Performance Attribution

Core Concepts

Brinson-Fachler Attribution (Single Period)

The classic equity attribution model decomposes active return (portfolio return minus benchmark return) into three effects:

• Allocation effect: Value added by over/underweighting sectors relative to the benchmark
  • A_i = (w_p,i - w_b,i) × (R_b,i - R_b)
  • Rewards overweighting sectors that outperform the total benchmark
• Selection effect: Value added by picking better securities within each sector
  • S_i = w_b,i × (R_p,i - R_b,i)
  • Rewards outperforming the sector benchmark regardless of weight
• Interaction effect: Combined effect of both overweighting and outperforming (or vice versa)
  • I_i = (w_p,i - w_b,i) × (R_p,i - R_b,i)
  • Captures the joint benefit of overweighting a sector AND selecting better securities in it
• Total active return: R_p - R_b = Σ A_i + Σ S_i + Σ I_i

Where: w_p,i = portfolio weight in sector i, w_b,i = benchmark weight in sector i, R_p,i = portfolio return in sector i, R_b,i = benchmark return in sector i, R_b = total benchmark return.