Risk Methodology
Stress testing framework used in PrimeRisk portfolio risk reports.
Equity Stress Scenarios
Three independent stress scenarios are computed for every equity (non-SPAC) position.
| Scenario | Name | Formula | Description |
|---|---|---|---|
| S1 | 200 DMA | MV × (MA₂₀₀ − Price) / Price | P&L if the stock price reverts to its 200-day moving average. Longs lose when trading above MA; shorts gain. |
| S2 | Cap % | `- | MV |
| S3 | 1Sd Vol | MV × (-√(10/252) × IV) | 10-day 1-sigma vol shock. Uses implied volatility (IV) when available, otherwise beta × 18% market vol proxy. |
| 3Sd | 3Sd Vol | 3 × S3 | Extreme tail stress — three standard deviations of the 10-day vol move. |
| Extreme | Worst-case | min(S1, S2, 3Sd) | The single worst outcome across all equity scenarios for each position. |
Directional SD Columns
For equity positions the report also shows signed SD moves (using signed MV):
- -3 SD / -2 SD / -1 SD: P&L if the underlying drops by N sigma (positive for shorts)
- +1 SD / +2 SD / +3 SD: P&L if the underlying rises by N sigma (negative for shorts)
- -25% / +25%: P&L for a flat 25% price move in each direction
Market-Cap Stress Grid
The Cap % scenario uses a tiered minimum return based on market capitalization. Smaller companies get larger adverse stress returns.
The default grid is calibrated from the empirical CVaR 99.9% of 3-day returns, based on a study of 5.37 million observations across 2,509 US equities over 21 years. See the full Cap Stress Paper for methodology and robustness analysis.
| Bucket | Market Cap Range | Long Stress (CVaR 99.9%) |
|---|---|---|
| 1 | < $280M | -50% |
| 2 | $280M – $630M | -44% |
| 3 | $630M – $1B | -40% |
| 4 | $1B – $2B | -37% |
| 5 | $2B – $4B | -34% |
| 6 | $4B – $8B | -32% |
| 7 | $8B – $23B | -30% |
| 8 | ≥ $23B | -27% |
In the portfolio builder, the Cap Stress Grid panel provides:
- Preset selector — switch between the empirical 8-bucket grid (default) and the legacy 4-bucket grid
- Editable boundaries — adjust the market cap breakpoints between buckets
- Long Stress % — the base stress applied to long positions (pre-filled from empirical CVaR 99.9%)
- Custom % — an override column; enter a multiplier at the top (e.g. 150) to scale the base stress, then adjust individual buckets
- Short Stress % — separate stress for short positions (blank by default; when filled, applies to short positions instead of Long %)
Industry Overrides
Certain industries (e.g. Biotechnology) may exhibit significantly different tail risk than the broad market. The Industry Overrides panel lets you define separate stress grids for specific industries. When a position's industry matches an override, the industry-specific grid is used instead of the default.
Each industry override includes:
- Industry selector — choose from common industries or type a custom name
- Full stress grid — independent cap boundaries, long %, custom %, and short % columns
- Multiple overrides can be active simultaneously for different industry groups
A legacy 4-bucket grid is also available:
| Market Cap Range | Minimum Stress Return |
|---|---|
| Less than $1B | -15% |
| $1B to $10B | -10% |
| $10B to $1T | -5% |
| $1T and above | -3% |
SPAC Stress Scenario (S4)
SPAC positions are stressed to 95% of the $10 trust floor (stress price = $9.50).
The CIT (cash-in-trust) per share is resolved using a four-level hierarchy:
- External source — user-supplied trust per share
- SEC filing — parsed from 10-Q/10-K filings via EDGAR
- Accrued trust — trust per share + accrued T-bill interest from issuance date
- Default — $10.00 par value
The stress P&L = Quantity × (StressPrice − CurrentPrice).
Option Stress Scenarios
Options are repriced using the Black-Scholes model under three categories of stress.
S5 — Underlying Price Stress (Vol Flat)
The underlying price is shocked by N standard deviations while implied volatility remains unchanged.
| Scenario | Underlying Move | Vol Change |
|---|---|---|
| -3 SD | Price × (1 − 3σ√(10/252)) | Flat |
| -2 SD | Price × (1 − 2σ√(10/252)) | Flat |
| -1 SD | Price × (1 − 1σ√(10/252)) | Flat |
| +1 SD | Price × (1 + 1σ√(10/252)) | Flat |
| +2 SD | Price × (1 + 2σ√(10/252)) | Flat |
| +3 SD | Price × (1 + 3σ√(10/252)) | Flat |
S6 — Implied Volatility Shock (Price Flat)
The underlying price is held constant while implied volatility is shifted.
| Scenario | Price Change | Vol Change |
|---|---|---|
| Vol -25% | Flat | IV × 0.75 |
| Vol +25% | Flat | IV × 1.25 |
| Vol +50% | Flat | IV × 1.50 |
Term-Structure Adjustment
All vol shocks (S6 and the vol component of S7) are term-adjusted to reflect the fact that short-dated options are more sensitive to vol changes than longer-dated ones:
effective shock = base shock × √(30 / max(DTE, 5))
- 30-day options are the anchor point — they receive the base shock unscaled (√(30/30) = 1.0).
