Perturbations (v0)
Perturbations (v0)
Purpose
The goal of perturbations in Pathspace Lab is not to predict market shocks, hedge tail risk, or generate alpha.
Instead, perturbations are used to: stress portfolio construction procedures, expose sensitivity to assumptions, and illustrate fragility in otherwise “reasonable” optimization pipelines.
All perturbations are exogenous, non-predictive, and agnostic to asset identity.
Guiding Principles
- Exogeneity Perturbations are injected externally and are not inferred from the data.
- Path Dependence The timing and sequencing of volatility matters more than its marginal distribution.
- Model-Agnostic Stress Perturbations do not rely on economic narratives, factor interpretations, or alternative data.
- Reproducibility All perturbations are parameterized and fully reproducible via random seeds.
Perturbation Classes
- Resampled Time-Paths (Baseline)
Description Standard bootstrap resampling of historical returns, preserving cross-sectional correlations but altering temporal order.
Purpose
- Establish a baseline level of estimation uncertainty.
- Demonstrate that instability exists even without regime changes.
What It Tests
- Sensitivity of optimized weights to small sample variations
- In-sample vs out-of-sample Sharpe degradation
What It Does Not Test
- Structural breaks
- Non-stationary volatility
- Volatility Regime Shifts (Exogenous)
Description Inject discrete volatility multipliers over contiguous time windows (e.g., low → high → low).
Volatility regimes are: independent of realized returns, applied uniformly or partially across assets, non-predictive by construction.
Purpose
- Mimic opacity of real-world regime changes without modeling their causes.
- Stress assumptions of stationarity in covariance estimation.
What It Tests
- Weight instability under regime shifts
- Portfolio concentration behavior
- Rebalancing sensitivity
Interpretation
The model does not “fail” because volatility rises — it fails because it cannot distinguish signal from structure.
- Volatility-Coupled Noise Injection
Description Additional noise is added as an increasing function of realized or injected volatility.
Example (conceptual):
- Low-vol regimes → minimal noise
- High-vol regimes → amplified noise
Purpose
- Reflect reduced signal clarity during market stress
- Capture the intuition that “estimation gets worse when you need it most”
What It Tests
- Fragility of mean-variance optimization under degraded signal quality
- False confidence induced by historical calibration
Perturbation Scope (Explicit Exclusions)
The following are intentionally excluded from v0:
- Tail-hedging strategies
- Predictive regime detection
- Structural macro shocks
- Alternative or proprietary data
- Asset-specific shock modeling
- Alpha generation
These exclusions are deliberate: the focus is on exposing the problem, not solving it.
Relation to the First Artifact
The first artifact uses perturbations to show:
- Optimized portfolios exhibit high sensitivity to time-path realizations
- Equal-weight portfolios display lower variance but lower efficiency
- In-sample performance masks out-of-sample fragility
- Small, plausible perturbations can dominate optimization outcomes
The artifact does not attempt to: propose a superior portfolio, mitigate fragility, or protect against black swan events.
Design Philosophy
If a portfolio optimizer is fragile under mild, non-adversarial perturbations, its real-world robustness should be questioned — regardless of backtested performance.
Status
- Perturbations are parameterized but not yet implemented
- No tuning or calibration is performed
- Parameters will be fixed prior to optimization runs