# Block 015 — Batch 2 verification (rates, 008-014) + batch synthesis note

**Status:** ✓ done — Session 22 (2026-07-12)
**Phase:** Phase 1 (Rates)

## Topic scope

Verification gate for Batch 2 rates items (blocks 008-014). Re-probe any flagged items. Write batch synthesis note. Update competence-map, coverage-tracker.

## Plan

**Prerequisite:** Block 00a/00b — verification block re-probes the rubric and anti-patterns as part of prior-batch verification. (Block 00c withdrawn 2026-07-02.)
_Filled at session close of prior block, per 2026-06-23 convention._

**Status:** ✓ done — Session 22 (2026-07-12). 8 cold-recall probes across Blocks 008, 010, 011, 012, 013, 014. 4 items demoted Working+ → Working, 1 sequence substrate slip on diagnostic priority. Batch synthesis note (below) covers three-leg signal-layer diagnostic as load-bearing insight. Block 007/015/022 W26/W27/W28 labels retired in favor of "Batch 1 / Batch 2 / Phase 1 closeout" language; "weekly note" → "batch synthesis note". Week-system cleanup codified.

**Process changes filed at session close (codified in macro-mentor skill):**
- **2026-07-12 — Verification gate extends to mentor recall:** the Block 015 Probe 7 BF sign-convention incident is the third instructor-side precision slip in the rates batch (after Block 011 off-the-run paper, Block 014 swap points). The pattern: mentor recall slips on a precision point, accepts own framing as truth, corrects user who was right. **Going-forward rule:** the verification gate is bidirectional — when correcting a user, cross-check the substrate (block file + competence map + session log) before scoring. The user doing the pushback is a feature, not a friction.
- **2026-07-12 — Week-system cleanup (Batch 2 verification):** retired W26/W27/W28 labels from active block files and curriculum table; renamed "weekly note" → "batch synthesis note" in verification-block language. Filenames retained for git stability. Phase 6 live-trade "weekly review" cadence is unrelated and unchanged.

## Carry-forward to next block

Block 016 (Fed communication & reaction function) opens with cold-recall probes on Batch 1 (term-structure / real-vs-nominal / curve dynamics) and Batch 2 (vol surface / MBS / SOFR / breakeven / cross-currency) weak points — 4 items demoted Working+ → Working this session, plus 1 sequence substrate slip. Pre-read assigned at session close: Hull Ch. 30 (central bank / reaction function), Bernanke 2004 "Great Moderation" speech, 2-3 Powell speeches spanning regime changes (2018-2026), FRED FEDFUNDS/DFEDTARU/DFEDTARL/SOFR methodology pages.

---

# Batch 2 (rates, blocks 008-014) — batch synthesis note

**Block:** 015
**Coverage:** 2026-07-04 (Block 010) → 2026-07-11 (Block 014)
**Verification status:** ✓ partial — 4 items demoted Working+ → Working, 1 sequence substrate slip on diagnostic priority; see Probe log below.

---

## The load-bearing insight: the three-leg signal-layer diagnostic

The single most important insight from this batch is the **three-leg diagnostic for rates-microstructure reads**. Each leg is a separate dollar-funding-plumbing read; the diagnostic power comes from *separation* — which combination of the three legs moves tells you which layer of the dollar-funding plumbing broke.

| Leg | Source block | What it reads | Layer of plumbing | Regime lead/lag in crisis |
|---|---|---|---|---|
| **MBS-Treasury basis** | 011 | Prepayment option / mortgage market liquidity | Most distal (requires a rate move to actually trigger) | **Lags** — last to move |
| **SOFR-OIS** | 012 | Domestic bank funding / tenor premium | Most proximate to source | **Leads** — first to move |
| **Cross-currency basis** | 014 | Global dollar funding / dealer balance-sheet constraint | Intermediate | **Second** — propagates from domestic to global |

**Diagnostic priority in a crisis:** watch SOFR-OIS first, cross-currency second, MBS last. The order is the *sequence in which they blow out* in a crisis. SOFR-OIS is the leading indicator (domestic bank funding, breaks first); MBS is the lagging indicator (prepayment/option, breaks last because it requires a rate move to actually trigger). If you watch MBS first, you'll be late to every crisis.

