Why bond prices fall when yields rise
Bond prices and yields move in opposite directions. Here is the arithmetic behind that rule, what duration measures, and why it matters for savers, banks and the government.
One of the most repeated lines in financial news is that bond prices fall when yields rise. It sounds like a technicality, but it explains a lot: why bond funds lost money in 2022, why some banks found themselves holding large unrealized losses in 2023, and why higher interest rates change the value of almost every investment. The relationship comes from simple arithmetic.
What a bond is
A bond is a loan. The buyer lends money to a government or company and in return receives a fixed schedule of payments: regular interest payments, called coupons, and the return of the face value, called principal, on the maturity date. A 10-year Treasury note with a $1,000 face value and a 4% coupon pays $40 a year, in two semiannual payments of $20, and returns $1,000 after 10 years.
The key word is fixed. Once a bond is issued, its coupon and principal do not change. What changes is the price people will pay for those fixed payments in the market.
The seesaw
Suppose you own that 4% note and, a month later, new 10-year Treasury notes are being sold with a 5% coupon. Nobody will pay you $1,000 for a bond that pays $40 a year when they can buy a new one that pays $50 for the same price. To sell yours, you must accept a lower price. The price falls until the buyer's total return, counting both the $40 coupons and the gain from buying below $1,000 and receiving $1,000 at maturity, roughly matches the 5% available on new bonds. That total return is the bond's yield to maturity.
The reverse is also true. If new bonds pay only 3%, your 4% bond becomes more attractive and its price rises above $1,000. Price and yield are two ways of describing the same thing, so they always move in opposite directions.
Present value
The formal reason is present value. A dollar received in the future is worth less than a dollar today, because today's dollar could be invested and earn interest. To find what a bond is worth, you discount each future payment back to today using the current market interest rate. When that rate goes up, each future payment is discounted more heavily and the total, the bond's price, goes down.
Duration: how sensitive is the price?
Not all bonds react equally. A bond that matures in one year will barely move when rates change, because you will soon get your principal back and can reinvest at the new rate. A bond that matures in 30 years locks in its coupon for a long time, so a change in rates has a much larger effect on its price.
The measure for this is duration, expressed in years. As a rough rule, a bond's price changes by about its duration, in percent, for each one-percentage-point change in yield, in the opposite direction. A bond with a duration of seven years would lose roughly 7% of its value if yields rose by one point. Duration is longer for bonds with longer maturities and lower coupons. Zero-coupon bonds, which pay nothing until maturity, have a duration equal to their maturity.
Fund companies report the average duration of their bond funds, and the Securities and Exchange Commission's investor education site recommends checking it as a way to gauge interest rate risk.
Why it mattered in 2022 and 2023
In 2022 the Federal Reserve raised its policy rate rapidly to fight inflation, and Treasury yields across maturities rose sharply. Because prices move inversely to yields, the market value of existing bonds fell, and many broad bond funds posted losses that surprised investors who thought of bonds as the safe part of a portfolio.
Banks hold large amounts of Treasury and mortgage-backed securities. When yields rose, those holdings lost market value. Under accounting rules, securities classified as held to maturity are carried at amortized cost, so the losses did not show up in reported earnings. That is fine if the bank never has to sell. Silicon Valley Bank, facing large deposit withdrawals in March 2023, sold securities at a loss, and the announcement helped trigger the run that led to its failure.
What it means if you hold a bond to maturity
If you buy an individual bond and hold it until it matures, and the issuer does not default, you receive every coupon and the full face value regardless of what happens to market prices in between. Price swings matter only if you need to sell early. That is one reason some savers prefer individual Treasury securities or certificates of deposit to bond funds, which never mature and whose share prices move with the market.
Rising yields also have an upside for buyers. New bonds and newly reinvested coupons earn the higher rate. Over long periods, the reinvestment effect can offset the initial price loss for an investor with a long horizon.
Other things that move yields
Market interest rates are not the only influence on a particular bond's yield. Credit risk matters: if investors become worried that a company may not repay, its bonds fall in price and their yields rise even when Treasury yields are steady. Inflation expectations matter, because inflation erodes the value of fixed payments. Supply and demand matter too, including how much debt the Treasury is issuing and how much the Fed or foreign buyers are purchasing.
The bottom line
A bond's payments are fixed, so its price is the only thing that can adjust when market rates change. Higher rates mean lower prices, and longer bonds feel the effect more. Keeping that one relationship in mind makes a wide range of financial news easier to follow.
This article is general information, not investment advice.
Sources
- SEC Investor.gov: Interest Rate Risk, When Interest Rates Go Up, Prices of Fixed-Rate Bonds Fall
- FINRA: Duration, Understanding the Relationship Between Bond Prices and Interest Rates
- TreasuryDirect: Treasury Notes
- Federal Reserve: Review of the Federal Reserve's Supervision and Regulation of Silicon Valley Bank (April 2023)