A 10-year Treasury bond paying 4% interest becomes less valuable the moment market rates climb to 5%.
Bonds are loans. When an investor buys a bond, they lend money to an issuer for a set period in exchange for fixed interest payments. The U.S. Department of the Treasury issues the most common version of this debt, the Treasury note. These securities have a face value, usually $1,000, and a coupon rate that determines the annual dollar payment. A 4% coupon on a $1,000 bond pays $40 every year until maturity.
The market price of that bond is not fixed. It fluctuates based on what investors can earn elsewhere. The Federal Reserve influences these alternatives by setting the federal funds rate, which ripples through the broader economy to affect Treasury yields. If the Treasury issues a new 10-year note at 5%, existing bonds paying only 4% become less attractive. Buyers will not pay full price for the old bond. They will pay less, until the effective yield of the cheaper bond matches the new 5% market rate. This is the mechanism behind the price drop.
The Math of the Drop
To see why the price must fall, compare the cash flows of the old bond against the new market rate. A 10-year bond has 10 remaining payments of $40, plus one final payment of $1,000 at the end. To find the fair price today, each future dollar must be discounted back to the present using the current market yield.
The table below shows the present value of those cash flows. In the first column, the bond is valued at its original 4% yield. In the second column, the same cash flows are valued at the new 5% market yield. The discount factor in each column represents how much a future dollar is worth today at that specific interest rate.
| Time | Cash Flow | Value at 4% Yield | Value at 5% Yield |
|---|---|---|---|
| Years 1-10 | $40 coupon | $324.42 | $308.87 |
| Year 10 | $1,000 principal | $675.56 | $613.91 |
| Total Price | $1,000.00 | $922.78 |
The difference between the two totals is the capital loss incurred by holding the old bond when rates rise. The principal payment of $1,000 is discounted more heavily in the second column because that money is further away in time. The coupon payments are also worth less in present-value terms. The sum of these reductions equals roughly $77 per bond. This is not a theoretical loss until the bond is sold, but it is the mark-to-market reality that financial institutions use to value portfolios on their balance sheets.
What the Picture Shows
The table reveals that duration amplifies the pain of a rate hike. A bond with only one year remaining would lose far less value because the principal is returned sooner, meaning less discounting occurs. A 10-year bond locks the investor into a lower rate for a decade. The Federal Reserve tracks this sensitivity in its monetary policy reports, noting that long-term yields are more volatile to rate changes than short-term bills.
The specific tradeoff is between yield and price. When an investor buys a bond, they accept a fixed income stream in exchange for the risk that interest rates will move against them. The price drop compensates new buyers for the lower coupon. Without the price adjustment, no one would buy the 4% bond when 5% is available. The market forces the price down until the total return of the old bond equals the total return of the new bond. This adjustment happens continuously on secondary markets like those tracked by Bloomberg.
The numbers show that a 1 percentage point move in yield costs a 10-year holder roughly 7.7% of their principal value. This is not a small margin. It explains why bond funds can have negative returns in rising rate environments even if the issuer never defaults. The risk is not the borrower running out of money; it is the borrower paying a rate that the market no longer considers fair. The U.S. Department of the Treasury guarantees the payment of principal and interest, but it does not guarantee the market price of the bond before maturity.
The Closer
For an investor holding a 10-year Treasury at 4% yield, a shift to 5% rates costs approximately $77 on every $1,000 invested. The math says the bond loses value because the future cash flows are discounted at a higher rate. The behavior says selling now realizes that loss, while holding avoids it only if the investor can wait for maturity to receive the full face value. The tradeoff is between locking in a loss today or waiting ten years for the market to align with the original purchase price. Most bond investors who need liquidity should understand that the 7.7% drop is the price of having a fixed rate in a variable world.