**Regime combinations:**
- *Single-layer stress (one leg wide, two normal):*
  - MBS only = prepayment/refi wave stress
  - SOFR-OIS only = domestic bank funding stress
  - Cross-currency only = global dollar scarcity without US bank stress
- *Multi-layer (in sequence):* SOFR-OIS → cross-currency → MBS = systemic crisis unfolding
- *All three simultaneously* = systemic crisis
- *Cross-currency + MBS but not SOFR-OIS* = anomaly, possible non-bank-led or non-US-led crisis (rare, flag for review)

---

## Mid-2026 reads (current regime for each leg)

**MBS-Treasury basis — NORMAL**
- 30y UST: 4.97%
- 30y mortgage rate (Freddie PMMS): 6.43%
- Current production 30y UMBS TBA coupon: ~5.58%
- Gross secondary spread: +61bp
- Net basis: option-overpriced (negative)
- PSA: 200-250 on 5.5% coupon pool
- 30y MBS dollar price for 5.5% coupon: ~$95 area
- *Read:* the pool is ~80bp out-of-the-money on a refi (5.5% coupon vs 6.43% mortgage rate). No refi wave. Gross spread is wide for normal regime but net basis is option-overpriced — the option premium the dealer charges exceeds the realized negative convexity. No MBS-Treasury stress.

**SOFR-OIS — NORMAL**
- SOFR overnight: 3.62% (2026-07-11)
- 30d term SOFR: 3.636%
- 30d OIS (geometric-SOFR compounded): 3.636%
- SOFR-OIS basis: ~0bp
- Repo volume: $3.154T (normal distribution 3.60-3.67%)
- No specials; no quarter-end window-dressing in effect
- *Read:* tenor premium ~0bp, credit premium ~0bp, total decomposition flat. Textbook quiet regime. No domestic bank funding stress.

**Cross-currency basis — CONSTRAINED (mid-band)**
- 3m USD/JPY basis: -42bp (Convex Q2 2026)
- USD/JPY spot: ~155
- BoJ policy rate: 0.50% (normalized Jan 2026)
- USD one-side share: 89.2% (BIS Triennial 2025, up from 88.4% in 2022, ~88% in 2019 — structurally stable but at new high)
- *Read:* -42bp is in the constrained band (-30 to -80bp), well wide of normal (-10 to -30bp), not crisis (> -100bp). Drivers: BoJ normalization (Jan 2026) + Basel III endgame (Apr 2026) reducing US-bank willingness to intermediate FX swap balance sheet at quarter-ends. This is the **only leg currently flashing a non-normal regime.**

**Net read:** two of three legs are normal; the cross-currency basis is constrained but mid-band, not crisis. The market is signaling that **global dollar funding is tight at the dealer-balance-sheet layer, but US domestic bank funding is not stressed, and the mortgage market is not seeing a refi wave**. Single-layer stress: cross-currency only. Diagnostic: constrained-but-not-crisis, watch for propagation to the other two legs (especially SOFR-OIS at quarter-end, which is the most predictable propagation mechanism).

---

## Substrate clusters covered in the batch

### Vol surface (Block 010) — 4 items

The vol-surface cluster was the highest-density new-material batch. Key substrate:
- **Swaption mechanics:** payer = call on bond (not put), receiver = put on bond. Black's model: lognormal forward = ATM strike × exp((σ²/2)T); swaption price = annuity factor × Black formula on the swap rate.
- **Risk reversal (RR):** payer vol − receiver vol. Positive RR = clients buying receivers, dealers short receiver / long payer (cut-hedge demand). Reads as positioning, not probability.
- **Butterfly (BF):** (25Δ payer + 25Δ receiver)/2 − ATM. **Convention LOCKED 2026-07-08** (per `bf-convention.md`, dealer-cost-of-carry framing): **positive BF = wings cheap = body bid = orderly move priced (market complacent, dealer long gamma on wings, incentivized to pin the spot). Negative BF = wings rich = body cheap = disorderly move priced (clients paying for tail protection, market pricing tail risk, dealer short gamma on wings).** Mechanical formula sign convention can read either way depending on framing — the locked convention is the dealer's cost-of-carry framing (BF+ = dealer's wings cheap to carry). Three recurrences of a contradictory sign convention surfaced in Session 22 (real-time Probe 7, Anki card push, post-push user flag); traced back to a stale sign convention in `daily-vol-routine.md`. **Cleanup 2026-07-12:** BF read removed from daily-vol-routine until convention is re-verified across the vault.
- **Vol-of-vol:** the size of the vol move IS the signal. Vol-of-vol is dynamic (vs static RR/BF). The 2026-07 Block 010 ZN surface: 1-sigma 10y yield move ±27bp; Black-implied probability of 50bp move ~9% vs empirical 20%+ = vol-of-vol premium in action.
- **Rate-cut probability extraction (four-layer):** ATM vol → ATM receiver → 25Δ → RR/BF. Common failure modes: (1) using Black vol (%) when market quotes normal (bp) vol, (2) treating ATM vol as probability directly, (3) annualizing 1m vol to single-meeting event (overstates), (4) treating RR/BF levels as probability (they're positioning).

