Basket Deadline-Contagion Slippage Playbook

When One Underfilled Leg Forces Toxic Catch-Up Across the Entire Basket

Why this note: Many desks model each symbol’s slippage independently, then wonder why basket execution tails explode near the deadline. In practice, underfill in one leg creates urgency spillover to correlated legs (risk neutrality, hedge constraints, tracking-error limits), turning a local lag into portfolio-wide cost convexity.

1) Failure Mode in One Sentence

If your slippage model is symbol-local only, you will underprice cross-leg urgency contagion and pay late-session catch-up tax even when each single-name model looks calibrated.

2) Cost Decomposition with Cross-Leg Coupling

For a basket of legs (i=1..N), at time (t):

[ \mathbb{E}[IS_t^{basket}] = \sum_i \mathbb{E}[IS_{i,t}^{local}] + C_{div}(t) + C_{deadline}(t) ]

Where:

• (\mathbb{E}[IS_{i,t}^{local}]): single-leg spread/impact/queue cost
• (C_{div}(t)): completion-divergence penalty across legs
• (C_{deadline}(t)): convex catch-up penalty as time-to-close shrinks

A practical divergence penalty:

[ C_{div}(t)=\lambda_{div}\sum_{i,j} A_{ij}\big(c_i(t)-c_j(t)\big)^2 ]

• (c_i(t)): completion ratio of leg (i)
• (A_{ij}): coupling weight (correlation/hedge linkage/index co-membership)

This explicitly prices the “one leg late, everyone panics” effect.

3) Core Modeling Blocks

A) Leg-local baseline (keep existing model)

For each leg:

[ \mathbb{E}[IS_{i,t}^{local}] = C_{spread}+C_{impact}+C_{queue}+C_{fees} ]

No need to throw away the current stack—add contagion overlays.

B) Contagion pressure feature

Define residual progress (r_i(t)=1-c_i(t)). Then:

[ P_i(t)=\sum_{j\neq i} A_{ij},r_j(t) ]

Use (P_i(t)) as a first-class feature in each leg’s marginal cost and aggressiveness policy:

[ \Delta IS_{i,t}^{contagion} = \beta_i P_i(t) + \gamma_i,\frac{r_i(t)}{\tau_t+\epsilon} ]

• (\tau_t): time remaining to deadline
• (\epsilon): numerical stabilizer

C) Deadline convexity (the real tail driver)

A robust approximation:

[ C_{deadline}(t)=\lambda_{dl}\sum_i \left(\frac{r_i(t)}{\tau_t+\epsilon}\right)^2 ]

Near close, the same residual inventory becomes much more expensive.

4) Regime State Machine (Basket-Aware)

• B0 BALANCED: completion ratios aligned; normal per-leg policy
• B1 LOCAL_LAG: one/few legs behind; targeted catch-up only
• B2 CONTAGION_RISK: divergence spilling to coupled legs
• B3 COMPRESSED_DEADLINE: high residual + low time left (convex zone)
• B4 SAFE_COMPLETION: controlled completion mode with cost caps

Use hysteresis + minimum dwell to prevent state flip-flop.

5) Telemetry You Must Capture at Decision Time

Basket-level

• basket_completion_ratio
• completion_dispersion (e.g., stddev of (c_i))
• time_to_deadline_ms
• tracking_error_proxy
• hedge_constraint_utilization

Leg-level

• leg_completion_ratio
• leg_residual_notional
• leg_contagion_pressure
• local_liquidity_state
• marginal_cost_estimate_bps

Outcomes

• leg_realized_is_bps
• basket_realized_is_bps
• deadline_miss_flag
• late_catchup_notional
• markout_1s/5s/30s

No basket-level completion telemetry = no way to detect contagion early.

6) KPIs That Expose Hidden Cross-Leg Damage

1. BCI (Basket Contagion Index): average (\sum_i P_i(t)) in active windows
2. CDI (Completion Divergence Index): weighted dispersion of (c_i(t))
3. CCB (Cross-leg Catch-up Bps): extra bps from contagion-triggered aggression
4. DSE (Deadline Stress Elasticity): cost sensitivity to (1/(\tau+\epsilon))
5. LME (Late Miss Exposure): residual notional left in last execution bucket

If per-leg models look fine but CCB/DSE rise, your issue is coupling, not local microstructure.

7) Policy Coupling (How to Operate)

B0 BALANCED

• standard local execution logic

B1 LOCAL_LAG

• isolate lagged legs for moderate urgency lift
• keep healthy legs near baseline to avoid unnecessary impact

B2 CONTAGION_RISK

• cap simultaneous aggression across highly coupled legs
• use staggered urgency windows to avoid self-induced cross-impact bursts
• rebalance urgency by marginal completion value, not raw residual only

B3 COMPRESSED_DEADLINE

• explicit deadline budget split by leg importance and liquidity
• freeze non-essential repricing churn
• prioritize certainty of completion for high-coupling legs

B4 SAFE_COMPLETION

• deterministic completion profile with hard risk caps
• alert operator with divergence snapshot + expected residual cost

8) Calibration & Validation Ladder

1. Shadow (1–2 weeks)
   • compute contagion features/KPIs, no policy change
2. Replay
   • simulate coupled vs uncoupled policy on historical baskets
3. Canary
   • enable B1/B2 logic on low-notional baskets
4. Scale (promotion gates)
   • CDI and CCB improve
   • deadline misses do not increase
   • no adverse jump in market-impact tails

Rollback triggers:

• contagion feature instability by regime
• rising late-bucket notional concentration
• increased cross-impact tail undercoverage

9) Common Anti-Patterns

• Treating basket execution as independent single-name tasks
• Driving urgency purely by each leg’s residual, ignoring coupled residuals
• Letting multiple correlated legs enter panic mode simultaneously
• Optimizing average IS while deadline-tail costs worsen
• No explicit state for “divergence high, time low” periods

10) Fast Checklist

[ ] Add completion-ratio telemetry per leg + basket
[ ] Build coupling matrix A_ij (correlation/hedge/index link)
[ ] Add contagion pressure feature P_i(t)
[ ] Deploy B0..B4 state machine with hysteresis
[ ] Gate rollout on CDI/CCB/DSE, not mean IS only
[ ] Keep emergency SAFE_COMPLETION deterministic and auditable

References

• Almgren, R., Chriss, N. (2000), Optimal Execution of Portfolio Transactions.
• Gatheral, J., Schied, A. (2013), Dynamical Models of Market Impact and Algorithms for Order Execution.
• Benzaquen, M., Mastromatteo, I., Eisler, Z., Bouchaud, J.-P. (2017), Dissecting Cross-Impact on Stock Markets.
• Cartea, Á., Jaimungal, S., Penalva, J. (2015), Algorithmic and High-Frequency Trading.

TL;DR

Basket slippage tails often come from completion divergence contagion, not single-leg model errors. Add cross-leg residual coupling, deadline convexity, and basket-aware control states so one lagging leg does not drag the whole basket into toxic late aggression.