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

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

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

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

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

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
• Cross-Asset Relationships
• Risk And Portfolio
• Real-Time Risk Monitor
• Drawdown Playbook