What is a bond (simple definition)
– A bond is a fixed‑income security: a loan that an investor makes to an issuer (a government, municipality, or company). The issuer promises to pay periodic interest and to return the principal (face value or par value) at a specified future date (the maturity).
Key terms (defined once)
– Face value / par: the amount repaid at maturity.
– Coupon: the periodic interest payment, usually expressed as a percentage of par (coupon rate).
– Maturity: the date when the principal must be repaid.
– Debtholder / creditor: an investor who owns the bond.
– Yield‑to‑maturity (YTM): the annualized internal rate of return if you hold the bond to maturity and all payments occur as scheduled.
– Duration (modified duration): an estimate of how much a bond’s market price will change for a 1 percentage point change in interest rates (expressed as a percentage).
How bonds work (mechanics)
1. Issuance: An issuer sells bonds to raise money and states the coupon rate, face value, and maturity.
2. Payments: The issuer makes coupon payments at the stated intervals (e.g., annually or semiannually) and repays principal at maturity.
3. Secondary market: Bondholders can sell before maturity; market prices fluctuate based on interest rates, issuer credit quality, and time to maturity.
Why bond prices move (core relationship)
– Bond prices and market interest rates move in opposite directions. If prevailing interest rates rise, existing bonds with lower coupons become less attractive and trade at a discount. If rates fall, existing higher‑coupon bonds trade at a premium. This price movement equalizes the effective yield that new buyers receive.
Worked numeric illustration (simple, transparent assumptions)
Assume a bond with:
– Par = $1,000
– Annual coupon = 10% → $100 per year
– For a simplified illustration, treat the bond as a perpetual cash flow (a perpetuity) to show how coupon versus market yield drives price.
If market interest rates = 10%:
– Price = coupon / market rate = $100 / 0.10 = $1,000 (par)
If market interest rates fall to 5% (all else equal):
– Price = $100 / 0.05 = $2,000 (the bond trades at a premium so its $100 coupon yields 5% to a new buyer)
If market interest rates rise to 15%:
– Price = $100 / 0.15 ≈ $666.67 (the bond trades at a discount so the $100 coupon yields 15%)
Note: The perpetuity assumption simplifies the math to P = C / r. For standard bonds with finite maturity use the present‑value formula:
P = sum_{t=1}^{N} C/(1+y)^t + F/(1+y)^N
where C = coupon payment, F = face value, N = number of periods, and y = yield per period. YTM is the y that solves this equation.
Yield to maturity (YTM)
– YTM is the single discount rate that equals the present value of all future coupon and principal payments to the current price. Practically, deriving YTM requires solving the bond’s present‑value equation for y (often via a calculator or spreadsheet).
Duration (interest‑rate sensitivity)
– Modified duration gives an approximate percentage change in bond price for a 1 percentage point change in yield:
Approx % change ≈ –(modified duration) × Δyield.
– Longer maturities and lower coupons generally increase duration and therefore price sensitivity.
Bond characteristics and common variations
– Coupon type: fixed, floating, or inflation‑adjusted (e.g., Treasury Inflation‑Protected Securities).
– Credit risk: some issuers are considered safer (sovereigns, high‑grade corporates), others riskier (high‑yield or “junk” bonds).
– Special features: callable (issuer can redeem early), putable (holder can sell back early), convertible (convert into issuer’s equity).
– Tax status: some municipal bonds have tax advantages; rules vary by jurisdiction.
How coupon rate is determined
– At issuance the coupon rate is typically set relative to prevailing market rates and the issuer’s credit standing. A lower credit quality or longer maturity usually requires a higher coupon to attract buyers.
How bonds are rated
– Independent rating agencies (e.g., S&P Global, Moody’s, Fitch) assess issuer creditworthiness and assign letter grades that indicate likelihood of timely payment. Ratings affect the yield investors demand.
How to invest in bonds (practical steps)
Checklist before buying:
1. Confirm issuer type and credit rating.
2. Note coupon type and frequency.
3. Check maturity date and whether the bond is callable or has other options.
4. Calculate/compare current yield and yield‑to‑maturity.
5. Assess liquidity (can you sell easily?) and minimum purchase size.
6. Consider tax treatment and whether you need tax‑exempt bonds.
7. Understand how interest‑rate changes will affect price (duration).
8. Decide whether to buy individual bonds or use bond funds/ETFs.
Ways to buy:
– Directly on broker platforms (most online brokers offer corporate, municipal, and Treasury securities).
