Core Economic Definitions & Theoretical Mechanisms
Bonds pay fixed coupon payments. When prevailing market interest rates rise, newly issued bonds offer higher yields, making existing bonds with lower coupons less attractive. To compensate, the price of existing bonds must fall until their yield matches the new market rate.
Underlying Mathematical Formulas & Equations
Bond Price (P) = Sum [ C / (1+r)^t ] + F / (1+r)^T, where C=coupon, r=discount rate, F=face value, T=maturity. Macaulay Duration measures price sensitivity.
Concrete Worked Numerical Example
Consider a 10-year bond with a face value of $1,000 and a 5% annual coupon. If the market rate is 5%, the bond prices at $1,000. If the market rate rises to 6%, the present value of the bond’s cash flows drops to approximately $926.40.
Real-World Empirical Application: Historical Case Study
During the 2022 Federal Reserve tightening cycle, interest rates rose rapidly from near zero to over 4%, causing historic losses in long-duration Treasury bonds as prices plummeted to adjust to new yields.
Limitations, Criticisms, and Competing Schools of Thought
While the inverse relationship is an ironclad mathematical certainty for fixed-rate bonds, floating-rate bonds mitigate this risk. Convexity means price declines are cushioned as rates rise, but price gains accelerate when rates fall.
Comprehensive FAQ Section
What is bond duration?
Duration measures a bond’s price sensitivity to interest rate changes. A duration of 5 means a 1% rate increase causes a 5% price drop.
Academic References & Primary Source Citations
- Fabozzi, F. J. (2012). Fixed Income Analysis. John Wiley & Sons.
- Macaulay, F. R. (1938). The Movements of Interest Rates, Bond Yields and Stock Prices in the United States.