Price-Yield Relationship

The inverse price-yield relationship is the foundation of bond market behavior. It is not a rule of thumb or a market convention; it flows directly from present-value mathematics and the certainty of bond redemption. When yields move, bond prices move the opposite direction. This chapter builds your understanding of why, how much, and what it means for investors holding individual bonds or bond funds.

The relationship seems simple: yields up, prices down. But the mechanics are rich. A bond's price is the sum of all its future cash flows discounted at the market yield. When the yield increases, those future cash flows are worth less today. The magnitude of price movement depends on two key factors: the bond's coupon (how much you collect upfront) and the bond's maturity (how far away the final payment is). Lower-coupon, longer-maturity bonds are far more sensitive to yield changes.

This sensitivity is essential for understanding interest-rate risk. In 2022, when the Federal Reserve raised rates sharply, long-term bond funds experienced losses of 15–30%, even though the bonds themselves were of high quality. The mechanism was not default risk but pure price appreciation and depreciation driven by the inverse relationship. Understanding this relationship prevents panic and enables rational decision-making about asset allocation, duration targets, and rebalancing.

You will also learn the real-world mechanics of bond trading and quotation. Bonds are quoted at clean prices (excluding accrued interest), but you pay the dirty price (clean price plus accrued interest). Day-count conventions (Actual/Actual, 30/360, Actual/360) determine how interest accrues and slightly affect yields. These details seem tedious, but they are important for accurate pricing and for understanding why a bond you see quoted at 100 does not actually cost $1,000.

By the end of this chapter, you will be able to calculate bond prices given yields, estimate how yields affect holdings, and understand why bond fund values fluctuate. You will also have concrete spreadsheet examples that you can adapt for your own analysis. The inverse relationship is not mysterious; it is math in action.

What's in this chapter

📄️ The Inverse Price-Yield Relationship

When bond yields rise, prices fall. When yields fall, prices rise. The fundamental mechanism that makes bonds move.

📄️ Why Prices Fall When Yields Rise

When new bonds offer higher coupons, old bonds with lower coupons become less valuable. The supply-and-demand mechanism behind the inverse relationship.

📄️ The Pull to Par

As a bond nears maturity, its price converges to face value, regardless of what it traded for earlier. A powerful stabilizing force.

📄️ Bond Pricing from Discounted Cash Flows

How to calculate the exact price of a bond by discounting its future cash flows at the market yield. The foundational formula.

📄️ Coupon Effect on Price Sensitivity

Lower-coupon bonds experience larger price swings when yields change. Higher-coupon bonds are more stable. Why coupon determines rate sensitivity.

📄️ Maturity Effect on Price Sensitivity

Longer-maturity bonds experience much larger price swings when yields change. Maturity is the primary driver of interest-rate risk in fixed income.

📄️ Pricing a Zero-Coupon Bond

Zero-coupon bonds have no coupons and return only face value at maturity. The simplest pricing formula, but the most volatile behavior.

📄️ Bond Price vs Time Graphs

Visualize how a bond's price evolves from issuance to maturity. The pull to par, yield changes, and the relationship between time and value.

📄️ Clean Price Quotes Explained

Bond prices are quoted as clean prices, excluding accrued interest. What you see is not what you pay. Understanding the difference.

📄️ Dirty Price and Accrued Interest

The dirty price is the true economic price you pay or receive. It includes accrued interest earned since the last coupon date. The practical cost of bond ownership.

📄️ Day-Count Conventions

Different bond markets use different conventions for counting days between coupon dates. Actual/Actual, 30/360, and Actual/360 produce different yields and prices.

📄️ Bond Pricing Spreadsheet Example

A worked spreadsheet example showing how to price a bond, calculate accrued interest, and compute yield to maturity. You can copy and modify.

📄️ Yield Changes of 1%

How to estimate bond price changes when yields move by 1%, using duration as a practical tool.

📄️ Large Shifts & Non-Linearity

Why duration underestimates losses in large yield moves; introduction to convexity.

📄️ Shifting Yield Curves

How yield curve shape and movement affect portfolios differently based on maturity composition.

📄️ Parallel vs Non-Parallel Shifts

The difference between yields moving uniformly and curve shape changes, and why both matter.

📄️ Key Rate Shifts

How sensitivities to specific maturities (2, 5, 10-year yields) reveal portfolio risk beyond average duration.

📄️ Spread Widening & Prices

How credit spreads widen independently of Treasury yields, causing bond price drops even when risk-free rates are stable.

📄️ Spread vs Rate Shift

Distinguishing between interest rate risk and credit risk as separate sources of bond losses.

📄️ Risk-Free Yield Decomposition

Real yields, inflation expectations, and term premiums are the three components of Treasury yields.

📄️ Pricing a Callable Bond

When an issuer can call a bond away, price appreciation is capped but yield is enhanced.

📄️ Effective Yield of Callable

Measuring the true return of a callable bond using option-adjusted spread and scenario analysis.

📄️ 2022 Bond Bear

Why 2022 was the worst year for long-duration bonds in modern history and what the losses reveal about bond behavior.

📄️ Price-Yield Summary

A one-page practitioner's reference for understanding bond price behavior and managing yield risk.

How to read it

Start with the first article on the inverse price-yield relationship itself; it establishes the core concept and its causes. Then move through the mechanics: why prices fall when yields rise (article 2), the pull to par (article 3), and the present-value pricing formula that ties everything together (article 4).

Once you understand the formula, explore the two main drivers of price sensitivity: coupon effect (article 5) and maturity effect (article 6). These articles explain why zero-coupon bonds are more volatile than high-coupon bonds, and why 30-year bonds react more sharply to yield changes than 2-year bonds.

The final six articles address practical real-world details: zero-coupon bond pricing (article 7), price-time graphs (article 8), clean versus dirty prices (articles 9–10), day-count conventions (article 11), and a spreadsheet worked example (article 12) that you can copy and adapt.

You do not need to memorize formulas or master advanced spreadsheet skills. Read for understanding. The goal is to develop intuition: when yields move, you immediately grasp why bond prices move, by how much, and what it means for your holdings.