correlation-crisis

> **Skill:** Correlation Crisis & Tail Risk | **Domain:** trading/risk-and-portfolio | **Category:** risk | **Level:** advanced > **Tags:** `correlation`, `tail-risk`, `hedging`, `crisis`, `regime`, `diversification` # Correlation Crisis & Tail Risk ## 1. The Correlation Problem ### Normal Times vs Crisis ``` NORMAL REGIME (VIX < 20): Correlations are moderate and stable Diversification works as expected Asset A: +1% Asset B: -0.3% Asset C: +0.5% Portfolio: smoothed returns ✓ CRISIS REGIME (VIX > 30): Correlations spike toward 1.0 "All correlations go to 1 in a crash" Asset A: -5% Asset B: -4% Asset C: -6% Portfolio: concentrated loss ✗ Exception: USD, Treasuries, Gold often decouple (but not always — March 2020 everything sold) ``` ### Correlation Is Not Constant ```python def rolling_correlation(asset_a: pd.Series, asset_b: pd.Series, window: int = 60) -> pd.Series: """60-day rolling correlation reveals regime shifts.""" return asset_a.rolling(window).corr(asset_b) # Key insight: when rolling correlation breaks out of its # historical range, regime change is likely in progress ``` ## 2. Measuring Tail Risk ### Beyond Standard Deviation ``` Standard deviation assumes normal distribution. Markets have fat tails. Use: 1. Value at Risk (VaR) - 95% VaR: "I expect to lose no more than X on 95% of days" - Limitation: says nothing about the worst 5% 2. Conditional VaR (CVaR / Expected Shortfall) - "When I DO exceed VaR, what's my expected loss?" - Average of losses beyond VaR threshold - This is the metric that matters for tail risk 3. Maximum Drawdown - Empirical worst case (so far) - Rule of thumb: future MDD ≈ 1.5-2× historical MDD 4. Tail Ratio - 95th percentile gain / abs(5th percentile loss) - >1.0 = positive skew (good) - <1.0 = negative skew (hidden risk) ``` ### Fat Tail Detection ```python from scipy.stats import kurtosis, jarque_bera def tail_risk_report(returns: pd.Series) -> dict: kurt = kurtosis(returns) # >0 means fat tails jb_stat, jb_pval = jarque_bera(returns) var_95 = returns.quantile(0.05) cvar_95 = returns[returns <= var_95].mean() tail_ratio = returns.quantile(0.95) / abs(returns.quantile(0.05)) return { 'kurtosis': kurt, # Normal = 0, fat tails > 3 'is_normal': jb_pval > 0.05, # Almost always False for markets 'var_95': var_95, 'cvar_95': cvar_95, 'tail_ratio': tail_ratio, 'worst_day': returns.min(), 'best_day': returns.max(), } ``` ## 3. Regime-Dependent Correlation Matrix ### Building Conditional Correlation ```python def regime_correlations(returns: pd.DataFrame, vix: pd.Series) -> dict: """Compute separate correlation matrices per regime.""" regimes = { 'low_vol': vix < vix.quantile(0.33), 'mid_vol': (vix >= vix.quantile(0.33)) & (vix < vix.quantile(0.66)), 'high_vol': vix >= vix.quantile(0.66), 'crisis': vix > vix.quantile(0.95), } matrices = {} for name, mask in regimes.items(): regime_returns = returns[mask] matrices[name] = regime_returns.corr() return matrices # USE THIS for portfolio construction: # - Size positions using CRISIS correlations # - Don't trust calm-period diversification benefits ``` ### Correlation Breakout Alert ```python def correlation_alert(rolling_corr: pd.Series, lookback: int = 252) -> str: current = rolling_corr.iloc[-1] mean = rolling_corr.iloc[-lookback:].mean() std = rolling_corr.iloc[-lookback:].std() z_score = (current - mean) / std if z_score > 2.0: return "ALERT: Correlation spike — diversification degrading" elif z_score < -2.0: return "NOTE: Correlation breakdown — unusual divergence" return "NORMAL" ``` ## 4. Hedging Strategies ### Portfolio Hedges by Regime ``` LOW VOLATILITY (VIX 10-15): ├── Hedges are cheap → buy tail protection ├── OTM puts on portfolio (1-3% of portfolio value quarterly) ├── Long VIX calls (3-6 month expiry) └── Cost: drag on returns during calm periods RISING VOLATILITY (VIX 15-25): ├── Hedges getting expensive → be selective ├── Reduce gross exposure by 10-20% ├── Shift to shorter holding periods ├── Tighten stops └── Increase cash allocation HIGH VOLATILITY (VIX 25-40): ├── Hedges are expensive → use position sizing instead ├── Reduce position sizes by 40-60% ├── Only A+ setups ├── Consider inverse correlation trades └── No overnight exposure in uncertain direction CRISIS (VIX > 40): ├── Capital preservation mode ├── Flatten all non-core positions ├── Cash is a position ├── Look for dislocation opportunities (small size) └── This is when fortunes are made AND lost ``` ### Cross-Asset Hedges ``` If long equities: ├── Long treasuries (TLT) — works most of the time ├── Long gold (GLD) — works in inflation + crisis ├── Long USD (DXY) — works in global risk-off ├── Long VIX futures — works fast but decay kills you └── CAUTION: March 2020 showed all can fail simultaneously If long forex carry: ├── Long JPY, CHF — classic safe havens ├── Short AUD, NZD — risk-sensitive commodity currencies └── Position size is the best hedge If long crypto: ├── Stablecoin allocation (capital preservation) ├── Short perpetuals on portion of holdings ├── Options if liquid (BTC/ETH only practically) └── Crypto correlations to equities are regime-dependent ``` ## 5. Stress Testing Protocol ```python def stress_test_portfolio(positions: list[Position], scenarios: dict) -> pd.DataFrame: """ scenarios = { '2008_GFC': {'SPY': -0.55, 'TLT': +0.20, 'GLD': +0.25, 'VIX': +300%}, '2020_COVID': {'SPY': -0.34, 'TLT': +0.15, 'GLD': -0.05, 'BTC': -0.50}, 'Flash_Crash': {'SPY': -0.10, 'all_corr': 0.95, 'liquidity': -80%}, 'Rate_Shock': {'TLT': -0.25, 'SPY': -0.15, 'USDJPY': +10%}, 'Custom': {...} } """ results = [] for name, shocks in scenarios.items(): portfolio_pnl = sum( pos.value * shocks.get(pos.symbol, shocks.get('default', -0.10)) for pos in positions ) results.append({ 'scenario': name, 'portfolio_pnl': portfolio_pnl, 'pct_loss': portfolio_pnl / total_portfolio_value, 'survives': abs(portfolio_pnl / total_portfolio_value) < max_allowed_dd, }) return pd.DataFrame(results) ``` ## 6. Rules 1. **Size for the crisis, not the calm.** Use crisis-regime correlations for position sizing. 2. **When hedges are cheap, buy them.** Low VIX = cheap insurance. 3. **Diversification is a regime-dependent feature.** It works until you need it most. 4. **Cash is a position.** 20-30% cash in uncertain regimes is not "missing out." 5. **Stress test monthly.** Run portfolio through historical crises. If you can't survive 2008 on paper, you can't survive the next one live. --- ## Related Skills - [Portfolio Optimization](portfolio-optimization.md) - [Cross-Asset Relationships](../market-foundations/cross-asset-relationships.md) - [Risk And Portfolio](risk-and-portfolio.md) - [Real-Time Risk Monitor](real-time-risk-monitor.md) - [Drawdown Playbook](drawdown-playbook.md)