Library/CFA (Chartered Financial Analyst)/FIXED INCOME: CFA® Program Curriculum, 2026 • Level I • Volume 6/Learning Module 6 Fixed-Income Bond Valuation: Prices and Yields

Learning Module 6 Fixed-Income Bond Valuation: Prices and Yields

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Pricing bonds and yield-to-maturity5 min

Bond valuation is discounted cash flow analysis: the price equals the present value of promised coupon and principal payments discounted at the market discount rate(s). For fixed-coupon bonds with N periods, PV = sum_{t=1..N} PMT_t/(1+r)^t + FV/(1+r)^N. When coupon rate equals market discount rate, bond issues at par; coupon < market rate implies discount; coupon > market rate implies premium. Yield-to-maturity (YTM) is the single internal rate of return that equates present value of cash flows to price; an investor earns the YTM only if the bond is held to maturity, the issuer makes all payments, and coupons are reinvested at the YTM. Bonds trade on coupon dates or between them: dealers quote the flat (clean) price; accrued interest = (days since last coupon / days in coupon period) * PMT using a day-count convention (common: actual/actual, 30/360). Full (dirty) price = clean price + accrued interest. Bond prices and yields move inversely. Price sensitivity to yield changes depends on coupon and maturity: lower coupon and longer maturity produce greater percentage price change for a given yield move (coupon and maturity effects). The price-yield curve is convex: price increases more for a yield decline than it decreases for a yield increase of equal magnitude. Constant-yield price trajectories show prices approach par over time (pull-to-par). Matrix pricing estimates yields/prices for illiquid bonds using comparable, traded bonds of similar coupon, maturity, and credit; interpolation (often linear) across maturities yields an estimate for the target bond. Periodicity matters: yields are annualized with assumed compounding frequency (periodicity usually matches coupon frequency). Converting APRs across compounding frequencies uses (1+APR_m/m)^m = (1+APR_n/n)^n. Money-market instruments use special quoting (discount rates or add-on rates) and periodicity (360 or 365), so convert to a common basis for comparison (bond-equivalent yield). Day-count conventions affect accrued interest and government-equivalent yields. Floating-rate instruments have quoted margins over a reference rate; discount margin is the required spread that equates price to market. Embedded options (callable bonds) require yield-to-call, yield-to-worst, and option-adjusted spreads (OAS); callable bonds are valued considering option value, which reduces investor price. Zero and negative yields are possible; zero-coupon bonds yield r from PV = FV/(1+r)^t. Spreadsheet functions (PV, FV, YIELD, PRICE, RATE, IRR) are commonly used for valuation. Key practical points: quote conventions (clean price), compute accrued interest with stated day-count, use spot or par or forward curves for term-structure valuation when needed, and apply matrix pricing when market transactions are scarce.

Key Points

Bond price = PV of coupons + PV of principal using market discount rates
Par, discount, premium determined by coupon vs market rate
YTM is IRR if held to maturity and coupons reinvested at YTM
Flat (clean) price + accrued interest = full (dirty) price
Lower coupon and longer maturity increase price sensitivity to yield
Convexity: asymmetric price response to yield changes

Inter-period pricing, day counts, and conventions5 min

When a bond trades between coupon dates, calculate accrued interest = (t/T)PMT where t is days since last coupon and T is days in coupon period using a stated day-count (common conventions: actual/actual and 30/360). Full price = flat price + accrued interest. Spreadsheet PRICE function computes flat price (clean price). Exact settlement and coupon dates, and whether payments fall on weekends/holidays, determine street vs true yield conventions. Government-equivalent yields convert corporate 30/360 yields to actual/actual by scaling (e.g., multiply by 365/360 as an approximation). Matrix pricing: identify comparable bonds by maturity, coupon, and credit, compute their yields, average or interpolate yields across maturities, then discount the target bond’s cash flows using the interpolated yield to get an estimated price. For money-market instruments quoted on discount rates: PV = FV(1 - Days/Year DR). For add-on quoted money-market instruments: PV = FV / (1 + Days/Year AOR). Convert discount-rate quotes to bond-equivalent yields for comparison.

Key Points

Accrued interest depends on day-count convention
Flat price quoted; full price paid includes accrued interest
PRICE and PV spreadsheet functions are standard tools
Government-equivalent yield restates corporate yields to actual/actual
Matrix pricing uses comparable, actively traded bonds

Yields, spreads, and callable bond issues5 min

Yield periodicity affects stated yield (semiannual bond basis, quarterly, monthly). Convert yields across compounding frequencies using (1+APR_m/m)^m = (1+APR_n/n)^n. Current yield = annual coupon / flat price (simple measure). Z-spread is a constant spread over the benchmark spot curve that equates PV of cash flows to price. G-spread is yield minus government benchmark yield (single tenor); I-spread is yield minus swap rate for the tenor. Embedded options require yields-to-call and yield-to-worst calculations; option-adjusted spread (OAS) adjusts Z-spread for option value. Floating-rate instruments quote a margin over a reference rate (MRR). Discount margin is required spread to match market price; if quoted margin > discount margin floater trades at a premium, and vice versa. Important practical metrics: yield-to-maturity, current yield, G-spread, I-spread, Z-spread, OAS, yield-to-call, and yield-to-worst. Matrix pricing and tools such as Bloomberg FIRV provide relative-value spreads, z-spread and other analytics.

Key Points

Yield periodicity must be consistent when comparing yields
G-spread, I-spread, Z-spread decompose YTM relative to benchmarks
Callable bonds need yield-to-call and yield-to-worst measures
OAS adjusts for option values; discount margin applies to floaters

Questions

Question 1

A 5-year fixed-rate bond with semiannual coupons has a stated coupon of 4.0% and the market's required semiannual discount rate is 2.5% per period. Which statement is correct about the bond's price at issuance?

Learning Module 6 Fixed-Income Bond Valuation: Prices and Yields

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