Bond Prices and Yields: Why They Move in Opposite Directions

Pricing a Bond

Price = Σ coupon ÷ (1 + y)^t + face ÷ (1 + y)^n. Consider a 10-year bond with a face value of $100 and a 5% annual coupon ($5 a year). If the market yield is 5%, the price is exactly $100. If the yield rises to 6%, the present value of the cash flows falls to $92.64. If it falls to 4%, the price rises to $108.11. At 7%, the price is $85.95.

The bond's contractual payments have not changed. What changed is the return investors demand, so the price adjusts until a buyer earns the market yield.

Maturity Magnifies the Effect

The longer the time until maturity, the more sensitive the price is to yield changes, because the final repayment is discounted over more years and more coupons are affected. A 2-year 5% bond falls only to 98.17 when yields rise to 6%, a 1.8% decline. The 10-year bond falls 7.4%. A 30-year 5% bond falls to 86.24, a loss of 13.8% from the same one-point rise. If yields fall to 4%, the 30-year bond rises to 117.29.

Duration is the measure used to summarize this sensitivity. A rough rule: the percentage price change is about minus the duration times the yield change. A bond with a duration of 8 years loses about 8% when yields rise by one percentage point.

What It Means for Bond Investors

If you hold an individual bond to maturity, you receive the face value regardless of price swings in between, assuming the issuer does not default. If you must sell before maturity, you receive the market price, which could be above or below what you paid. Bond funds have no maturity date, so their value fluctuates with yields, although rising yields eventually increase the income earned by newly purchased bonds.

That is why bond fund investors can see losses when rates rise sharply, even though the funds hold safe government bonds. Over a time horizon longer than the fund's duration, higher yields tend to offset the earlier price decline.

Credit Risk and Other Factors

Yield also includes compensation for credit risk. A company bond has a higher yield than a Treasury of the same maturity because there is a chance of default. Inflation expectations, taxes, liquidity, and call features also affect bond yields and prices. Changes in the perceived creditworthiness of the issuer can move the price independently of general interest rates.

Using This in Practice

Match bond maturities to when you need the money, for example by using a ladder. Compare yields on a like-for-like basis, such as yield to maturity, which accounts for price, coupon, and time. Diversify across issuers, and understand the duration of any bond fund you buy.