Fixed Income — Study Notes

CFA® Level I topic weight 11–14% · pricing, risk measures, and credit

Bond features & structures

The indenture is the legal contract: principal, coupon, maturity, collateral, and covenants. Affirmative covenants require actions (pay taxes, maintain insurance); negative covenants restrict them (limits on additional debt, asset sales, dividends) — negative covenants are what actually protect bondholders.
Coupon structures: fixed, floating (reference rate + quoted margin, resetting each period), zero-coupon (issued at a discount, all return at maturity), step-up, and payment-in-kind. Floaters have very low interest rate risk because coupons reset toward market rates.
Embedded options: a call favors the issuer (bond is called when rates fall, capping price upside); a put favors the investor; convertibles add equity upside. Option value explains why callable bonds yield more and putable bonds yield less than otherwise-identical straight bonds.

Pricing & yields

Price and yield move inversely. A bond priced above par (premium) carries a coupon above its yield; below par (discount), below its yield. As maturity approaches, price is pulled to par regardless of direction.
YTM is the single discount rate equating a bond’s promised cash flows with its price — it assumes the bond is held to maturity and coupons are reinvested at the YTM. Spot rates discount each cash flow at its own maturity’s rate; the no-arbitrage price uses spots.
Forward rates are future-period rates implied by today’s spot curve — e.g., the 1-year rate one year from now makes investing two years at the 2-year spot equivalent to rolling two 1-year investments.
Full vs flat price: the buyer pays the full (dirty) price = flat (clean) quoted price + accrued interest. Bonds are quoted flat but settle full.
Money market yields differ by convention: discount-rate instruments (T-bills) understate the investor’s true return relative to add-on yields — conversion questions are common.

Duration & convexity

Macaulay duration is the weighted-average time to receive cash flows; modified duration = Macaulay ÷ (1 + yield per period) and gives price sensitivity: %Δprice ≈ −ModDur × Δyield.
What drives duration: longer maturity generally raises it; higher coupon and higher yield lower it (more value arrives earlier). A zero-coupon bond’s Macaulay duration equals its maturity — the maximum for a given maturity.
Effective duration uses parallel curve shifts and repricing — required for bonds with embedded options, whose cash flows change as rates move.
Convexity corrects the duration line for curvature: price rises more when yields fall than it drops when yields rise (for option-free bonds). The full estimate: %Δprice ≈ −ModDur×Δy + ½×Convexity×(Δy)². Callable bonds exhibit negative convexity at low yields as the call caps appreciation.
Money duration scales duration by position size; the price value of a basis point (PVBP) is the money change for a 1 bp yield move.
Reinvestment vs price risk: rising rates hurt prices but help coupon reinvestment; the investment horizon relative to Macaulay duration decides which effect dominates.

Credit & securitization

Expected loss = probability of default × loss given default. Loss given default = 1 − recovery rate. Credit spreads compensate for expected loss plus a risk premium; spreads widen when the economy weakens.
Seniority ranking: secured before unsecured, senior before subordinated. Recovery rates follow the ranking; structural subordination puts holding-company creditors behind operating-company creditors.
The “four Cs” of credit analysis: capacity (leverage and coverage ratios), collateral, covenants, character. Ratings agencies grade issuers and issues; notching separates an issue’s rating from the issuer’s based on seniority and security.
Securitization: assets (mortgages, auto loans) are sold to a bankruptcy-remote special purpose entity that issues tranched securities. Tranching redistributes credit risk (senior/subordinated waterfall); mortgage pools add prepayment risk — contraction when rates fall, extension when rates rise.

Common traps

Assuming longer maturity always means higher duration — the coupon and yield effects can produce exceptions among deep-discount long bonds.
Forgetting the buyer pays accrued interest — quoted (flat) price is not the settlement amount.
Using modified duration for callable bonds — embedded options require effective duration, and callables show negative convexity when yields are low.
Reading a call feature as investor-friendly — calls benefit issuers; the investor is compensated through a higher yield.
Equating YTM with a guaranteed realized return — it holds only if coupons are reinvested at the YTM and the bond is held to maturity.

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