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Introduction to Fixed Income Bonds, Market Terms, and Interest Calculations
FINANCIAL
Ryan Cheng
7/19/20253 min read
Fixed income securities represent a foundational pillar of global financial markets. For investors, they offer a source of steady income and play a crucial role in diversifying portfolios and mitigating risk. To navigate this landscape successfully, however, a firm grasp of its core principles is essential.
An Overview of Bond Categories
At its core, a bond is a loan. An issuer borrows capital from an investor and, in return, promises to make periodic interest payments (known as coupons) and repay the principal amount at a future date, known as maturity. These instruments vary widely based on who issues them.
Among the most prevalent are corporate bonds, which are issued by companies to raise capital for operations or expansion. The risk and potential return of these bonds are directly tied to the financial health and creditworthiness of the issuing corporation, making thorough due diligence a prerequisite for investment.
On the safer end of the spectrum are Treasury bonds, long-term debt instruments issued by the U.S. federal government with typical maturities of 10, 20, or 30 years. Backed by the full faith and credit of the government, they are considered to have minimal credit risk and serve as a benchmark for safety in the financial world.
Municipal bonds, often called "munis," are issued by state, city, or other local governments to fund public projects like schools, hospitals, and infrastructure. Their most distinct feature is that the interest income is often exempt from federal taxes, and sometimes state and local taxes as well, making them particularly attractive to certain investors.
Finally, agency bonds are issued by government-sponsored enterprises (GSEs) or federal agencies. While not directly guaranteed by the U.S. government, their close association provides them with a high degree of security. These bonds are often used to fund public interest projects, such as mortgage financing, and may include provisions that allow the issuer to repay the bond before its maturity date.
Language of the Bond Market
To engage with the fixed-income market, one must first understand its language. The price a dealer is willing to pay for a security is known as the bid price, while the price at which they are willing to sell is the ask price or offer price.
Changes in rates and yields are measured in basis points (bps). A single basis point is equivalent to one-hundredth of a percentage point (0.01%), meaning 100 basis points equal 1%.
While many financial assets are quoted in decimals, the pricing for U.S. Treasury bonds follows a unique convention. The minimum price fluctuation, or tick, is based on fractions. Treasury prices are quoted in units of 32nds of a dollar. For example, a quote of "98-22" represents 98 and 22/32, which translates to a decimal price of 98.6875. A plus sign + in a quote, such as "100-13+", indicates an additional half of a 32nd (or 1/64), so this quote means 100 and 13.5/32nds, for a decimal price of 100.421875.
Interest: Simple, Compound, and Continuous
The method used to calculate interest dramatically impacts an investment's return over time.
The most straightforward method is simple interest, which is calculated solely on the original principal amount. It is commonly used for short-term instruments like repurchase agreements (repos). The future value (FV) is found using the formula: FV = PV (1 + r (t/365)), where PV is the present value, r is the annual interest rate, and t is the number of days.
A more powerful engine for growth is compound interest, where interest is calculated on the initial principal plus all of the accumulated interest from previous periods—often described as "interest on interest." The frequency of compounding significantly affects the outcome. For an investment compounded m times per year for n years at an annual rate R, the future value is given by the general formula: FV = PV (1 + R/m)^(nm).
The theoretical limit of this concept is continuous compounding, where the frequency of compounding becomes infinite. While a theoretical construct, it is a cornerstone of financial theory, especially in pricing derivatives, because of its elegant mathematical properties. The future value under continuous compounding is calculated as FV = PV * exp(rt), where ris the continuously compounded rate and t is the time in years. This simplifies many calculations and helps in understanding advanced concepts like duration and convexity.
It is important to know how to convert between discrete (e.g., annual, semi-annual) and continuous rates, as they are simply different ways of expressing the same effective return. The formulas for conversion are:
To convert a discrete rate R (compounded m times per year) to a continuous rate r: r = m * ln(1 + R/m)
To convert a continuous rate r back to a discrete rate R: R = m * (e^(r/m) - 1)