SKILL.md
Risk Metrics Calculation
Comprehensive risk measurement toolkit for portfolio management, including Value at Risk, Expected Shortfall, and drawdown analysis.
When to Use This Skill
- Measuring portfolio risk
- Implementing risk limits
- Building risk dashboards
- Calculating risk-adjusted returns
- Setting position sizes
- Regulatory reporting
Core Concepts
1. Risk Metric Categories
Category
Metrics
Use Case
Volatility
Std Dev, Beta
General risk
Tail Risk
VaR, CVaR
Extreme losses
Drawdown
Max DD, Calmar
Capital preservation
Risk-Adjusted
Sharpe, Sortino
Performance
2. Time Horizons
Intraday: Minute/hourly VaR for day traders
Daily: Standard risk reporting
Weekly: Rebalancing decisions
Monthly: Performance attribution
Annual: Strategic allocationImplementation
Pattern 1: Core Risk Metrics
import numpy as np
import pandas as pd
from scipy import stats
from typing import Dict, Optional, Tuple
class RiskMetrics:
"""Core risk metric calculations."""
def __init__(self, returns: pd.Series, rf_rate: float = 0.02):
"""
Args:
returns: Series of periodic returns
rf_rate: Annual risk-free rate
"""
self.returns = returns
self.rf_rate = rf_rate
self.ann_factor = 252 # Trading days per year
# Volatility Metrics
def volatility(self, annualized: bool = True) -> float:
"""Standard deviation of returns."""
vol = self.returns.std()
if annualized:
vol *= np.sqrt(self.ann_factor)
return vol
def downside_deviation(self, threshold: float = 0, annualized: bool = True) -> float:
"""Standard deviation of returns below threshold."""
downside = self.returns[self.returns < threshold]
if len(downside) == 0:
return 0.0
dd = downside.std()
if annualized:
dd *= np.sqrt(self.ann_factor)
return dd
def beta(self, market_returns: pd.Series) -> float:
"""Beta relative to market."""
aligned = pd.concat([self.returns, market_returns], axis=1).dropna()
if len(aligned) < 2:
return np.nan
cov = np.cov(aligned.iloc[:, 0], aligned.iloc[:, 1])
return cov[0, 1] / cov[1, 1] if cov[1, 1] != 0 else 0
# Value at Risk
def var_historical(self, confidence: float = 0.95) -> float:
"""Historical VaR at confidence level."""
return -np.percentile(self.returns, (1 - confidence) * 100)
def var_parametric(self, confidence: float = 0.95) -> float:
"""Parametric VaR assuming normal distribution."""
z_score = stats.norm.ppf(confidence)
return self.returns.mean() - z_score * self.returns.std()
def var_cornish_fisher(self, confidence: float = 0.95) -> float:
"""VaR with Cornish-Fisher expansion for non-normality."""
z = stats.norm.ppf(confidence)
s = stats.skew(self.returns) # Skewness
k = stats.kurtosis(self.returns) # Excess kurtosis
# Cornish-Fisher expansion
z_cf = (z + (z**2 - 1) * s / 6 +
(z**3 - 3*z) * k / 24 -
(2*z**3 - 5*z) * s**2 / 36)
return -(self.returns.mean() + z_cf * self.returns.std())
# Conditional VaR (Expected Shortfall)
def cvar(self, confidence: float = 0.95) -> float:
"""Expected Shortfall / CVaR / Average VaR."""
var = self.var_historical(confidence)
return -self.returns[self.returns <= -var].mean()
# Drawdown Analysis
def drawdowns(self) -> pd.Series:
"""Calculate drawdown series."""
cumulative = (1 + self.returns).cumprod()
running_max = cumulative.cummax()
return (cumulative - running_max) / running_max
def max_drawdown(self) -> float:
"""Maximum drawdown."""
return self.drawdowns().min()
def avg_drawdown(self) -> float:
"""Average drawdown."""
dd = self.drawdowns()
return dd[dd < 0].mean() if (dd < 0).any() else 0
def drawdown_duration(self) -> Dict[str, int]:
"""Drawdown duration statistics."""
