Risk & Portfolio

Three sectors. The portfolio overweights tech (50% against 40%), which beat the benchmark, and picks better stocks in tech and energy. Brinson–Fachler splits the 1.2% active return into allocation 0.3%, selection 0.6% and interaction 0.3% — and the three add up exactly.

• Interaction has no natural owner; many reports fold it into selection, which changes the story.
• Over several periods the effects do not add up without a linking method, and different methods give different splits (Bacon 2008).
• Sectors are not the only way to slice; a factor tilt can show up as “selection” in a sector model.

t = pd.DataFrame({'wp': [0.50, 0.30, 0.20], 'wb': [0.40, 0.40, 0.20],    # portfolio and benchmark weights
                  'rp': [0.10, 0.04, 0.02], 'rb': [0.08, 0.05, 0.01]},  # sector returns
                 index=['tech', 'finance', 'energy'])
Rb = (t.wb * t.rb).sum()
allocation = ((t.wp - t.wb) * (t.rb - Rb)).sum()           # Brinson-Fachler
selection = (t.wb * (t.rp - t.rb)).sum()
interaction = ((t.wp - t.wb) * (t.rp - t.rb)).sum()
active = (t.wp * t.rp).sum() - Rb

Assumes import numpy as np and import pandas as pd. Each snippet carries its own example numbers; the comments say which are made up or simulated.