Chapter 3: Fixed Income Securities
This is the descriptive survey chapter that Ch. 2's math gets applied to — a tour of what actually trades: money markets, government and corporate bonds, munis, swaps, mortgages, and asset-backed debt. It's institutional detail rather than new theory, but it comes with a genuinely useful trap to know about: a T-bill's quoted "yield" isn't a yield at all.
- Source
- Extracted directly from the chapter text in /references
- Chapter type
- Descriptive market survey — applies Ch. 2's PV/duration toolkit to real instruments
- Priority note
- Lower priority for personal trading per this project's own curriculum plan — institutional detail rather than direct strategy math
Money vs. capital markets — a legal line, not an economic one
The book's own framing: money market instruments mature in under a year; capital market instruments in more than a year (including stocks, whose "maturity" is infinite). It calls this split "largely artificial and due to different legal requirements" — worth remembering, since it shapes which instruments get which quoting conventions and regulatory treatment, not their underlying economics.
T-Bills — quoted in a convention that isn't a price or a real yield
About a fifth of all US marketable government debt is T-Bills — zero-coupon, sold at a discount. The book's own real Wall Street Journal quote from April 23, 2003: the June 19 T-Bill (57 days to maturity) shows a bid/ask discount yield of 1.13%/1.12%. The book is blunt: this is "not a real yield, but a strange shorthand for price," using the formula y_disc = [(100−P)/100] × (360/Act).
| Step | Formula | Result |
|---|---|---|
| 1. Price from discount yield | 100 − 100×0.0112×(57/360) | 99.8227 |
| 2. Real yield (Act/365 basis) | (100−99.8227)/99.8227 × (365/57) | 1.14% |
What this means: the quoted "1.12% yield" and the actual return an investor earns (1.14%) are two different numbers, from the same instrument, on the same day — a 2-basis-point gap that comes purely from the quoting convention, not from any real economic difference. Anyone (or any algorithm) that reads "1.12%" off a T-Bill screen and treats it as a real yield is silently underestimating the actual return by this margin every single time. The convention exists for historical reasons, not because it's a good measure — the book calls it "most unappealing" outright.
Repos — collateralized borrowing, and a real arbitrage inside it
A repo is legally a spot sale plus a forward repurchase of the same security at a higher price; economically, it's a collateralized loan, with the price difference being the interest. The book's own point on dealer economics: dealer firms routinely run a matched book — simultaneously entering repos and reverse repos of the same maturity, capturing the spread between what they lend at (reverse repos, higher rate) and what they borrow at (repos, lower rate). This is pure arbitrage in the Ch. 1 sense: lending at a higher rate than borrowing, ideally against matched-quality collateral, though real spreads partly come from mismatched collateral quality.
Corporate bonds and munis — where credit risk and tax status enter the math
Corporate bonds are rated by agencies (S&P, Moody's) from AAA/Aaa down to C/D; the top four grades are investment-grade, the rest high-yield/junk. Corporate yields = government rate + a credit spread with its own term structure, quoted relative to the government curve or swap rates.
Munis (US municipal bonds) are exempt from federal income tax, so their yield is compared to taxable alternatives via the taxable-equivalent yield: y_taxequiv = y_muni / (1−m), where m is the investor's marginal tax rate. The book's own real example of what breaks this: in summer 2004, $15 billion of California bonds hit the market at the same time other states and cities issued their own — supply overwhelmed demand, and muni spreads widened enough that muni yields briefly exceeded Treasury yields, despite the tax exemption that should make munis cheaper to the issuer (lower required yield) in normal conditions.
- Context
- A muni yields 3.5%; an investor in the 35% federal tax bracket compares it to taxable alternatives.
- Algo-relevant?
- Yes — the taxable-equivalent yield is a real, mechanical relative-value screen, directly usable in a systematic muni/taxable-bond comparison.
- What's applied
- y_taxequiv = 3.5% / (1 − 0.35) = 5.38%. Any taxable bond of comparable credit quality yielding less than 5.38% is objectively worse for this specific investor, after tax — a real, computable answer, not a judgment call.
- Action
- A systematic muni-vs-taxable screener applies this formula per-investor-bracket across the whole muni universe, flagging bonds where the after-tax-equivalent yield beats comparable taxable credits — and, per the California example, watching for supply-driven muni cheapening events specifically, since those are exactly when this screen finds the most mispricings.
- Why
- The tax exemption is priced into munis on average, but supply shocks (like $15B hitting the market at once) can temporarily overwhelm that pricing — creating a genuine, if temporary, relative-value opportunity the formula makes precisely quantifiable.
Mortgage securities — a bond with a hidden option sold to the homeowner
A mortgage-backed security (MBS) is collateralized by a pool of mortgages, but the homeowner has the right to prepay — partially or fully — at any time, especially when rates fall and refinancing becomes attractive. Prepayment speed is measured in PSA (Public Securities Association) units: 100% PSA means a 6%/year prepayment rate for pools over 30 months old.
This prepayment right is, structurally, a call option the investor has implicitly sold to the homeowner — the book states this explicitly. It creates two distinct risks: contraction risk (prepayments speed up, principal comes back faster than expected — bad when you wanted the yield to keep compounding) and extension risk (prepayments slow down, your money is locked in longer than expected — bad when rates have risen and you'd rather have your principal back to reinvest).
The book's own structural response: CMOs (collateralized mortgage obligations) slice a mortgage pool into tranches with different priority — early tranches get principal first (protected from extension risk, exposed to contraction risk), later tranches face the opposite. IO/PO strips go further: an IO (interest-only) holder's payments shrink if prepayments speed up (bad), while a PO (principal-only) holder benefits from faster prepayment (good) since they bought the principal at a discount and get it back sooner.
The book states directly that MBS valuation can't be pure PV discounting — because the cash flows themselves depend on the path of interest rates (via prepayment behavior), correctly valuing an MBS requires Monte Carlo or tree simulation, the same class of technique used for option pricing — not the closed-form duration math from Ch. 2. This is a direct, explicit bridge forward to Ch. 9's options primer: prepayment risk is a real embedded option, and the option-adjusted spread (OAS) — the extra yield over a static PV calculation — is literally the market's price for that option's optionality. Any systematic MBS strategy is, whether it names itself this way or not, running an options-pricing model.
Swaps and asset-backed securities — a preview, not the full treatment
The chapter introduces interest-rate swaps as customized private contracts (not exchange-traded securities) that are often created alongside bond issuance specifically to reshape an issuer's liability profile — the same "desks collaborate to strip out unwanted risk" pattern Ch. 1 described. Full swap mechanics get their own dedicated chapter (Ch. 8) later in the book, so this chapter's treatment is deliberately just a pointer forward, not the complete picture.
Before moving to Chapter 4
- 1
Pull a real current T-Bill quote and decode it the way §02 does — compute the actual price and real Act/365 yield from the quoted discount yield, and see how large the gap is at today's rate levels.
- 2
Pick a muni bond you can find data for, and compute its taxable-equivalent yield at your own (or a hypothetical) marginal tax rate — compare it to a same-maturity Treasury or corporate bond.
- 3
Chapter 4 moves to equities, currencies, and commodities — the instruments most directly relevant to personal trading, and a higher-priority chapter in this project's own curriculum plan than this one.