29 — Active Share, Style Tilt, and Shareholder Yield¶

Free learning pack¶

1. reference/equity/active_share.md
2. reference/equity/equity_factor_investing.md
3. reference/equity/shareholder_yield.md

Do not search for more material until these are insufficient.

PREDICT¶

A fund holds 98% of the same names, at nearly the same weights, as its benchmark. Without calculating, is its active share close to 0%, close to 50%, or close to 100%? Could this fund still justify an active management fee?

Formula (active share)¶

active_share = 0.5 * sum(|w_portfolio_i - w_benchmark_i|)

In [ ]:

portfolio_weights = [0.60, 0.40]
benchmark_weights = [0.50, 0.50]

# MANUAL FIRST:
# compute active share by hand from the active weights.
active_share_value = None
print(active_share_value)

portfolio_weights = [0.60, 0.40] benchmark_weights = [0.50, 0.50] # MANUAL FIRST: # compute active share by hand from the active weights. active_share_value = None print(active_share_value)

PREDICT (style tilt)¶

A portfolio's value-factor exposure is +0.6, its benchmark's is +0.1. Without calculating, is this portfolio tilted toward value or away from it, relative to the benchmark — and is that the same question as asking whether the portfolio's raw exposure is positive?

Formula (style tilt)¶

style_tilt = portfolio_exposure - benchmark_exposure

Get each side's exposure first with pm.factors.portfolio_factor_exposure(weights, factor_scores) — the same generic function Phase 4's risk-model work uses, applied here to a single equity style factor's scores.

In [ ]:

portfolio_value_exposure = 0.6
benchmark_value_exposure = 0.1

# MANUAL FIRST:
# compute the active style tilt by hand.
tilt = None
print(tilt)

portfolio_value_exposure = 0.6 benchmark_value_exposure = 0.1 # MANUAL FIRST: # compute the active style tilt by hand. tilt = None print(tilt)

PREDICT (shareholder yield)¶

Company A pays a 1% dividend yield and buys back 4% of its market cap a year. Company B pays a 5% dividend yield and buys back nothing. Without calculating, do these two companies return the same amount of cash to shareholders, more for A, or more for B?

Formula¶

shareholder_yield = dividend_yield + buyback_yield

total_shareholder_return = (price_end - price_start + dividends_paid) / price_start

In [ ]:

dividend_per_share, price = 1.0, 100.0  # 1% dividend yield
buyback_value, market_cap = 400.0, 10_000.0  # 4% buyback yield

price_start, price_end, dividends_paid = 100.0, 108.0, 2.0

# MANUAL FIRST:
# compute Company A's shareholder yield, and a separate stock's total
# shareholder return from the price/dividend numbers above.
shareholder_yield_value = None
total_shareholder_return_value = None
print(shareholder_yield_value, total_shareholder_return_value)

dividend_per_share, price = 1.0, 100.0 # 1% dividend yield buyback_value, market_cap = 400.0, 10_000.0 # 4% buyback yield price_start, price_end, dividends_paid = 100.0, 108.0, 2.0 # MANUAL FIRST: # compute Company A's shareholder yield, and a separate stock's total # shareholder return from the price/dividend numbers above. shareholder_yield_value = None total_shareholder_return_value = None print(shareholder_yield_value, total_shareholder_return_value)

Experiment¶

Recompute active share for a fund with 20% active weight concentrated in just one name out of ten versus one spread evenly across all ten at 2% each. Same total active share — does that change how much you'd trust the position sizing?

Reference¶

reference/equity/active_share.md reference/equity/equity_factor_investing.md reference/equity/shareholder_yield.md

Promote¶

Use src/pm/equity/factors.py (active_share, style_tilt) and src/pm/equity/income.py (shareholder_yield, total_shareholder_return) only after your own implementation.

Test¶

pytest tests/test_equity.py

ORAL CHECK¶

Explain to a PM why active share and tracking error can disagree about how "active" the same portfolio is, and why a buyback-heavy company isn't returning less cash to shareholders than a dividend-heavy one just because its dividend yield looks small.

Try /tutor active share or /tutor equity factor investing for an adaptive walkthrough.