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

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(),
    }