New on FinoLib · Volume II: Capital Markets
I have just published a new article on FinoLib, my free finance education library: Bond Duration and Bond Pricing: Macaulay vs Modified. It is part of Volume II: Capital Markets. Below is a summary of the topic in plain, expert language, so you can follow the idea even before you open the full article.
3.1 Bond Pricing Basics — Price, Yield, and the Inverse Relationship
The idea in plain words
A bond is a loan that pays you fixed interest, and its price is what those future payments are worth today. Prices and yields move in opposite directions. When market yields rise, new bonds pay more, so older bonds with lower payments become less valuable and their price falls. In this chapter’s example, a three-year bond with a 5% coupon and $1,000 face value costs $972.91 when the market yield is 6%. The buyer also pays accrued interest on top of the quoted price.
Key points
■Coupon below yield means a discount price, equal means par, above means a premium; every price is pulled to face value at maturity.
■Yield to maturity is your return only if you hold to maturity, are paid in full and reinvest at the same yield.
■You pay the dirty price (clean price plus accrued interest); US corporates accrue on a 30/360 basis.
A closer look
A bond is a loan in tradeable form: the issuer promises to pay periodic coupon payments and return the face value (or “par value”) at maturity. Once issued, a bond trades in the secondary market at whatever price buyers and sellers agree — and that price moves in the opposite direction to prevailing interest rates. This single inverse relationship is the mechanical foundation for everything else in this Part.
Decision rule
Compare bonds on yield, never on coupon. With no embedded option, rank on YTM; if callable, rank on yield to worst, the lowest of the yield to maturity and the yield to each call date. If you will sell before maturity, YTM is not your return; the exit price decides it. Budget cash on the dirty price, and use current yield (annual coupon ÷ price) only as an income measure.
The costliest mistake
Treating current yield as return on a premium bond. The 5% bond priced at $1,028.01 to yield 4% shows a current yield of 50 ÷ 1,028.01 = 4.86%, 0.86 points above the 4.00% it actually earns, because the $28.01 premium shrinks to zero by maturity. On $1 million face that is $28,007 of price that disappears by design. Avoid it: read the YTM or yield to worst on the ticket.
3.2 Duration — Measuring Interest Rate Sensitivity
The idea in plain words
Duration tells you how sharply a bond’s price will move when interest rates change. Think of a seesaw: a longer bond sits farther out, so it swings more. Macaulay duration is the average time you wait for the bond’s cash, weighted by value. Modified duration turns that into a percentage price change for each 1% move in yield. In the chapter’s example, modified duration is 2.74, while a 20-year bond with a 7% coupon at par has about 10.7, so it swings far more.
Key points
■% price change ≈ −modified duration × change in yield; it works best for small, parallel moves in option-free bonds.
■DV01 = modified duration × price × 0.0001 turns duration into dollars that add across positions.
■Hedge by matching DV01, not face value: about $14.1 million of a 2-year note offsets $10 million of the Part 3 bond.
Decision rule
Use modified duration or DV01 to size rate risk when the bond has no embedded option, the move is under about 100 bp and the curve shifts roughly in parallel. Hedge by matching DV01, not face value: hedge face = position DV01 ÷ hedge DV01 per unit of face. For $10 million of the Part 3 bond ($2,664 per bp) hedged with a 2-year Treasury at par yielding 4.78% (DV01 about $188.60 per $1 million), short 2,664 ÷ 188.60 ≈ $14.1 million face.
The costliest mistake
Funding long-duration assets with short-duration money. Silicon Valley Bank held 55% of its assets in securities, and its held-to-maturity portfolio had a weighted-average duration of 6.2 years at the end of 2022 (Federal Reserve review, April 2023). The 5-year Treasury yield rose from 1.26% to 3.99% during 2022: −6.2 × 2.73% ≈ −16.9%, about $169 million per $1 billion of securities, funded by deposits that could leave in a day. Avoid it: compute the duration gap (asset minus liability duration, weighted by size) and the dollar loss at +200 bp before you buy.
What the full article covers
In the full article I take you through these sections:
■3.1 Bond Pricing Basics — Price, Yield, and the Inverse Relationship
■3.2 Duration — Measuring Interest Rate Sensitivity
It includes worked examples, a look under the hood at the mechanics, a clear decision rule, the one mistake that costs people the most, a recap, a reveal-on-click quiz and the official sources behind every figure.
Volume II: Capital Markets
Read the full article on FinoLib
The complete article, Bond Duration and Bond Pricing: Macaulay vs Modified, with every worked example, diagram, quiz and source, is free to read in Volume II, Capital Markets on finolib.com.
Explore the Finance Education Series: Vol. II — Capital Markets · Vol. I — Global Economy · Vol. III — Finance Encyclopedia · Vol. IV — Finance Careers · Vol. V — Personal Finance