– TreasuryDirect (for U.S. Treasury securities) at the U.S. Treasury’s website.
– Bond mutual funds or exchange‑traded funds (ETFs) for diversified exposure without buying many individual issues.
Short checklist to carry with you before an order
– Issuer name and credit rating
– Par value and coupon rate
– Coupon frequency and maturity date
– Price (market) and computed YTM
– Call/put provisions
– Expected holding horizon and liquidity needs
– Tax implications
Practical notes
– If you plan to hold
to maturity, remember that interim price movements matter less for total return but reinvestment and credit events still matter.
Practical notes (continued)
– If you plan to hold to maturity: price volatility is less important for the final principal return, but reinvestment risk is real — the coupons you receive may have to be reinvested at lower (or higher) rates than the bond’s coupon. Also check call provisions: a callable bond can be redeemed early, shortening your expected cash‑flow horizon.
– If you plan to trade before maturity: focus on liquidity (bid–ask spread), accrued interest, and how interest‑rate moves affect price (duration and convexity).
– Laddering: buy bonds with staggered maturities so portions of principal mature regularly; this reduces reinvestment risk and smooths cash flows.
– Barbell and bullet strategies: a barbell concentrates in short and long maturities (higher income + liquidity); a bullet concentrates around one maturity (reduces refinancing needs).
– Use bond funds/ETFs for diversification and daily liquidity, but remember they don’t have a maturity date (no guaranteed return of principal) and are subject to market price fluctuations.
Key mechanics and formulas (short)
– Current yield = annual coupon payment / current market price.
Example: $1,000 par, 5% coupon, price $950 → current yield = 50 / 950 = 5.263%.
– Approximate YTM (yield to maturity) shortcut:
YTM ≈ [Annual coupon + (Par − Price)/Years to maturity] / [(Par + Price)/2].
Example: $1,000 par, 5% coupon (annual $50), price $950, 5 years to maturity:
YTM ≈ [50 + (1,000 − 950)/5] / [(1,000 + 950)/2] = (50 + 10) / 975 ≈ 6.15% (approximate).
Note: exact YTM requires solving for the discount rate that sets discounted cash flows = price (use a financial calculator or spreadsheet RATE/IRR).
– Accrued interest (between coupon dates) = coupon per period × (days since last coupon / days in coupon period).
Example: semiannual coupon = $25, 60 days since last coupon, period = 182 days → accrued = 25 × (60/182) ≈ $8.24.
– Clean vs. dirty price: clean price excludes accrued interest; dirty (or invoice) price = clean price + accrued interest. Brokers commonly show clean prices.
– Duration (price sensitivity): modified duration ≈ Macaulay duration / (1 + YTM/periods per year). Rule of thumb: approximate % price change ≈ −(modified duration) × (change in yield in decimal).
Example: modified duration = 6 years, yield rises 1% → price ≈ −6% change (ignoring convexity).
– Convexity adjusts the duration estimate for larger yield moves; use it for more accuracy.
Credit, taxes, and settlement — practical checklist
– Credit risk: check issuer ratings from S&P, Moody’s, or Fitch; read the bond’s offering documents for covenants and collateral. Ratings can change.
– Taxes: many municipal bonds are exempt from federal income tax; some are also state‑exempt if you live in the issuer’s state. Some municipals may be subject to the Alternative Minimum Tax (AMT). Corporates and Treasuries have different tax treatments—confirm with IRS guidance and your tax advisor.
– Settlement and trading details:
– Settlement conventions vary by market and security type. Many corporate and municipal trades settle T+2 (trade date plus two business days); U.S. Treasuries often
settle T+1 (trade date plus one business day). International bond markets and special instruments (repo, sovereign issues, Eurobonds) may use different cycles, so always confirm the convention for the specific security and market.
Settlement and trading — practical checklist (continued)
– Confirm the settlement date: verify whether the trade is T+0, T+1, T+2, or some other convention for that market and security.
– Verify the security identifier: CUSIP (U.S.), ISIN (international), or other unique ID to avoid a delivery error.
