Bond
A bond is a fixed income debt security in which the issuer (government, corporation, or municipality) borrows capital from investors for a defined period, committing to pay periodic interest payments (coupons) and repay the principal (face value) at maturity, in exchange for the funds received at issuance.
Key takeaways
- The key economic variables of a bond are: face value (par), coupon rate, maturity date, yield to maturity (YTM), and current price — with price and yield moving inversely.
- Bond prices are the present value of all future cash flows (coupons plus face value) discounted at the prevailing yield to maturity.
- Duration measures a bond's price sensitivity to changes in yield; a bond with 5 years modified duration will decline approximately 5% in price for a 1% rise in yield.
- Credit risk (default probability and recovery rate), interest rate risk (duration), and inflation risk are the three primary risks borne by bond investors.
- The yield curve — plotting yields for bonds of the same credit quality but different maturities — is the central analytical framework for fixed income markets and a key indicator of monetary policy and economic expectations.
Explanation
A bond's cash flow structure is simple: the issuer receives the principal (or proceeds) at issuance and commits to (1) paying periodic coupon interest — typically semi-annually for U.S. corporate and government bonds — and (2) repaying the full face value at maturity. The coupon rate is fixed at issuance and expressed as a percentage of face value; a $1,000 face value bond with a 5% coupon pays $25 every 6 months. The bond's price in the secondary market fluctuates with interest rates and credit perceptions, but the coupon and maturity are fixed contractual obligations.
The fundamental pricing equation is: Price = Σ[C_t / (1+y)^t] + FV / (1+y)^T, where C_t is the coupon payment at time t, FV is face value, T is time to maturity, and y is the yield to maturity (YTM) per period. This inverse relationship between price and yield is the most important concept in bond mathematics: when market interest rates rise, the fixed cash flows of existing bonds are discounted at a higher rate, reducing their present value and price. Conversely, when rates fall, existing bond prices rise. A bond trading at par (price = 100) has a YTM equal to its coupon rate; a bond at a discount (price < 100) has a YTM above its coupon; a bond at a premium (price > 100) has a YTM below its coupon.
Duration is the primary risk metric for fixed income portfolios. Macaulay duration is the weighted average time to receipt of all cash flows, where weights are the present value proportions. Modified duration — derived from Macaulay duration — measures the percentage change in price per 1% change in yield: ΔP/P ≈ −D_mod × Δy. For a 10-year Treasury with modified duration of 7.5, a 100bps rise in yields produces approximately 7.5% price decline. Portfolio duration management — extending duration when rates are expected to fall, shortening when rates are expected to rise — is the primary active strategy in fixed income portfolio management.
Beyond the vanilla coupon-paying bond, the market includes numerous variations: zero-coupon bonds (no coupons, issued at deep discount); floating rate notes (coupon resets periodically to a reference rate plus spread); inflation-linked bonds (principal and/or coupon linked to a price index); callable bonds (issuer can redeem early); convertible bonds (can be converted to equity); and asset-backed securities (cash flows collateralized by specific assets). Each variation modifies the basic bond risk/return profile in specific ways relevant to different investment objectives.
Formula
Bond Price = Σ[C / (1+y)^t] + FV / (1+y)^T, for t = 1 to T Current Yield = Annual Coupon / Price Yield to Maturity: solve for y in the above equation Modified Duration = Macaulay Duration / (1 + y/m), where m = coupon frequency
Example
A 10-year U.S. Treasury bond is issued with a 4.5% coupon and a face value of $1,000. The bond pays $22.50 every 6 months and $1,000 at maturity in year 10. If the 10-year Treasury yield subsequently rises from 4.5% to 5.5% (a 100bps increase), the bond's price falls from $1,000 to approximately $924 — a loss of $76, or 7.6%. This price change is consistent with the bond's modified duration of approximately 7.6 years. An investor who bought the bond at $1,000 and holds to maturity receives all coupons and the full $1,000 face value regardless of intermediate price fluctuation — illustrating the distinction between mark-to-market volatility and the 'return if held to maturity' concept central to fixed income investing.
Related terms
Coupon Rate Current Yield Dirty Price Duration Equity Exchange Face Value Inflation Macaulay Duration Mark To Market Modified Duration Normal Yield Curve