• A debt security (also called a debt instrument or fixed‑income security) is a financial asset created when one party lends money to another. The borrower (issuer) agrees to pay interest and to return the original amount lent (the principal) at a specified future date (the maturity). Common forms are bonds, certificates of deposit (CDs), municipal bonds, preferred stock when structured as debt-like instruments, and securitized products such as mortgage‑backed securities (MBS) or collateralized debt obligations (CDOs).
Key terms (brief)
– Principal: the original amount lent.
– Coupon (coupon payment): periodic interest paid by the issuer to the holder.
– Maturity: date when principal must be repaid.
– Default: failure of the issuer to make payments as promised.
– Credit rating: an independent agency’s assessment of an issuer’s ability to meet obligations.
How debt securities work (mechanics)
1. Issuance: Governments, corporations, and other entities sell debt securities to raise funds.
2. Income stream: Investors receive predetermined interest payments (coupons) during the life of the instrument.
3. Repayment: At maturity the issuer returns the principal to the investor (unless a default occurs).
4. Variations: Some debt instruments pay no periodic coupon (zero‑coupon securities) and instead are sold at a discount to face value. Others are backed by collateral (e.g., MBS, CDOs) or have municipal tax advantages.
Who issues debt securities
– Governments (sovereign and local governments) issue bonds to finance projects and operating needs.
– Corporations issue corporate bonds to fund growth, operations, or refinance other debt.
– Financial institutions package loans into collateralized securities (e.g., MBS, CDOs).
Why debt is often viewed as lower risk than equity
– Debt holders have a contractual right to interest and principal and are paid before shareholders if a company becomes insolvent. Because of this seniority and fixed payment structure, debt is generally considered less risky than equity, though not risk‑free.
Credit quality and yields
– Credit ratings (from agencies such as Moody’s, S&P, and Fitch) summarize perceived default risk. Higher-rated issuers (lower default risk) typically pay lower yields; lower-rated issuers must offer higher yields to attract investors.
– Example data
• Example data — hypothetical yields by credit rating (illustrative only)
• AAA/AA: 10‑year yield ~ 2.0% (lowest default risk)
• A/BBB: 10‑year yield ~ 3.5% (investment grade)
• BB/B: 10‑year yield ~ 6.5% (high yield / “junk”)
• CCC and below: yields vary widely, often > 10% (high default risk)
Note: these numbers are for illustration. Actual yields change with market conditions, issuance size, liquidity, and macro factors.
Worked pricing and interest‑rate sensitivity example (step‑by‑step)
Scenario: a plain vanilla coupon bond
• Par (face) value = $1,000
• Coupon = 5% annually, paid semiannually (coupon payment = $25 every 6 months)
• Remaining maturity = 10 years (n = 20 semiannual periods)
• Initial yield to maturity (YTM) = 5% annual (2.5% semiannual) -> price = par ($1,000)
Question: what is the price if market YTM falls to 4% annual (2.0% semiannual)?
Steps
1) Compute PV of coupon annuity:
PVcoupons = C * [1 − (1 + r)^−n] / r
where C = 25, r = 0.02, n = 20
PVcoupons = 25 * [1 − (1.02)^−20] / 0.02 ≈ 25 * 16.35145 = 408.79
2) Compute PV of principal:
PVprincipal = 1000 / (1.02)^20 ≈ 672.97
3) Bond price = PVcoupons + PVprincipal ≈ 408.79 + 672.97 = 1,081.76
Interpretation
• Price rises from $1,000 to $1,081.76 when YTM falls 100 basis points (1.00%).
• Percentage price change ≈ +8.18%.
• Approximate modified duration = −(%ΔP) / (Δy) ≈ 8.18 years (useful as a first‑order measure of rate sensitivity).
Key formulas and definitions
• Present value (price) of a fixed‑rate bond:
Price = Σ (Ct / (1 + r)^t) + (Par / (1 + r)^N)
where Ct = coupon at time t, r = periodic YTM
• Yield to maturity (YTM): the internal rate of return on a
bond if held to maturity and if all coupon payments are reinvested at the same rate. In practice YTM is the internal rate of return (IRR) that solves
Price = Σ (Ct / (1 + r)^t) + (Par / (1 + r)^N)
where Ct = coupon at time t, r = periodic YTM, N = total periods. Because r appears in each discount factor, YTM is found numerically (trial‑and‑error, financial calculator, or spreadsheet IRR function). YTM assumes no default and reinvestment of coupons at r.
