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November 2025

Bond Pricing Mechanics Refresher
by Richard Zott, Former Senior Examiner, Supervision, Credit and Learning, Federal Reserve Bank of St. Louis*

The notion of “rates up, prices down” is nothing new for those familiar with bond prices. The risks associated with unrealized losses within a bank’s investment portfolio can be significant as interest rates fluctuate. Supervisors review and assess a bank’s unrealized losses on its securities in relation to the total investment portfolio as well as the implications for its tangible equity capital.

Unrealized losses across banks of all sizes worsened from the third quarter of 2024 to the fourth quarter of 2024 despite the Federal Reserve easing the federal funds rate by 100 basis points over that same period. This article explains bond prices and their relationship with interest rates and briefly discusses some of the basic pricing principles of bonds.

Basics of Bond Pricing

There are two important considerations with bond pricing: (1) interest rates (not just the federal funds rate set by the Federal Open Market Committee) and (2) credit spreads (the additional compensation an investor receives for bearing the risk of default). For bonds that are backed by the U.S. Department of the Treasury or U.S. government–sponsored agencies with implied guarantees, the credit spread component is less important and is not the focus of this article.

A key attribute of bonds is that, in general, their prices move opposite of interest rates. A bond’s current price is a function of the coupon rate¹ (if one exists), the par value,² and the interest rate used to discount coupons and the par value back to the time of purchase (see Figure 1).

When market interest rates are higher, the rate used in the discounted cash flow analysis is also higher. The bond’s coupon rate and par value are constant in the bond pricing formula. However, if the bond’s coupon rate and the par value are subject to a higher discount rate in the denominator, the bond’s value will be lower accordingly.

Consider this example:

• If a bond with a 5 percent coupon that yields 5 percent is purchased on a Monday, but interest rates rise to the extent that the bond now yields 6 percent on Tuesday, the bond is worth less because an investor can now buy a bond with a 6 percent coupon for the same price the investor paid for the 5 percent bond the day before.
• Conversely, if a bond with a 5 percent coupon that yields 5 percent is purchased on a Monday, but interest rates dropped such that the 5 percent bond would yield only 4 percent on Tuesday, the bond would be valued higher, as it yields more than the current market rate.

In the pandemic period prior to the interest rate hikes starting in 2022, many banks purchased significant investments yielding between 1 percent and 3 percent. A year later, similar bonds were yielding closer to 5 percent or 6 percent. As a result, the prices on the bonds yielding 3 percent decreased in value substantially. Therefore, the bond price is simply a variable in the relationship between the coupon yield and par value as previously mentioned.

Typically, a bond has semiannual coupon payments over the life of the bond and one big “lump sum” payment at maturity. Therefore, because of the nature and timing of bond cash flows, these cash flows are sensitive to many different points on the yield curve. When longer-term rate expectations increase, the lump sum payment is discounted by a much higher rate than was originally expected, resulting in the current price declining by a larger amount. Additionally, each of the coupon payments made over the life of the bond are discounted to the present value. This highlights the importance of the concept of compound interest, as cash flows later in the life of the bond are discounted more times and, therefore, have higher degrees of sensitivity to interest rates. With all things being equal, longer maturity bonds with more coupons will also have a higher degree of sensitivity to interest rate fluctuations than shorter maturity bonds.

For example:

Assumptions:

• Start with a zero coupon bond, and, therefore, we can ignore coupon payments for simplicity.
• The 10-year bond is purchased when the 10-year rate is 4 percent.
• The present value of a $1,000 bond is $675 ($1,000/1.04¹⁰).

What happens if the 10-year rate jumped to 6 percent immediately after purchase?

The price of the bond would decline to $558, a nearly 17 percent decline in its price.

Real-World Example: 2024 Scenario

When the federal funds rate dropped by 100 basis points at the end of 2024, why did unrealized investment losses worsen for certain institutions (see Figure 2)?

• Market expectations shifted dramatically; investors initially were anticipating many rate cuts (some market participants initially expected as many as six 25 basis points cuts) in 2025, but these expectations were scaled back.
• Simultaneously, term premia (compensation an investor requires for holding a bond for a certain length of time over which rates may change) increased significantly. For example, this is particularly true for the 10-year term premium, for which the increase accounts for nearly three-quarters of the total increase in the 10-year rate.
• These factors individually would result in changes to the yield curve and impact bond prices adversely. Together, their impact, as outlined in Figure 2, was even more punitive, pushing yields up and bond prices down despite a declining federal funds rate.

Over the period in which the federal funds rate was lowered, the market expected several interest rate cuts in 2024, which influenced the 10-year interest rate and other interest rates. More recently, in 2025, the market has continued to expect lower interest rates. While bond prices changed to reflect current rates and expected future rates (the shape of the yield curve), recent movements were driven more by increases in the term premia.

A way of measuring the sensitivity of a bond’s price considering changes in interest rates is known as duration.³ While imperfect, duration measures the approximate change in the price of a bond for a 1 percent move in interest rates. For example, a duration of four would indicate that the price would decline (since prices move opposite to rates) roughly 4 percent for every 1 percent of an increase in the interest rate. Bonds with higher coupons and lower maturities have lower durations when all things are equal.

Summary

Bond pricing mechanics are technical and complex. Multiple variables impact bond prices, which require a deeper understanding of finance. The goals of this article were to highlight a few key variables that can affect bond pricing and to highlight how the shape and expectations for the yield curve alone do not drive bond prices. In fact, there are many other forces (i.e., the impact of current and future bond prices). Staying aware of these nuances is key to navigating the bond market effectively and mitigating risks associated with unrealized losses.

• * Richard Zott was a senior examiner at the Federal Reserve Bank of St. Louis when this article was written.
• ¹ The coupon rate is calculated by taking the sum of annual interest payments made by the issuer to the investor divided by the bond’s par value.
• ² Par value is the value of a bond at its stated maturity date, also known as its face value.

• ³ There are several types of duration, but effective duration is the type most used, as it adjusts for optionality, unlike modified duration.