, which lowers their present value. Companies whose cash flows are far in the future, such as fast-growing ones, are often described as more sensitive, though many other factors are in play (see discount rate and CAPM and discounted cash flow basics).
• Competition for money. Higher bond yields give investors a better alternative to stocks, which can weigh on stock prices in some periods.
• Borrowing costs. Higher rates raise the cost of debt for companies, which can pressure profits.

None of these effects is automatic. Stock prices also depend on earnings, growth and sentiment, and stocks and bonds have sometimes moved in the same direction for long stretches.

Common mistakes and limits

• Confusing the coupon with the yield. The coupon is fixed; the yield changes with the price.
• Thinking only losses are possible from rising yields. Higher yields hurt existing holders, but they raise the income earned on new purchases and reinvested coupons.
• Ignoring credit risk. The relationship shown here assumes the issuer will pay. A credit scare can cut a price even if rates do not move.
• Applying duration to big moves. It is an estimate; with large yield changes, convexity matters.
• Mixing up rates. The central bank sets short-term policy rates, but longer-term yields are set by the market (see interest rates and the Fed).

Where to see it on StocksXray

StocksXray does not track individual bonds. The link to stocks shows up in valuation: the fair value models discount future cash flows, and the site uses Damodaran datasets for betas and the equity risk premium. See the methodology for the details. The Market Compass also summarizes broader market conditions.

Key takeaways

• A bond's cash flows are fixed, so when market yields rise, its price must fall to offer a competitive return.
• Price = present value of coupons and face value, discounted at the yield.
• Longer maturities and lower coupons mean greater price sensitivity; duration measures it.
• Holding to maturity fixes the promised payments, but selling early realizes any price change.
• Rising yields can also pressure stock valuations through higher discount rates, but the effect is not automatic.

This article is educational and is not investment advice.