risk-metrics-calculation

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 allocation

Implementation

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),
        }