The Analyst's Path

Phase 12 · Finance Plus, AI and the quant-code track · free

Bond Pricing & Yield Measures

FI1.01 · 13,967 words

A note on synthetic instruments and real mechanics, before anything else. Every bond, curve, bank, and issuer used for arithmetic in this module (G-Secs, corporate NCDs, T-bills, CDs, callable notes) is synthetic: invented so the numbers are clean and no real…

Learning objectives

By the end you can:

  1. 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).
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. (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.
  9. 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.

This page is an excerpt

The full module runs to 13,967 words and carries the worked examples, the tables, the quiz that gates the next module and the spaced-repetition deck built from it. All of it is free and none of it needs an account.