Portfolio Analytics: Performance Attribution and Measurement

Module: Fintech AI | Difficulty: Advanced

Brinson Attribution

Risk-Adjusted Returns

| Metric | Formula | Interpretation | |--------|---------|---------------| | Sharpe | | Return per risk | | Treynor | | Return per systematic risk | | Jensen | | Alpha |

import numpy as np

class PerformanceAttribution:
    def __init__(self, portfolio_weights, benchmark_weights,
                 portfolio_returns, benchmark_returns):
        self.wp = portfolio_weights; self.wb = benchmark_weights
        self.rp = portfolio_returns; self.rb = benchmark_returns
    def brinson_attribution(self):
        allocation = (self.wp - self.wb) * (self.rb - self.rb.sum())
        selection = self.wb * (self.rp - self.rb)
        interaction = (self.wp - self.wb) * (self.rp - self.rb)
        return {
            'allocation': allocation.sum(),
            'selection': selection.sum(),
            'interaction': interaction.sum(),
            'total': self.rp.sum() - self.rb.sum()
        }

Research Insight: Performance attribution reveals the sources of portfolio returns. The Brinson model decomposes active return into allocation and selection effects. This helps identify whether a manager adds value through asset allocation or security selection.