Other common yield measures
– Current yield = Annual coupon / Price. Simple snapshot of income return; ignores principal gain/loss and timing. Example: if annual coupon = $50 and price = $1,081.76, current yield = 50 / 1,081.76 ≈ 4.62%.
– Yield to call (YTC) = IRR assuming issuer calls the bond at the call date/price; used for callable bonds.
– Yield to worst = The lowest yield of all possible yields (YTM, YTCs); conservative measure for callable/putable issues.
– Real yield = Nominal yield adjusted for inflation: (1 + nominal) / (1 + inflation) − 1 (approx: nominal − inflation for small rates).
Duration and convexity (rate sensitivity)
– Macaulay duration (years) = weighted average time to receive cash flows, weights = PV of each cash flow / Price.
– Modified duration = Macaulay / (1 + y) where y = yield per period. Modified duration approximates percent price change for a small parallel shift in yields: %ΔP ≈ −Modified_D × Δy.
– Convexity measures the curvature of the price–yield relationship. A second‑order approximation for small Δy:
%ΔP ≈ −Modified_D × Δy + 0.5 × Convexity × (Δy)^2.
Use convexity to improve accuracy for larger yield moves.
Types of debt securities (brief)
– Treasury bills, notes, bonds: Issued by the U.S. government; T‑bills mature ≤1 year, notes 2–10 years, bonds >10 years. Low credit risk; Treasuries are liquid.
– Corporate bonds: Issued by companies; range of credit quality, coupons, maturities; may be secured or unsecured, callable or convertible.
– Municipal bonds: Issued by state/local governments; many are exempt from federal income tax (and sometimes state/local taxes).
– Commercial paper: Short‑term unsecured corporate paper, typically <270 days.
– Certificates of deposit (CDs): Bank deposits with fixed maturity; FDIC insurance up to limits for U.S. banks.
– Asset‑backed and mortgage‑backed securities: Cash flows backed by pools of loans; introduce prepayment and pool‑specific risks.
Credit risk, seniority, and covenants
– Credit (default) risk: Probability issuer fails to pay interest or principal. Credit rating agencies (S&P, Moody’s, Fitch) assign ratings that summarize default risk.
– Seniority and security: Senior secured debt has claim on specific collateral; subordinated or junior debt is paid after senior claims in bankruptcy.
– Covenants: Contractual terms that restrict issuer actions (e.g., limits on additional debt); important for creditor protection.
Tax considerations (U.S. examples)
– Interest on U.S. Treasuries is subject to federal tax but exempt from state and local income taxes.
– Municipal bond interest is often exempt from federal tax and sometimes from state/local taxes if issued in the investor’s state.
– Corporate bond interest is taxable at federal and state levels. Check local rules and consult tax guidance.
Practical checklist for evaluating a debt security
1. Identify issuer and credit rating; check recent rating reports and trends.
2. Note coupon type (fixed, floating, zero), coupon frequency, and next coupon date.
3. Confirm maturity and any embedded options (call, put, convertibility).
4. Calculate yield measures: current yield, YTM (use IRR), and yield to call if applicable.
5. Compute or obtain duration and convexity to assess interest‑rate sensitivity.
6. Check liquidity (secondary market activity), issue size, and typical bid/ask spreads.
7. Review covenants, security/collateral, and seniority in capital structure.
8. Consider tax treatment and how it fits your portfolio needs.
9. Stress test scenarios: credit downgrade, interest‑rate shocks, and issuer default recovery assumptions.
Worked numeric recap (using prior numbers)
– Par = $1,000, coupon = 5% → annual coupon = $50.
– Price after YTM falls to 2% = $1,081.76 (from the earlier calculation).
– Current yield = 50 / 1,081.76 ≈ 4.62%.
– Given the price rose by ≈8.18% for a −1