25 — Brinson Attribution, Transaction Costs, and Rebalancing¶

Free learning pack¶

1. CFA active portfolio management page
2. reference/concepts/brinson_attribution.md, transaction_costs_and_rebalancing.md

Do not search for more material until these are insufficient.

PREDICT¶

A PM was overweight a sector that outperformed (good allocation) but picked the worst-performing names within it (bad selection). Could the portfolio still beat the benchmark overall? Could it still lose to the benchmark despite the good sector call?

Formula¶

allocation = (w_p - w_b) * r_b

selection = w_b * (r_p - r_b)

interaction = (w_p - w_b) * (r_p - r_b)

These sum to total active return.

In [ ]:

import numpy as np

sectors = ["Tech", "Financials", "Energy"]
w_p = np.array([0.45, 0.25, 0.30])
w_b = np.array([0.30, 0.35, 0.35])
r_p = np.array([0.12, 0.05, -0.02])
r_b = np.array([0.15, 0.06, 0.01])

# MANUAL FIRST:
# compute allocation, selection, and interaction per sector, then confirm
# they sum (across all three effects and all three sectors) to
# w_p @ r_p - w_b @ r_b.
allocation = None
selection = None
interaction = None
print(allocation, selection, interaction)

import numpy as np sectors = ["Tech", "Financials", "Energy"] w_p = np.array([0.45, 0.25, 0.30]) w_b = np.array([0.30, 0.35, 0.35]) r_p = np.array([0.12, 0.05, -0.02]) r_b = np.array([0.15, 0.06, 0.01]) # MANUAL FIRST: # compute allocation, selection, and interaction per sector, then confirm # they sum (across all three effects and all three sectors) to # w_p @ r_p - w_b @ r_b. allocation = None selection = None interaction = None print(allocation, selection, interaction)

PREDICT (rebalancing cost)¶

Rebalancing back to target weights always has a transaction cost. Under what circumstance would a PM choose not to fully rebalance despite drift from target?

Formula¶

trade_i = (target_weight_i - current_weight_i) * PortfolioValue

cost_i = |trade_i| * cost_bps / 10,000

In [ ]:

current_weights = np.array([0.45, 0.25, 0.30])
target_weights = np.array([0.30, 0.35, 0.35])
portfolio_value = 50_000_000
cost_bps = 8

# MANUAL FIRST:
# compute the dollar trade needed in each sector to rebalance to target,
# then the total transaction cost across all three trades.
trades = None
total_cost = None
print(trades, total_cost)

current_weights = np.array([0.45, 0.25, 0.30]) target_weights = np.array([0.30, 0.35, 0.35]) portfolio_value = 50_000_000 cost_bps = 8 # MANUAL FIRST: # compute the dollar trade needed in each sector to rebalance to target, # then the total transaction cost across all three trades. trades = None total_cost = None print(trades, total_cost)

Not implemented here: liquidity-aware cost¶

This uses a flat cost_bps regardless of trade size or market conditions. Read reference/concepts/liquidity.md for why realistic market-impact modeling is out of scope here.

Experiment¶

Recompute the Brinson decomposition with w_p = w_b (no active weights at all). Confirm allocation and interaction both vanish, leaving only selection.

Reference¶

reference/concepts/brinson_attribution.md
reference/concepts/fixed_income_attribution.md
reference/concepts/transaction_costs_and_rebalancing.md

Promote¶

Use src/pm/attribution.py (brinson_attribution, transaction_cost, rebalancing_trades) only after your own implementation.

Test¶

pytest tests/test_attribution.py

ORAL CHECK¶

Explain to a PM why allocation and selection can point in opposite directions and roughly cancel, and why that's a meaningfully different outcome from "nothing happened."

Try /tutor concept brinson attribution for an adaptive walkthrough.