Learning objectives
By the end you can:
- Price a bond off a discount (spot-rate) curve (discount each cash flow at the spot rate matching its own maturity rather than one flat assumed yield) and explain, with a worked case, when and why curve-consistent pricing and flat-yield pricing diverge (and by how much, for a normal, an inverted, and a humped curve).
- Solve for yield to maturity (YTM) by iteration given an observed market price, explaining why no closed-form formula exists and connecting the calculation explicitly to an internal-rate-of-return (IRR) solve.
- Compute current yield, and correctly state, and prove numerically, both directions, the ordering among coupon rate, current yield, and YTM for a premium bond and for a discount bond.
- Compute the full chain of money-market yield measures for a discount instrument (a T-bill, a CD, commercial paper) (bank-discount yield, holding-period yield, money-market (add-on) yield, bond-equivalent yield (BEY), and effective annual yield (EAY)) and explain why each fixes a specific limitation of the one before it.
- Compute yield to call (YTC) across a full call schedule and identify yield to worst (YTW), and demonstrate (with a numeric counter-example) why YTW can never be assumed to sit at the nearest call date or at maturity without actually computing every redemption scenario.
- Decompose a bond's realized total return over a holding period into its three sources (coupon income, reinvestment income, and capital gain/loss) and use that decomposition to explain, quantitatively, how a rate move splits its effect between reinvestment income and resale price.
- Price a corporate bond as risk-free-rate-plus-spread, applying (not re-deriving) E11.01's credit-triangle relationship to translate an observed spread into an implied default probability.
- (Productivity objective: R10 duality.) Use an AI tool to accelerate drafting a yield-conversion function or explaining a convention, while treating every AI-stated number, call price, or day-count fact as unverified until traced to a primary source (a term sheet, the FIMMDA handbook, SEC EDGAR, FBIL/CCIL data), because this region is where a fluent, wrong number does the most damage.
- Situate every calculation in both India and US institutional conventions, on-the-run G-Secs, CCIL/FBIL/FIMMDA quoting conventions, SDLs, and INR OIS/MIBOR on one side; on-the-run UST, agency MBS, corporate callables, and CDX on the other, enough to know which convention governs a given instrument and where to confirm it.
The duality, stated once (R10). Objectives 1–7 and 9 are the understanding gate, the mastery check rewards computing correctly, not knowing which button to press. Objective 8 is the productivity payoff you carry forward: knowing that AI can draft the scaffolding of a pricing script or explain a convention in plain language, but that in this region, where a wrong number is invisible until it costs money, verification against your own Python arithmetic and a named primary source is never optional.
Prerequisites & connections
Builds on. M3.01 (time value of money): you already price a bond given one flat yield ("a bond is an annuity plus a zero"); this module keeps that arithmetic and does two new things to it: generalizes the single discount rate to a full spot-rate curve, and inverts the equation to solve for the yield a market price implies. M1.08 §4.1 (debt at amortized cost), you already built effective-interest amortization schedules for a bond already on an issuer's books at a given market yield; that is the accounting lens, looking backward from a known yield. This module is the investor's lens, looking forward from an observed price to the yield, and from a curve (not one rate) to a price. M7.03 §4.10–4.13 (the yield curve, curve shapes, and duration), you already know what a spot/discount curve is, what determines its shape (expectations plus term premium), how it moves (the four steepener/flattener moves), and the intuition behind duration; this module does not re-derive any of that, it takes a curve as a given input and does the pricing arithmetic on top of it. E11.01 §11.2 (spreads for credit), you already decomposed a corporate yield into risk-free rate plus credit spread, and spread into PD × LGD (the credit triangle); this module applies that relationship as a given building block in one worked example, it does not re-teach it.