– Check accrued interest: brokers quote “clean” prices (price excluding accrued interest); the buyer pays the “dirty” or full price (clean price + accrued interest) at settlement.
– Day-count convention: determine whether the bond uses Actual/Actual, 30/360, or another convention — it affects accrued interest and yield calculations.
– Delivery and clearing method: confirm whether the issue is book-entry through a central securities depository (e.g., DTC/Depository Trust Company in the U.S.) or requires physical certificate handling.
– Corporate actions: check for upcoming coupon dates, call/put provisions, sinking-fund requirements, or conversion rights that may affect value before settlement.
– Tax and withholding: confirm tax status (federal/state exemptions for municipals, possible AMT exposure, foreign withholding) ahead of settlement.
Worked numeric example — accrued interest and cash required at settlement
Assumptions:
– Face (par) value = $1,000
– Coupon = 6% per year, paid semiannually → $30 every 6 months
– Clean price quoted = 101.25% of par = $1,012.50
– Days since last coupon = 60
– Coupon period length = 182 days (approximate; actual may follow actual/actual)
Step 1 — accrued interest formula:
Accrued interest = (Coupon per year × Par) × (Days since last coupon / Days in coupon period)
= (0.06 × $1,000) × (60 / 182)
= $60 × 0.32967 ≈ $19.78
Step 2 — cash to be paid at settlement (dirty price):
Dirty price = Clean price + Accrued interest
= $1,012.50 + $19.78 = $1,032.28
So the buyer will pay approximately $1,032.28 at settlement for one $1,000 par bond under these assumptions. Note: use the exact day-count and calendar days from the bond’s documentation for precise amounts.
Practical pre‑trade and post‑trade checklists
Pre‑trade (before order)
1. Read the offering documents and prospectus for covenants, collateral, and call/put features.
2. Check current credit rating(s) and recent rating actions.
3. Confirm tax status and potential AMT impact.
4. Verify settlement convention and required cash/margin.
5. Note liquidity: average daily volume and bid-ask spread.
Post‑trade (after order)
1. Review trade confirmation for CUSIP/ISIN, coupon, coupon dates, settlement date, price (clean), and accrued interest.
2. Confirm clearing/custody instructions (broker, DTC number, or custodian).
3. Monitor settlement: ensure funds are available and delivery occurs; report fails immediately to broker.
4. Track corporate actions and upcoming payments; update your portfolio records.
Common pitfalls and how to avoid them
– Misunderstanding quotes: remember bond quotes often omit accrued interest (clean price). Always ask for the dirty price or compute accrued interest yourself.
– Ignoring day-count convention: small differences in day counts can change accrued interest and yield calculations—use the bond’s specified convention.
– Overlooking call or put features: callable bonds can be redeemed early, which affects duration and expected cash flows.
– Assuming constant credit quality: ratings can change; monitor issuer financials and news.
Where to check authoritative details
– Prospectus/Offering Memorandum: the definitive source for settlement, call features, covenants, coupon schedule, and day-count convention.
– Broker trade confirmation: legal record of the transaction, including settlement instructions.
– Central securities depositories and clearinghouses: e.g., DTCC provides operatational details for U.S. securities.
Selected references
– Investopedia — Bond Definition and Basics: https://www.investopedia.com/terms/b/bond.asp
– U.S. Department of the Treasury — TreasuryDirect: settlement and payment details for Treasury securities: https://www.treasurydirect.gov
– U.S. Securities and Exchange Commission — Investor Bulletin: Bonds: https://www.sec.gov/oiea/investor-alerts-and-bulletins/ib_bonds
– Additional useful references
– FINRA — Bonds: basic rules, markets, and investor education: https://www.finra.org/investors/learn-to-invest/types-investments/bonds
– Municipal Securities Rulemaking Board (MSRB) — EMMA (official municipal market info): https://emma.msrb.org
– Federal Reserve Economic Data (FRED) — historical yields and series: https://fred.stlouisfed.org
Quick pre-trade checklist (use this every time)
1. Confirm instrument identity
– CUSIP/ISIN, issuer name, issue date, maturity date, coupon schedule.
2. Read the prospectus/offering memorandum
– Note call/put features, sinking-fund provisions, covenants, and day-count convention.
3. Check settlement and tax treatment
– Settlement date, accrued interest rules, withholding/tax status for your jurisdiction.
