workflow-fi-mbs-prepayment

# Fixed Income: MBS Prepayment and Analytics ## What this skill covers A three-phase pipeline for modelling mortgage-backed securities: prepayment speed estimation, MBS pass-through cash-flow analytics (OAS, WAL, effective duration), and convexity-adjustment interpretation. Captures negative convexity — the defining structural feature of mortgage securities — and sizes hedge requirements. ## Core Rules - 100% PSA is the standard prepayment ramp; 150–200% PSA during strong rate rallies; 50–75% PSA in rising-rate environments. - Agency MBS OAS benchmarks: 30–80 bps for on-the-run agency pass-throughs; flag OAS outside this range. - Negative convexity must be documented: callable/prepayable securities always show convexity < 0 for premium-priced bonds. - WAC (weighted average coupon), WAM (weighted average maturity), and servicing fee must be stated before any tool call. ## Workflow ### Phase 1 — Security Specification and Prepayment Modelling 1. Collect MBS security characteristics: | Field | Notes | |---|---| | Pool type | Agency (FNMA / FHLMC / GNMA) or non-agency | | Coupon (pass-through rate) | Net of servicing fee | | WAC | Gross coupon of underlying mortgages | | Servicing fee | WAC − pass-through rate | | WAM | Weighted average remaining maturity (months) | | Original term | 30Y, 15Y, etc. | | Pricing speed assumption | PSA or CPR | 2. Call `prepayment_analysis` with pool characteristics and current mortgage rate environment. - Inputs: WAC, WAM, current 30Y mortgage rate, model type (PSA or CPR), base PSA assumption. - Outputs: - **PSA speed** (% of standard ramp) - **CPR** (conditional prepayment rate, annual) - **SMM** (single monthly mortality = 1 − (1 − CPR)^(1/12)) - **Refinancing incentive** (WAC vs current mortgage rate spread) - **Burnout adjustment** — seasoned pools show lower sensitivity (apply when WAM << original term) - Justify the PSA assumption: document rate environment, pool seasoning, loan size, FICO distribution if available. 3. Sensitivity: run `prepayment_analysis` at PSA −50%, PSA base, PSA +50% to bracket prepayment uncertainty. ### Phase 2 — MBS Cash Flow Analytics 4. Call `mbs_analytics` with pool characteristics and prepayment output from Phase 1. - Inputs: pass-through rate, WAC, WAM, face balance, prepayment speed (SMM or CPR), discount curve (government spot or OAS-shifted). - Outputs: - **Projected monthly cash flows** (principal + interest schedule) - **WAL** (weighted average life in years) - **OAS** (option-adjusted spread over the benchmark spot curve) - **Effective duration** (OAS-based; accounts for prepayment optionality) - **Effective convexity** (negative for premium MBS) - **DV01** per $1M face 5. Interpret OAS: - Agency MBS: OAS 30–80 bps = fairly priced; OAS < 20 bps = rich (prepayment risk underpriced); OAS > 100 bps = cheap or structural/liquidity issue. - Non-agency: wider OAS reflects credit risk premium in addition to prepayment optionality. 6. Interpret negative convexity: - Discount MBS (price < par): positive convexity — prepayments are slow; duration extends as rates rise. - Par MBS: approximately zero convexity. - Premium MBS (price > par): negative convexity — prepayments accelerate as rates fall, capping price appreciation. - Quantify: "For a −100 bps rate move, negative convexity reduces price appreciation by approximately [Convexity × (0.01)² / 2] × 100% of face." ### Phase 3 — Hedge Sizing 7. Compute the duration-equivalent Treasury hedge to neutralise rate risk: - Target: match the MBS effective DV01 with a short Treasury position. - Call `bond_duration` on the hedge Treasury (matched to MBS WAL). - Hedge ratio = MBS DV01 / Treasury DV01. - Note: the convexity mismatch (negative MBS convexity vs positive Treasury convexity) must be managed dynamically; flag the gamma requirement. 8. Convexity hedge (if required): an options overlay (cap / floor or swaption) is required to neutralise negative convexity. State the notional and tenor of the recommended options overlay. Refer to `workflow-fi-inflation-linked` or derivatives skill for pricing. ## Output Format **Prepayment Assumptions** | Parameter | Value | Notes | |---|---|---| | PSA speed | XXX% | Justified by rate environment | | CPR | XX.X% | Annual | | SMM | X.XX% | Monthly | | Refinancing incentive | +XX bps | WAC vs current mortgage rate | | Burnout applied | Yes / No | Pool seasoning | **MBS Analytics** | Metric | Discount PSA | Base PSA | Premium PSA | |---|---|---|---| | WAL (years) | XX.X | XX.X | XX.X | | OAS (bps) | +XXX | +XXX | +XXX | | Effective duration | X.XX | X.XX | X.XX | | Effective convexity | +X.XX | −X.XX | −X.XX | | DV01 ($M face) | $XXX | $XXX | $XXX | **Convexity Adjustment Summary** For ±100 bps rate shock, price appreciation drag from negative convexity: approximately −XX bps vs a duration-equivalent Treasury. **Hedge** | Instrument | Notional | DV01 match | Convexity | |---|---|---|---| | Short Treasury (WAL-matched) | $XXM | = MBS DV01 | Positive | | Swaption overlay (if needed) | $XXM | — | Offsets negative Δ | **Tool-Call Traceability Table** | # | Tool | Key Inputs | Output | |---|---|---|---| | 1 | `prepayment_analysis` | WAC, WAM, current rate, PSA | PSA speed, CPR, SMM | | 2 | `mbs_analytics` | pass-through, WAC, WAM, CPR, spot curve | WAL, OAS, eff duration, convexity | | 3 | `bond_duration` | hedge Treasury pricing inputs | DV01, modified duration | ## Quality Gates - [ ] PSA assumption justified with reference to rate environment and pool seasoning - [ ] Prepayment run at three PSA speeds (base, base−50%, base+50%) - [ ] Agency MBS OAS within 30–80 bps or deviation explained - [ ] Convexity sign correct: negative for premium MBS, positive for discount MBS - [ ] DV01 from `mbs_analytics` agrees with effective duration × price × 0.0001 (±2%) - [ ] Hedge ratio computed and stated - [ ] Gamma / convexity mismatch flagged if convexity hedge not in place ## Related Skills - `workflow-fi-bond-valuation` — plain-vanilla bond duration for comparison baseline - `workflow-fi-yield-curve-construction` — spot curve used as OAS discount reference - `workflow-fi-credit-spreads` — for non-agency MBS with credit component in OAS - `corp-finance-analyst-fixed-income` — deeper CLO / structured credit analytics