Bond Pricing
A bond's price is the present value of its future cash flows, namely the coupon stream and the face value at maturity. The most common shortcut uses a single yield to maturity to discount every cash flow. The theoretically correct method discounts each cash flow at the zero rate matching its date. Bond prices move inversely to yields, and the sensitivity is summarised by duration and convexity.
Why it matters
A bond is a stack of dated IOUs. The borrower owes a coupon every six months and the principal at maturity. Pricing turns all those promises into today's dollars by dividing each one by a compounded discount factor. Higher yields shrink every future dollar more aggressively, so the price falls. A 5-year 5% bond worth A$100 at par jumps to A$103.92 if yields fall 100 bp, and slides to A$96.23 if yields rise 100 bp. The slope of that line is duration.
Formulas
Worked examples
3-year bond, face value A$100, $5\%$ annual coupon, YTM . Compute the price.
P = 5/1.04 + 5/1.04^2 + 105/1.04^3 = 4.8077 + 4.6228 + 93.3503 = \text{A\}102.78$. Coupon yield, so this is a premium bond trading above par.
Same bond. If the YTM rises from $4\%$ to $5\%$, find the new price and verify it equals par.
At each cash flow discounts at $1.05$. P = 5/1.05 + 5/1.05^2 + 105/1.05^3 = 4.7619 + 4.5351 + 90.7029 = \text{A\}100.00$. When coupon equals yield, the bond trades at par. A 100 bp rate rise dropped the price by A$2.78, an approximate modified duration of $2.78/102.78/0.01 = 2.71$ years.
Common mistakes
- โBond prices and yields move together. They move inversely by construction. Higher discount rates shrink the present value of every future cash flow. A 100 bp yield rise on a 10-year bond can erase 8 to 10\% of price.
- โYTM is the return you actually earn. YTM is the return only if you hold to maturity and reinvest every coupon at the same yield. Realised return differs whenever reinvestment rates change or the bond is sold before maturity. Horizon return analysis is the appropriate metric for most investors.
- โAll coupon bonds with the same maturity have the same price. Price depends on the coupon rate as well as YTM and maturity. Two 10-year bonds, one at a $3\%$ coupon and one at a $7\%$ coupon, trade at very different prices because their cash flow profiles differ even if their YTMs are equal.
Revision bullets
- โขPrice equals present value of all future cash flows
- โขPrice and yield move inversely by construction
- โขCoupon yield gives a premium bond
- โขCoupon yield gives a discount bond
- โขCoupon yield gives a par bond
- โขDuration measures price sensitivity to yield changes
Quick check
When market yields rise, bond prices
A 4-year bond with a $6\%$ annual coupon trades at par. What is its YTM?
Connected topics
In learning paths
Sources
- Hull (2022), ยง4.4Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.Covers bond pricing with both YTM and zero-rate discounting, plus duration and convexity for price sensitivity.
- Fabozzi (2021), Ch. 4Fabozzi, Frank J. Bond Markets, Analysis, and Strategies. 10th ed. MIT Press, 2021. ISBN 978-0-262-04627-3.Comprehensive textbook treatment of bond pricing, YTM, premium and discount bonds, and total return analysis.
- Australian Office of Financial Management. Treasury Bonds. AOFM, accessed 2026.Official issuer overview of Australian Government Treasury Bonds, including coupon structure and pricing convention.
- U.S. Department of the Treasury. Treasury Notes and Bonds. TreasuryDirect, accessed 2026.Description of US Treasury Notes and Bonds, coupon mechanics, and the price/yield auction process.
- Tuckman and Serrat (2022)Tuckman, Bruce and Angel Serrat. Fixed Income Securities: Tools for Today's Markets. 4th ed. Wiley, 2022. ISBN 978-1-119-83555-0.Advanced reference on coupon bond pricing, replication with zeros, and the relationship between YTM and the spot curve.