# Block 008 — Carry & roll-down mechanics

**Status:** ✓ done
**Phase:** Phase 1 (Rates)
**Completed:** 2026-06-27 (Session 8)

## Topic scope

How duration is earned in a curve trade. Why 10y in a 2s10s steepener earns ~30bp/yr before any view. Roll-down along the curve path. Negative carry vs positive carry trades.

## Plan


**Prerequisite:** Block 00a (rubric), Block 00b (anti-patterns). DV01-sizing exercises need the framework risk numbers internalized (200bp/trade per `risk-framework.md` v0.3).
_(see Block 008 plan as written at Session 7 close)_

## Session 8 — completion summary

**Pre-read compliance:** L-S carry/roll-down sections + Ilmanen carry chapter done (~20 min, thematic). Cold-recall probes run.

**Drill block (4 probes, ~50 min):**

- **Q1 (carry/rolldown definitions):** HALF-RIGHT. Carry definition wrong (called 10y zero-coupon — actual is T-Note with ~4.25% semi-annual coupon). Rolldown framing off (called it "movement to par" — actual is mechanical pull-down along the curve as time-to-maturity shortens, not par-reversion). Both corrections taught in place.
- **Q2 (2s10s steepener P&L attribution):** HALF-RIGHT then CORRECTED — *correction itself was wrong, re-corrected Block 009 (2026-06-30)*. User got the carry signs right (short 10y pays, long 2y receives, net positive carry from long-leg dominance). User initially had rolldown signs INVERTED on both legs (said both negative); mentor correction applied during session was also wrong — it taught "long 2y leg has NEGATIVE rolldown (yield rises as 2y becomes 1.75y, price falls, you're long → loss)" which is the *inverted-curve* case. On the *upward-sloping* curve (2y 4.24, 5y 4.29, 10y 4.51), the long 2y leg actually has POSITIVE rolldown: as 2y becomes 1.75y, the 1.75y point on this curve is BELOW 2y, so yield drops, price rises, long gains. The short 10y leg is correctly negative (9.75y point is below 10y on the rising curve, yield drops, price rises, short loses). Net carry-and-rolldown on steepener ≈ −13bp/quarter on unchanged curve (correct conclusion, wrong per-leg mechanism). The trade's net is negative because the short 10y's DV01-equivalent loss dominates the long 2y's DV01-equivalent gain (~4.5x duration), not because both legs are negative. Anki card 1782552515987 replaced (Cloze "both legs negative" → Basic "long 2y POSITIVE, short 10y NEGATIVE, net DV01-negative due to duration dominance") — corrected card id 1782818841968. Lesson: when a student "agrees with the correction" too quickly, re-derive from first principles before recording.
- **Q3 (flattener asymmetry):** WORKING. Both carry and rolldown signs right this time (long 10y positive carry, short 2y negative carry; long 10y positive rolldown, short 2y positive rolldown). Net positive on unchanged curve (≈+13bp/quarter). Ilmanen asymmetry framed correctly: steepener = high-conviction asymmetric long-vol trade (paying for the privilege); flattener = low-conviction asymmetric short-vol trade (market pays you).
- **Q4 (numerical on current curve, dovish Fed view):** WORKING with corrections. Trade correct (long 2y / short 10y steepener, DV01-neutral). DV01 sizing wrong (yield-ratio approach — corrected to face(2y)/face(10y) ≈ duration(10y)/duration(2y) ≈ 4.5x). Invalidation framing loose (initially framed as "curve flattening" + "2y rallies" which is contradictory; cleaned up to "10y yields fall more than 2y yields = regime-shift invalidation = Block 007 PC3-emergence scenario").

**Anki cards generated:** 6 in `Macro Study::Phase 1 — Components::Rates`, tagged `session:2026-06-27`:
1. 10y UST NOT zero-coupon (T-Note with ~4.25% coupon; STRIPS for zero-coupon exposure)
2. Rolldown definition (yield drops as time-to-maturity shortens, NOT pull-to-par)
3. 2s10s steepener rolldown sign on both legs (both negative — structural drag)
4. Steepener vs flattener asymmetry + Ilmanen trade-selection framework
5. DV01-neutral sizing rule (face(2y)/face(10y) ≈ duration(10y)/duration(2y), NOT yield ratio)
6. Dovish-pivot steepener trade + regime-shift invalidation (PC3-emergence from Block 007)

**Status transitions:**
- **Rates — carry & roll-down mechanics:** NEW → **Working** (carry, rolldown, total-return decomposition, DV01 sizing, asymmetry all landed at Working with corrections)
- **Rates — Taper Tantrum PC3-emergence mechanism:** Re-surfaced in Q4 invalidation framing — partial causal mechanism still flagged for re-drill if case recurs (carry-forward per Block 007 session log)

**Carry-forward to Block 009:**
- Curve trade mechanics — steepener/flattener asymmetry (covered lightly in Q3; full block in Block 009)
- Trade-construction rubric (when is negative carry justified vs structurally bad — preview only here)
- Carry-and-rolldown numerical fluency (need reps on different curve shapes, e.g., inverted curve where rolldown signs flip)

## Open Weak items (no new ones this session)

- **Taper Tantrum PC3-emergence mechanism** — partial; full causal mechanism (flight-to-quality compressing 30y TP + hawkish Fed repricing expanding belly TP) not fully traced. Re-drill if case recurs.

## Pre-read for Block 009

- Litterman-Scheinkman (1991) "Understanding the Yield Curve" — full paper re-read for curve-trade mechanics (steepener/flattener asymmetry on different curve shapes)
- Ilmanen "Expected Returns" — value vs momentum chapter (preview: how carry interacts with value in rate trades)
- Tagged: [thematic, 25 min] — orientation; will be taught in session via TEACH+PROBE