Portfolio Risk: Factor Decomposition and Attribution

Module: Fintech AI | Difficulty: Advanced

Risk Decomposition

Factor Risk

where = factor loadings, = factor covariance, = specific risk.

Marginal Risk Contribution

import numpy as np

class PortfolioRiskAnalyzer:
    def __init__(self, weights, cov_matrix):
        self.w = weights; self.cov = cov_matrix
    def total_risk(self):
        return np.sqrt(self.w @ self.cov @ self.w)
    def risk_contribution(self):
        portfolio_vol = self.total_risk()
        marginal = self.cov @ self.w / portfolio_vol
        return self.w * marginal
    def factor_risk(self, factor_loadings, factor_cov):
        systematic = self.w @ factor_loadings @ factor_cov @ factor_loadings.T @ self.w
        specific = self.total_risk()**2 - systematic
        return {'systematic': systematic, 'specific': specific}

Research Insight: Risk attribution reveals where portfolio risk comes from. Most portfolios have 80%+ systematic risk, meaning diversification provides limited benefit during market stress. Understanding factor exposures is crucial for risk management.