dd = self.drawdowns()
in_drawdown = dd < 0
# Find drawdown periods
drawdown_starts = in_drawdown & ~in_drawdown.shift(1).fillna(False)
drawdown_ends = ~in_drawdown & in_drawdown.shift(1).fillna(False)
durations = []
current_duration = 0
for i in range(len(dd)):
if in_drawdown.iloc[i]:
current_duration += 1
elif current_duration > 0:
durations.append(current_duration)
current_duration = 0
if current_duration > 0:
durations.append(current_duration)
return {
"max_duration": max(durations) if durations else 0,
"avg_duration": np.mean(durations) if durations else 0,
"current_duration": current_duration
}
# Risk-Adjusted Returns
def sharpe_ratio(self) -> float:
"""Annualized Sharpe ratio."""
excess_return = self.returns.mean() * self.ann_factor - self.rf_rate
vol = self.volatility(annualized=True)
return excess_return / vol if vol > 0 else 0
def sortino_ratio(self) -> float:
"""Sortino ratio using downside deviation."""
excess_return = self.returns.mean() * self.ann_factor - self.rf_rate
dd = self.downside_deviation(threshold=0, annualized=True)
return excess_return / dd if dd > 0 else 0
def calmar_ratio(self) -> float:
"""Calmar ratio (return / max drawdown)."""
annual_return = (1 + self.returns).prod() ** (self.ann_factor / len(self.returns)) - 1
max_dd = abs(self.max_drawdown())
return annual_return / max_dd if max_dd > 0 else 0
def omega_ratio(self, threshold: float = 0) -> float:
"""Omega ratio."""
returns_above = self.returns[self.returns > threshold] - threshold
returns_below = threshold - self.returns[self.returns <= threshold]
if returns_below.sum() == 0:
return np.inf
return returns_above.sum() / returns_below.sum()
# Information Ratio
def information_ratio(self, benchmark_returns: pd.Series) -> float:
"""Information ratio vs benchmark."""
active_returns = self.returns - benchmark_returns
tracking_error = active_returns.std() * np.sqrt(self.ann_factor)
active_return = active_returns.mean() * self.ann_factor
return active_return / tracking_error if tracking_error > 0 else 0
# Summary
def summary(self) -> Dict[str, float]:
"""Generate comprehensive risk summary."""
dd_stats = self.drawdown_duration()
return {
# Returns
"total_return": (1 + self.returns).prod() - 1,
"annual_return": (1 + self.returns).prod() ** (self.ann_factor / len(self.returns)) - 1,
# Volatility
"annual_volatility": self.volatility(),
"downside_deviation": self.downside_deviation(),
# VaR & CVaR
"var_95_historical": self.var_historical(0.95),
"var_99_historical": self.var_historical(0.99),
"cvar_95": self.cvar(0.95),
# Drawdowns
"max_drawdown": self.max_drawdown(),
"avg_drawdown": self.avg_drawdown(),
"max_drawdown_duration": dd_stats["max_duration"],
# Risk-Adjusted
"sharpe_ratio": self.sharpe_ratio(),
"sortino_ratio": self.sortino_ratio(),
"calmar_ratio": self.calmar_ratio(),
"omega_ratio": self.omega_ratio(),
# Distribution
"skewness": stats.skew(self.returns),
"kurtosis": stats.kurtosis(self.returns),
}Pattern 2: Portfolio Risk
class PortfolioRisk:
"""Portfolio-level risk calculations."""
def __init__(
self,
returns: pd.DataFrame,
weights: Optional[pd.Series] = None
):
"""
Args:
returns: DataFrame with asset returns (columns = assets)
weights: Portfolio weights (default: equal weight)
"""
self.returns = returns
self.weights = weights if weights is not None else \
pd.Series(1/len(returns.columns), index=returns.columns)
self.ann_factor = 252
def portfolio_return(self) -> float:
"""Weighted portfolio return."""
return (self.returns @ self.weights).mean() * self.ann_factor
def portfolio_volatility(self) -> float:
"""Portfolio volatility."""
cov_matrix = self.returns.cov() * self.ann_factor
port_var = self.weights @ cov_matrix @ self.weights
return np.sqrt(port_var)
def marginal_risk_contribution(self) -> pd.Series:
"""Marginal contribution to risk by asset."""
