Introduction

Macro attribution measures the effects of the fund sponsor’s decisions on returns.

Micro attribution measures the impact of the individual portfolio manager’s decisions.

Equity Attribution

BHB Model

The allocation effect = \(\sum_{i}^{K}(w_i - W_i) \cdot B_i\) or the difference between portfolio and benchmark weights multiplied by the benchmark return summed over each asset class.

The selection effect is \(\sum_{i}^{K} W_i (R_i - B_i)\).

The two effects may not explain the entire excess return.

The interaction effect explains the remaining difference. It is \(\sum_{i}^{K} (w_i - W_i)(R_i - B_i)\).

Brinson-Fachler Model

Allocation: \[ A_i = (w_i - W_i) (B_i - B) \]