4. Measure credit risk
– Review latest ratings, issuer financial statements, and recent news; treat ratings as opinion, not guarantee.
5. Calculate expected cash flows
– Build a schedule of coupon dates, coupon amounts, principal repayment, and any embedded option dates.
6. Compute yield measures
– At minimum compute current yield and an approximate yield-to-maturity (YTM); get exact YTM from a calculator or spreadsheet.
7. Consider liquidity and transaction costs
– Bid–ask spread, broker commissions, market depth, and potential price impact for larger orders.
8. Match to your goals
– Check how the bond’s term, risk, and cash flows fit your time horizon and cash needs.
Worked numeric example — approximate yield to maturity (YTM)
Definition: Yield to maturity (YTM) is the single discount rate that equates a bond’s present value of future cash flows (coupons and principal) to its current market price. Exact YTM requires solving an equation; the following gives a quick approximation that is handy for screening.
Approximate YTM formula:
YTM ≈ [C + (F − P) / n] / [(F + P) / 2]
where
C = annual coupon payment
F = face (par) value
P = current price
n = years to maturity
Example:
– Face F = $1,000
– Coupon C = $60 (6% of $1,000)
– Price P = $950
– Years to maturity n = 5
Step-by-step approximate YTM calculation (use the approximate formula given earlier):
1) Compute the annual capital gain (or loss) component: (F − P) / n = ($1,000 − $950) / 5 = $50 / 5 = $10.
2) Add the coupon to get the numerator: C + (F − P) / n = $60 + $10 = $70.
3) Compute the average of face and price for the denominator: (F + P) / 2 = ($1,000 + $950) / 2 = $975.
4) Divide numerator by denominator: 70 / 975 ≈ 0.07179 → 7.18% approximate YTM.
Interpretation: the approximate YTM (≈7.18%) exceeds the coupon rate (6%), which is consistent with the bond trading at a discount (price below par). This approximation is useful for quick screening.
When to use the approximation and its limits
– Use it for quick, back-of-envelope comparisons or screening bonds.
– It assumes level annual coupon payments and evenly spread capital gain/loss over remaining years.
– It becomes less accurate for large price deviations from par, for long maturities, for non‑annual coupon frequencies, or for bonds with embedded options (callable, putable).
– Exact YTM solves the present-value equation: P = sum_{t=1}^{n} C/(1+YTM)^t + F/(1+YTM)^n. Solving requires a financial calculator, spreadsheet, or numerical root-finding.
How to get an exact YTM (practical options)
– Spreadsheet (Excel/Google Sheets): use the RATE or YIELD functions. Example: in Excel, YIELD(settlement, maturity, rate, pr, redemption, frequency).
– Financial calculator: use the bond or IRR/YTM routine (input N = n, PMT = coupon, FV = F, PV = −P).
– Programming / numerical solver: use a root-finding method (Newton‑Raphson, bisection) on the PV equation; start from the approximation above as an initial guess.
Checklist before relying on a YTM number
– Confirm coupon frequency (annual, semi‑annual) and adjust formulas accordingly.
– Check for embedded options (call/put) — yields to call/put or option‑adjusted yields may be more relevant.
– Consider taxes and transaction costs (they affect your net return).
– Remember reinvestment risk: YTM assumes coupons are reinvested at the same rate.
– For inflation-sensitive planning, compare real yields (nominal yield − expected inflation).
Worked numeric note (semiannual coupons): if coupons are semiannual, adjust C, n, and convert the periodic YTM to an annual nominal or effective rate before interpreting.
Educational disclaimer
This explanation is educational only and not personalized investment advice. YTM is a model-based measure with assumptions; use appropriate tools and consider consulting a licensed advisor for decisions that affect your portfolio.
References
– Investopedia — Bond Definition: https://www.investopedia.com/terms/b/bond.asp
– U.S. Securities and Exchange Commission — Bonds: https://www.sec.gov/reportspubs/investor-publications/investorpubsbondbasicshtm.html
– U.S. Department of the Treasury — Treasury Securities: https://www.treasurydirect.gov/indiv/research/indepth/treasurydirect.htm
– FINRA — Bonds: https://www.finra.org/investors/learn-to-invest/types-investments/bonds