### MBS / prepayment (Block 011) — 4 items

- **Pass-through structure:** single-class pro-rata after servicer (~25bp) and agency g-fee (~50-100bp); agency guarantee covers borrower default (not issuer).
- **Negative convexity:** WAM-extends-on-rally + WAC-drift-selection; MBS underperforms Treasury of equivalent duration in BOTH directions. Prepayment option framing: borrower owns free American call strike=par, investor short the option, negative convexity = cost.
- **MBS-Treasury basis trade:** DV01-matched long 30y UMBS / short 30y UST. Hedge ratio ~2.3x MBS face to Treasury face. Net carry ~30-50bp annualized. Convexity-adjusted breakeven = +200 PSA over hold period.
- **PSA prepayment mechanics:** 100 PSA = 6% CPR baseline, 0.2%/month ramp month 1-30, then flat 6% CPR. 300+ PSA = refi wave, 500+ = aggressive, 800+ = peak refi. Current 5.5% coupon pool running 200-250 PSA.

### SOFR / OIS / repo (Block 012) — 4 items

- **SOFR construction:** volume-weighted median of overnight Treasury-repo rates (tri-party + GCF + FICC-cleared bilateral), published by NY Fed ~8am ET.
- **OIS structure:** fixed-for-floating swap on geometric-average overnight rate. Geometric (compounded) average = economically equivalent to rolling overnight loans.
- **Repo mechanics:** two orthogonal axes — GC vs specific (collateral flexibility), tri-party vs bilateral vs FICC-cleared (settlement). Specific on special (CTD) can repo at NEGATIVE rates.
- **SOFR-OIS basis:** tenor risk only, NOT credit risk (both legs near-zero credit). Precision: SOFR-OIS = tenor; term unsecured − OIS = tenor + credit. Historical: 2008 350bp+, March 2020 130bp+, normal 0-15bp.

### Breakeven inflation (Block 013) — 3 items

- **DKW three-component decomposition:** T10YIE = expected inflation + IRP + liquidity premium. Naive read T10YIE = expected inflation wrong by ~80-150bp wedge.
- **FRED breakeven series:** T10YIE = DGS10 − DFII10 (spread, not yield); T5YIFR = 5y5y forward breakeven (years 5-10); DFII10/DFII30 = real-yield levels. T5YIFR < T10YIE = disinflationary path, not un-anchoring.
- **Liquidity premium sign convention:** TIPS less liquid → TIPS yields bid higher → T10YIE understates true breakeven → LP positive correction. LP can flip negative in flight-to-quality episodes.

### Cross-currency basis (Block 014) — 4 items

- **CIP/UIP:** CIP says zero-profit forward (textbook), post-2008 the basis is fundamental. USD at forward discount when USD rates > JPY rates (not premium).
- **DTV term structure of basis:** largest at short tenors (1m, 3m), shrinks to zero at 5y+. Fingerprint of balance-sheet/regulatory constraint.
- **Regime classification:** Normal -10 to -30bp / Constrained -30 to -80bp / Crisis > -100bp.
- **Dealer-intermediation vs CIP arbitrage:** the basis is the dealer's spread for warehousing the imbalance, not an arbitrage failure. Post-2008 the basis is fundamental, not a footnote.

---

## Verification log (Block 015 — 2026-07-12)

8 cold-recall probes across Blocks 008, 010, 011, 012, 013, 014. Verdict distribution:

- **Working+ re-affirmed (on second look):** 1 item (vol surface BF sign convention — recall was right, mentor correction was wrong; re-graded up. **2026-07-12 cleanup:** re-affirmed convention in synthesis note is now consistent with `bf-convention.md` locked 2026-07-08; daily-vol-routine stale sign convention removed.**)
- **Working+ → Working (precision slip, re-teach queued):** 4 items
  - Vol surface (Probe 1: vol-is-symmetric-not-directional, dealer-flow direction in RR, vol term structure vs BF)
  - Black's model + limitation (Probe 1: same precision layer)
  - FRED breakeven series (Probe 4: real-yield vs expected-inflation, DKW three-component)
  - Liquidity premium sign convention (Probe 4: same)
- **Working → Working with re-teach (magnitude/mechanism slipped):** 4 items
  - MBS-Treasury basis trade (Probe 2: gross spread widens on rally, net basis framing, convexity-bleed direction)
  - DKW three-component decomposition (Probe 4: secondary)
  - SOFR-OIS basis + tenor-vs-credit (Probe 3: tenor vs funding risk, quarter-end direction)
  - Cross-currency basis regime classification (Probe 5: cyclical-driver specifics, -75bp regime threshold)
- **Mixed Working+/Working (substrate intact, parts slipped):** 2 items
  - Vol-of-vol / ZN surface live data (Probe 1)
  - Dealer-intermediation vs CIP arbitrage (Probe 5)
- **Sequence substrate slip (cross-block):** 1 item
  - Cross-block signal-layer discipline (Probe 8: diagnostic priority — user said MBS first, substrate says SOFR-OIS first)

**Net assessment:** substrate is mostly there but the precision layer has slipped more than expected for a 3-day-old verification block. Three slip categories: (1) mechanism direction (substrate fires but direction-of-trade is wrong), (2) magnitude (substrate fires but math is shaky), (3) sequence (substrate fires but order is inverted). All flagged for re-drill in next session.

