12 — Attribution¶

Learning objectives¶

Reconcile a simple contribution-based P&L breakdown; then compute a real Brinson allocation/selection/interaction decomposition and confirm the three effects sum exactly to active return. (For the full multi-period version and a deeper Brinson treatment, see notebooks/integration/25_brinson_and_rebalancing.ipynb; the true end-to-end integration exercise is the capstone, notebooks/integration/30_capstone_portfolio_review.ipynb.)

Free learning pack¶

1. reference/concepts/brinson_attribution.md
2. CFA active portfolio management page
3. PIMCO fixed-income education hub

Do not search for more material until these are insufficient.

Distinction¶

Attribution asks: what caused realized performance? — as opposed to scenario analysis (notebook 11), which asks "what would happen." Attribution looks backward at what actually happened; a teaching decomposition: carry, rates, curve, spread, equity/factor, residual/selection.

In [ ]:

contributions = {
    "carry": 210_000,
    "rates": 470_000,
    "curve": -80_000,
    "credit_spread": 510_000,
    "selection_residual": 230_000,
}

# MANUAL FIRST: reconcile total P&L (just sum the dict's values).
total_pnl = None
print(total_pnl)

# CHECK (uncomment after your attempt):
# assert total_pnl == 1_340_000

contributions = { "carry": 210_000, "rates": 470_000, "curve": -80_000, "credit_spread": 510_000, "selection_residual": 230_000, } # MANUAL FIRST: reconcile total P&L (just sum the dict's values). total_pnl = None print(total_pnl) # CHECK (uncomment after your attempt): # assert total_pnl == 1_340_000

PREDICT¶

A portfolio holds the exact same assets as its benchmark, just at different weights — no stock-picking or bond-picking within any bucket, purely different sizing decisions. Before calculating: should the Brinson selection effect come out to exactly zero, roughly zero, or could it still be nonzero?

Formula (Brinson attribution)¶

allocation = (w_p - w_b) * r_b

selection = w_b * (r_p - r_b)

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

Identity: sum(allocation + selection + interaction) = active_return

In [ ]:

import numpy as np

# Portfolio and benchmark hold the same 3 segments, same realized returns
# per segment (rp == rb) - only the weights differ.
wp = np.array([0.5, 0.3, 0.2])
wb = np.array([0.4, 0.4, 0.2])
rp = np.array([0.08, 0.05, 0.03])
rb = np.array([0.08, 0.05, 0.03])  # identical to rp: no selection skill by construction

# MANUAL FIRST:
allocation = None
selection = None
interaction = None
print("allocation:", allocation, " sum:", None if allocation is None else allocation.sum())
print("selection:", selection)

portfolio_return = float(wp @ rp)
benchmark_return = float(wb @ rb)
active_return = portfolio_return - benchmark_return
print("active return:", active_return)

# CHECK (uncomment after your attempt):
# assert np.allclose(selection, 0.0) and np.allclose(interaction, 0.0), (
#     "with rp==rb per segment, only the weighting decision can differ - "
#     "selection and interaction must be exactly zero"
# )
# assert np.isclose(allocation.sum(), active_return)

import numpy as np # Portfolio and benchmark hold the same 3 segments, same realized returns # per segment (rp == rb) - only the weights differ. wp = np.array([0.5, 0.3, 0.2]) wb = np.array([0.4, 0.4, 0.2]) rp = np.array([0.08, 0.05, 0.03]) rb = np.array([0.08, 0.05, 0.03]) # identical to rp: no selection skill by construction # MANUAL FIRST: allocation = None selection = None interaction = None print("allocation:", allocation, " sum:", None if allocation is None else allocation.sum()) print("selection:", selection) portfolio_return = float(wp @ rp) benchmark_return = float(wb @ rb) active_return = portfolio_return - benchmark_return print("active return:", active_return) # CHECK (uncomment after your attempt): # assert np.allclose(selection, 0.0) and np.allclose(interaction, 0.0), ( # "with rp==rb per segment, only the weighting decision can differ - " # "selection and interaction must be exactly zero" # ) # assert np.isclose(allocation.sum(), active_return)

Now with real selection skill¶

Same weights, but this time the portfolio's realized returns differ from the benchmark's within each segment too.

In [ ]:

rp_skill = np.array([0.09, 0.04, 0.035])  # portfolio beat segment 1, lagged segment 2

# MANUAL FIRST:
from pm.attribution import brinson_attribution

allocation2, selection2, interaction2 = None, None, None
active_return2 = float(wp @ rp_skill - wb @ rb)
print("allocation:", allocation2.sum() if allocation2 is not None else None)
print("selection:", selection2.sum() if selection2 is not None else None)
print("interaction:", interaction2.sum() if interaction2 is not None else None)

# CHECK (uncomment after your attempt):
# assert np.isclose(allocation2.sum() + selection2.sum() + interaction2.sum(), active_return2)
# assert not np.allclose(selection2, 0.0), "this time selection should be genuinely nonzero"

rp_skill = np.array([0.09, 0.04, 0.035]) # portfolio beat segment 1, lagged segment 2 # MANUAL FIRST: from pm.attribution import brinson_attribution allocation2, selection2, interaction2 = None, None, None active_return2 = float(wp @ rp_skill - wb @ rb) print("allocation:", allocation2.sum() if allocation2 is not None else None) print("selection:", selection2.sum() if selection2 is not None else None) print("interaction:", interaction2.sum() if interaction2 is not None else None) # CHECK (uncomment after your attempt): # assert np.isclose(allocation2.sum() + selection2.sum() + interaction2.sum(), active_return2) # assert not np.allclose(selection2, 0.0), "this time selection should be genuinely nonzero"

Reference¶

reference/concepts/brinson_attribution.md

Promote¶

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

Test¶

pytest tests/test_attribution.py

ORAL CHECK¶

Explain to a PM why allocation and selection are genuinely different skills — a manager could get one right and the other wrong. Using your two examples above, what would you tell a PM whose portfolio shows large allocation effect and near-zero selection effect, versus the reverse?

Try /tutor Brinson attribution for an adaptive walkthrough. Continue to docs/PROGRESS.md to log what you've completed.