- Shorter-dated options (e.g. 7 DTE) see an amplified shock (√(30/7) ≈ 2.07×).
- Longer-dated options (e.g. 90 DTE) see a dampened shock (√(30/90) ≈ 0.58×).
- A floor of 5 DTE prevents the multiplier from blowing up near expiration.
For example, a Vol +25% shock on a 10-day-to-expiration option produces an effective vol shift of +25% × √(30/10) = +43.3%.
S7 — Combined Scenarios
Simultaneous price and volatility moves simulate realistic market regimes. The vol component of each scenario is term-adjusted as described above.
| Scenario | Underlying Move | Vol Change (base) | Market Regime |
|---|---|---|---|
| Crash | -2 SD | Vol × 1.25 (+25%) | Severe sell-off with volatility spike |
| Correction | -1 SD | Vol × 1.15 (+15%) | Moderate pullback with modest vol increase |
| Rally | +2 SD | Vol × 0.80 (-20%) | Strong rally with vol compression |
| Vol Spike | Flat | Vol × 1.50 (+50%) | No price move but extreme vol expansion |
Black-Scholes Pricing Model
All option repricing uses the Black-Scholes European option pricing model.
For a call option:
C = S·N(d₁) − K·e^(−rT)·N(d₂)
For a put option:
P = K·e^(−rT)·N(−d₂) − S·N(−d₁)
Where:
S= current underlying priceK= strike priceT= time to expiration in years (DTE / 365)r= risk-free rate (current T-bill rate)σ= implied volatility (annual, decimal)N(·)= standard normal CDFd₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T)d₂ = d₁ − σ√T
Greeks Definitions
| Greek | Symbol | Definition | Interpretation |
|---|---|---|---|
| Delta | Δ | ∂C/∂S | Rate of change of option price per $1 move in the underlying. Calls: 0 to +1; Puts: -1 to 0. |
| Gamma | Γ | ∂²C/∂S² | Rate of change of delta per $1 move in the underlying. Higher near ATM and near expiry. |
| Theta | Θ | ∂C/∂t | Daily time decay — how much the option loses per calendar day, all else equal. Always negative for long options. |
| Vega | ν | ∂C/∂σ | Option price change per 1 percentage point change in implied volatility. Always positive for long options. |
Position-Level Greeks
In the By Issuer tab, Greeks are aggregated at the position level:
- Net Delta = Σ (delta × quantity × 100) — expressed as equivalent shares
- Net Gamma = Σ (gamma × quantity × 100)
- Net Vega = Σ (vega × quantity × 100)
By Issuer Aggregation
The By Issuer view shows total risk per underlying, combining stock positions and all option positions on the same ticker.
- Stock MV — market value of the equity position
- Opt MV — total market value of all option positions on this underlying
- Total MV — Stock MV + Opt MV
- Combined SD columns — stock directional SD P&L + option S5 price-stress P&L at the matching SD level
- Opt Crash / Corr / Rally / VolSpk — sum of S7 combined-scenario P&L across all options
Portfolio Risk Metrics
| Metric | Formula | Description |
|---|---|---|
| Single Issuer Risk | min(Extreme) across all positions | Worst single-name loss |
| 5-Issuer Risk | Σ(5 worst Extremes) × 0.70 | Concentrated risk with 30% diversification discount |
| Sector Risk | 2 × (worst sector 1Sd) | 2-sigma sector-level stress |
| 3-Sector Stress | Σ(3 worst sector 1Sd) × 2 × 0.70 | Multi-sector stress with discount |
| 5 SPAC Risk | Σ(5 worst SPAC P&Ls) × 0.70 | Concentrated SPAC stress |
Other Prime Stress Methodologies
PrimeRisk's equity stress framework is modeled after the A Prime Stress proprietary 4-scenario approach. For comparison, here are the two most widely used retail/institutional prime broker margin methodologies:
Interactive Brokers (IBKR)
IBKR uses OCC TIMS as a base with proprietary house add-ons including global concentration charges, singleton margin, small-cap adjustments, per-contract minimums, and days-to-liquidate surcharges.
- IBKR Portfolio Margin; overview of IBKR's risk-based margin system
- IBKR Margin Requirements; published maintenance margin tables
Charles Schwab / TD Ameritrade
Schwab/TDA uses OCC TIMS as a base with a Risk-Based Concentration (RBC) model that adds margin when the volatility-implied price range exceeds the standard scan range, plus Point of No Return (PNR) monitoring and a 30% absolute minimum maintenance floor.
- Schwab Portfolio Margin; eligibility and overview
- Schwab Margin Requirements; published margin rates and maintenance requirements
- thinkorswim Margin Handbook (PDF); detailed margin methodology inherited from TD Ameritrade