cov_matrix = self.returns.cov() * self.ann_factor
port_vol = self.portfolio_volatility()
# Marginal contribution
mrc = (cov_matrix @ self.weights) / port_vol
return mrc
def component_risk(self) -> pd.Series:
"""Component contribution to total risk."""
mrc = self.marginal_risk_contribution()
return self.weights * mrc
def risk_parity_weights(self, target_vol: float = None) -> pd.Series:
"""Calculate risk parity weights."""
from scipy.optimize import minimize
n = len(self.returns.columns)
cov_matrix = self.returns.cov() * self.ann_factor
def risk_budget_objective(weights):
port_vol = np.sqrt(weights @ cov_matrix @ weights)
mrc = (cov_matrix @ weights) / port_vol
rc = weights * mrc
target_rc = port_vol / n # Equal risk contribution
return np.sum((rc - target_rc) ** 2)
constraints = [
{"type": "eq", "fun": lambda w: np.sum(w) - 1}, # Weights sum to 1
]
bounds = [(0.01, 1.0) for _ in range(n)] # Min 1%, max 100%
x0 = np.array([1/n] * n)
result = minimize(
risk_budget_objective,
x0,
method="SLSQP",
bounds=bounds,
constraints=constraints
)
return pd.Series(result.x, index=self.returns.columns)
def correlation_matrix(self) -> pd.DataFrame:
"""Asset correlation matrix."""
return self.returns.corr()
def diversification_ratio(self) -> float:
"""Diversification ratio (higher = more diversified)."""
asset_vols = self.returns.std() * np.sqrt(self.ann_factor)
weighted_vol = (self.weights * asset_vols).sum()
port_vol = self.portfolio_volatility()
return weighted_vol / port_vol if port_vol > 0 else 1
def tracking_error(self, benchmark_returns: pd.Series) -> float:
"""Tracking error vs benchmark."""
port_returns = self.returns @ self.weights
active_returns = port_returns - benchmark_returns
return active_returns.std() * np.sqrt(self.ann_factor)
def conditional_correlation(
self,
threshold_percentile: float = 10
) -> pd.DataFrame:
"""Correlation during stress periods."""
port_returns = self.returns @ self.weights
threshold = np.percentile(port_returns, threshold_percentile)
stress_mask = port_returns <= threshold
return self.returns[stress_mask].corr()Pattern 3: Rolling Risk Metrics
class RollingRiskMetrics:
"""Rolling window risk calculations."""
def __init__(self, returns: pd.Series, window: int = 63):
"""
Args:
returns: Return series
window: Rolling window size (default: 63 = ~3 months)
"""
self.returns = returns
self.window = window
def rolling_volatility(self, annualized: bool = True) -> pd.Series:
"""Rolling volatility."""
vol = self.returns.rolling(self.window).std()
if annualized:
vol *= np.sqrt(252)
return vol
def rolling_sharpe(self, rf_rate: float = 0.02) -> pd.Series:
"""Rolling Sharpe ratio."""
rolling_return = self.returns.rolling(self.window).mean() * 252
rolling_vol = self.rolling_volatility()
return (rolling_return - rf_rate) / rolling_vol
def rolling_var(self, confidence: float = 0.95) -> pd.Series:
"""Rolling historical VaR."""
return self.returns.rolling(self.window).apply(
lambda x: -np.percentile(x, (1 - confidence) * 100),
raw=True
)
def rolling_max_drawdown(self) -> pd.Series:
"""Rolling maximum drawdown."""
def max_dd(returns):
cumulative = (1 + returns).cumprod()
running_max = cumulative.cummax()
drawdowns = (cumulative - running_max) / running_max
return drawdowns.min()
return self.returns.rolling(self.window).apply(max_dd, raw=False)
def rolling_beta(self, market_returns: pd.Series) -> pd.Series:
"""Rolling beta vs market."""
def calc_beta(window_data):
port_ret = window_data.iloc[:, 0]
mkt_ret = window_data.iloc[:, 1]
cov = np.cov(port_ret, mkt_ret)
return cov[0, 1] / cov[1, 1] if cov[1, 1] != 0 else 0
combined = pd.concat([self.returns, market_returns], axis=1)
return combined.rolling(self.window).apply(
lambda x: calc_beta(x.to_frame()),
raw=False
).iloc[:, 0]
def volatility_regime(
self,
low_threshold: float = 0.10,
high_threshold: float = 0.20
) -> pd.Series:
"""Classify volatility regime."""
vol = self.rolling_volatility()
def classify(v):
if v < low_threshold:
return "low"
elif v > high_threshold:
return "high"
else:
return "normal"
return vol.apply(classify)Pattern 4: Stress Testing
class StressTester:
"""Historical and hypothetical stress testing."""
