Risk Metrics Calculator

For most purposes, start with simple historical volatility (standard deviation of returns over 20-60 days). Use EWMA (decay factor 0.94) if you want faster reaction to recent volatility changes. For more sophisticated analysis, Garman-Klass (using OHLC) is more efficient. Match the measure to your need: EWMA for current risk, simple for long-term average.

There's no universal 'good' VaR - it depends on your risk tolerance and strategy. General guidelines: 95% daily VaR of 2-3% is moderate risk. Above 4% is aggressive. Below 1% is conservative. More important is that VaR is consistent with your ability to handle losses. Can you psychologically and financially handle the 5% of days when VaR is exceeded?

Depends on trading frequency and market conditions. Daily: VaR, current volatility, concentration. Weekly: Comprehensive metrics review. Monthly: Deep analysis, stress tests, model validation. During high volatility periods, more frequent monitoring is prudent. Real-time if actively trading options or leveraged positions.

VaR is designed to be exceeded sometimes - that's what the confidence level means. 95% VaR will be exceeded on ~5% of days. Beyond that: (1) Fat tails - extreme events are more frequent than models predict, (2) Regime changes - volatility suddenly increases, (3) Model limitations - assumptions don't hold. VaR is a guide, not a guarantee. Always have protections for when VaR is exceeded.

The VIX (CBOE Volatility Index) measures expected 30-day S&P 500 volatility. Below 15: Low volatility, calm market. 15-20: Normal volatility. 20-30: Elevated volatility, caution advised. Above 30: High volatility, crisis territory. Use VIX context: if the VIX is 30 and your portfolio vol is calculated at 15%, your estimate may be stale. Increase your risk estimate when the VIX is elevated.

Historical VaR: When you have sufficient data (250+ days), want to capture fat tails, and don't want to assume normal distribution. Better for realistic tail risk. Parametric VaR: When you need fast calculation, have limited data, or for initial estimates. Simpler but underestimates tails. For serious risk management, prefer Historical or Cornish-Fisher adjusted Parametric.

Correlations typically spike toward 1 in stress. Model this by: (1) Using stress correlations (historical crisis correlations) rather than normal period correlations. (2) Applying a correlation multiplier (e.g., 1.3x normal correlation). (3) Running scenarios with correlation = 0.8-0.9 for equity positions regardless of normal correlation. This reveals true stress risk when diversification fails.

For parametric VaR: VaR = Z-score × Volatility × Portfolio Value. Higher volatility directly increases VaR. If volatility doubles, parametric VaR doubles. For historical VaR, the relationship is indirect - higher historical volatility means more extreme returns in the sample, leading to higher VaR. Always scale VaR discussions by current volatility regime.

Options require additional metrics: (1) Greeks - Delta (direction), Gamma (convexity), Theta (time decay), Vega (vol sensitivity). (2) Full revaluation VaR - recalculate option value under scenarios, not just delta approximation. (3) Scenario analysis across price and volatility dimensions. (4) Max loss = premium paid (for long options). Simple linear VaR is insufficient for options.

Consider: (1) Liquidity - can you exit without major impact? (2) Conviction - higher conviction may justify higher concentration. (3) Correlation - effectively one position if highly correlated. (4) Overall portfolio - more positions allows lower individual limits. Starting point: 10-15% per position for diversified portfolio. 20-25% only with high conviction and liquidity. Never more than 30% in single position unless very specific strategy.

Steps: (1) Estimate GARCH(1,1) parameters (ω, α, β) on historical returns. (2) Calculate conditional variance for tomorrow using today's return and variance. (3) Apply VaR formula using conditional volatility instead of historical. (4) For multi-day VaR, simulate paths or use variance term structure. Libraries: Python arch package. Benefits: Captures volatility clustering, reacts to recent shocks. Challenge: Parameter estimation requires sufficient data.

Key limitations: (1) Not subadditive - portfolio VaR can exceed sum of component VaRs (fails coherent risk measure axioms). (2) Says nothing about losses beyond VaR. (3) Backward-looking - uses historical data. (4) Model-dependent - sensitive to assumptions. (5) Can be gamed - optimize to minimize VaR while taking tail risk. Mitigate by: using CVaR (subadditive), stress testing, and multiple risk measures.

Regulatory validation requires: (1) Backtesting with Kupiec and Christoffersen tests. (2) Basel traffic light assessment. (3) Documentation of methodology, assumptions, limitations. (4) Independent validation by team not involved in development. (5) Comparison to benchmark models. (6) Stress testing the model itself. (7) Ongoing monitoring and periodic review. (8) Clear governance and approval process. Follow Fed/SEC guidelines for specific requirements.

Liquidity-adjusted metrics: (1) Add expected liquidation cost to VaR. (2) Model spread widening in stress (2-5x normal). (3) Calculate time-to-liquidate at acceptable impact (10-20% daily volume). (4) Liquidity-weighted VaR: Longer liquidation horizon for illiquid positions. (5) Stress test with reduced liquidity - what if volume drops 70%? Consider: Liquidity risk is non-linear and asymmetric - disappears exactly when needed most.

Architecture: (1) Data layer - real-time prices via WebSocket, positions from OMS. (2) Calculation engine - incremental updates, pre-computed sensitivities for speed. (3) Alert system - threshold monitoring, escalation procedures. (4) Dashboard - real-time metrics, historical trends. Technology: Redis/Kafka for streaming, TimescaleDB for time-series, Python/C++ for calculation, Grafana for visualization. Key requirements: Sub-second latency, high availability, audit trail, manual override capability.