---

## Cross-block ties (Batch 2 → Batch 1 + forward)

- **Block 008 carry/roll-down** (Batch 2) extends Block 003 curve dynamics (Batch 1) by adding the time-axis of yield-curve movement. The +200 PSA breakeven for MBS basis (Block 011) is structurally a *carry-with-prepayment-risk* trade, conceptually similar to a DV01-neutral curve trade (Block 009).
- **Block 010 vol surface** is the missing link between Block 004 term premium (which treats the curve as observable) and the live pricing of optionality in rates markets. Vol surface is *where* the cross-asset view (Block 014 cross-currency, Block 013 breakeven) gets expressed as a concrete trade.
- **Block 011 MBS / Block 012 SOFR / Block 013 breakeven / Block 014 cross-currency** form the rates-microstructure signal layer that runs underneath the macro view. Block 015 (this note) is the first explicit statement of the diagnostic as a *separation* problem — which leg moves tells you which layer broke.
- **Block 014 cross-currency basis** is the formal hand-off from Phase 1 Rates to Phase 1 FX (Blocks 023+). The cross-currency basis is the most concrete bridge: it's a dollar-funding-stress read priced in FX swap markets. Phase 3 Block 073 (Rates ↔ FX cross-asset) will do the full treatment, but Block 014 is the canonical rates-side foundation.

---

## Anki coverage (Batch 2)

Per Session 18-21 Anki pushes:
- Block 008: 7 cards (carry/rolldown, DV01 sizing, bond price convention)
- Block 010: 6 cards (swaption mechanics, RR/BF, Black's model, rate-cut extraction, ZN surface)
- Block 011: 7 cards (MBS pass-through, negative convexity, basis trade, PSA mechanics)
- Block 012: 8 cards (SOFR construction, OIS, repo, SOFR-OIS basis)
- Block 013: 6 cards (DKW decomposition, FRED breakeven series, T5YIFR formula, LP sign convention, signal-layer discipline, current snapshot recall)
- Block 014: 8 cards (CIP/UIP, BIS data, cross-currency regime, DTV term structure, dealer-intermediation, three-leg signal layer, diagnostic combinations)

**Total: 42 atomic cards across Batch 2 (sessions 15-21).**

**Anki cards to add (Block 015 weak-point re-drill queue):**
- Gross spread widens on rally (not narrows) — WAC-drift operates on dollar price, not yield basis
- Net basis = gross spread − option cost; option cost rises with prepay acceleration
- Convexity-bleed direction: short the option → option value rising → MTM hits you → negative for long-MBS position past +200 PSA breakeven
- BF sign convention: **positive BF = orderly move priced (wings cheap, body bid, market complacent, dealer long gamma); negative BF = disorderly priced (wings rich, body cheap, clients paying for tails, dealer short gamma). LOCKED 2026-07-08 per `bf-convention.md` (dealer-cost-of-carry framing).**
- SOFR-OIS = tenor, NOT funding risk; tenor-only decomposition since both legs near-zero credit
- Quarter-end basis widens (not narrows) — banks pull back from repo, balance-sheet-driven scarcity
- Three-leg diagnostic sequence: SOFR-OIS leads, cross-currency second, MBS lags
- Three-leg diagnostic priority: watch SOFR-OIS first (leading indicator), MBS last (lagging)

---

## Pre-read for next block (assigned at session close, per protocol)

Block 016 — Fed communication & reaction function.

- **Hull 10e Ch. 30** (Hull's section on central bank policy, monetary policy reaction functions) — focus on policy-rule section
- **Bernanke 2004** "The Great Moderation" speech — Fed reaction function framing
- **Powell 2018-2026 speeches archive** — bookmark + read 2-3 speeches covering regime changes (e.g., 2018 "we are a long way from neutral", 2020 framework review, 2022-2023 hiking cycle, 2025-2026 cutting cycle)
- **FRED series FEDFUNDS, DFEDTARU, DFEDTARL, SOFR** — bookmark + methodology pages (~5 min)
- **Skip:** detailed OIS curve construction (covered in Block 012); full Powell speech archive; academic Fed reaction function literature pre-2000.

**Total: ~45 min, [thematic].**