# Historical crisis periods
HISTORICAL_SCENARIOS = {
"2008_financial_crisis": ("2008-09-01", "2009-03-31"),
"2020_covid_crash": ("2020-02-19", "2020-03-23"),
"2022_rate_hikes": ("2022-01-01", "2022-10-31"),
"dot_com_bust": ("2000-03-01", "2002-10-01"),
"flash_crash_2010": ("2010-05-06", "2010-05-06"),
}
def __init__(self, returns: pd.Series, weights: pd.Series = None):
self.returns = returns
self.weights = weights
def historical_stress_test(
self,
scenario_name: str,
historical_data: pd.DataFrame
) -> Dict[str, float]:
"""Test portfolio against historical crisis period."""
if scenario_name not in self.HISTORICAL_SCENARIOS:
raise ValueError(f"Unknown scenario: {scenario_name}")
start, end = self.HISTORICAL_SCENARIOS[scenario_name]
# Get returns during crisis
crisis_returns = historical_data.loc[start:end]
if self.weights is not None:
port_returns = (crisis_returns @ self.weights)
else:
port_returns = crisis_returns
total_return = (1 + port_returns).prod() - 1
max_dd = self._calculate_max_dd(port_returns)
worst_day = port_returns.min()
return {
"scenario": scenario_name,
"period": f"{start} to {end}",
"total_return": total_return,
"max_drawdown": max_dd,
"worst_day": worst_day,
"volatility": port_returns.std() * np.sqrt(252)
}
def hypothetical_stress_test(
self,
shocks: Dict[str, float]
) -> float:
"""
Test portfolio against hypothetical shocks.
Args:
shocks: Dict of {asset: shock_return}
"""
if self.weights is None:
raise ValueError("Weights required for hypothetical stress test")
total_impact = 0
for asset, shock in shocks.items():
if asset in self.weights.index:
total_impact += self.weights[asset] * shock
return total_impact
def monte_carlo_stress(
self,
n_simulations: int = 10000,
horizon_days: int = 21,
vol_multiplier: float = 2.0
) -> Dict[str, float]:
"""Monte Carlo stress test with elevated volatility."""
mean = self.returns.mean()
vol = self.returns.std() * vol_multiplier
simulations = np.random.normal(
mean,
vol,
(n_simulations, horizon_days)
)
total_returns = (1 + simulations).prod(axis=1) - 1
return {
"expected_loss": -total_returns.mean(),
"var_95": -np.percentile(total_returns, 5),
"var_99": -np.percentile(total_returns, 1),
"worst_case": -total_returns.min(),
"prob_10pct_loss": (total_returns < -0.10).mean()
}
def _calculate_max_dd(self, returns: pd.Series) -> float:
cumulative = (1 + returns).cumprod()
running_max = cumulative.cummax()
drawdowns = (cumulative - running_max) / running_max
return drawdowns.min()Quick Reference
# Daily usage
metrics = RiskMetrics(returns)
print(f"Sharpe: {metrics.sharpe_ratio():.2f}")
print(f"Max DD: {metrics.max_drawdown():.2%}")
print(f"VaR 95%: {metrics.var_historical(0.95):.2%}")
# Full summary
summary = metrics.summary()
for metric, value in summary.items():
print(f"{metric}: {value:.4f}")Best Practices
Do's
- Use multiple metrics - No single metric captures all risk
- Consider tail risk - VaR isn't enough, use CVaR
- Rolling analysis - Risk changes over time
- Stress test - Historical and hypothetical
- Document assumptions - Distribution, lookback, etc.
Don'ts
- Don't rely on VaR alone - Underestimates tail risk
- Don't assume normality - Returns are fat-tailed
- Don't ignore correlation - Increases in stress
- Don't use short lookbacks - Miss regime changes
- Don't forget transaction costs - Affects realized risk