CFA Level III · Portfolio Management Pathway

Active Equity Investing: Strategies: formula sheet

Full chapter guide

Key formulas

Active return: Active return = Portfolio return − Benchmark return; Measures the excess over the benchmark before judging risk. Positive is not enough if the risk taken was large.
Tracking error (active risk): Tracking error = standard deviation of (Portfolio return − Benchmark return); Higher tracking error means a larger deviation from the benchmark. Concentrated, high-conviction strategies usually have higher tracking error.
Information ratio: IR = Active return ÷ Tracking error; Active return per unit of active risk. Use it to compare managers with different risk levels.
Earnings yield: Earnings yield = E ÷ P = 1 ÷ (P/E); Use it to compare cheapness across stocks or against bond yields. A low P/E means a high earnings yield.
Dividend yield: Dividend yield = annual dividend per share ÷ price per share; Check payout ratio and earnings coverage to judge whether the dividend is safe.
Price-to-book: P/B = price per share ÷ book value per share; Common asset-based screen. Book value may differ from market or liquidation value.
Net asset value per share: NAV per share = (market value of assets − liabilities) ÷ shares outstanding; Asset-based approach. Buy when price is below NAV per share, allowing for a margin of safety.
Dividend payout ratio: Payout ratio = dividends ÷ earnings; A very high ratio with a high yield is a warning sign of a possible cut.
PEG ratio: PEG = (P/E) ÷ expected annual earnings growth rate (in % points); Lower PEG suggests cheaper growth. Used in GARP. Compare with peers, and check that the growth forecast is reliable.
Growth style rule: Growth = high expected growth, high multiples; Value = low multiples, price below intrinsic value; Use to classify a manager from the facts given in the vignette.
Double hit of overpaying: Price change ≈ (change in earnings) combined with (change in P/E multiple); If growth disappoints, both fall, so losses can be larger than the earnings miss alone.
Returns-based style model: Rp,t = a + b1·R(style 1),t + b2·R(style 2),t + … + bn·R(style n),t + e,t; Weights b are usually constrained: each b ≥ 0 and Σb = 1. The weights are the effective style mix; a and e capture manager selection.
Style drift test: Drift = style exposure now − style exposure at the stated or earlier point; Compare holdings characteristics or rolling regression weights with the mandate. Persistent, unintended change is drift.
Style box structure: Size (large, mid, small) × Style (value, blend, growth); Holdings-based. Each security goes in a cell using its characteristics; the portfolio is the weighted spread.
Active share: Active share = ½ × Σ |wP,i − wB,i|; Sum over all securities held in the portfolio or the benchmark. Weights are in the same units. Result runs from 0% to 100% for long-only portfolios.
Active weight: Active weight = wP,i − wB,i; Positive means overweight, negative means underweight. Active weights sum to zero for fully invested long-only portfolios.
Active return: Active return = RP − RB; Return of the portfolio minus return of the benchmark in the same period.
Tracking risk: Tracking risk = standard deviation of (RP − RB); Use the sample standard deviation of periodic active returns, then annualize if asked. Annualizing: periodic value × √(periods per year).
Equivalent active share form: Active share = Σ of positive active weights = |Σ of negative active weights|; Works when both portfolios are fully invested with no leverage or shorting. Often quicker than halving the absolute sum.
Net exposure: Net exposure = long % − short %; A 130/30 portfolio has net exposure of 130% − 30% = 100%. Gross exposure = long % + short % = 160%.
Gross exposure: Gross exposure = long % + short %; Measures total leverage. Higher gross exposure means higher risk and trading cost.
Market-neutral condition: Portfolio beta ≈ 0, so Σ(wi × βi) ≈ 0; Dollar-neutral does not guarantee beta-neutral. Long and short books can have different betas.
Long-short return (simple): Return = long contribution + short contribution + interest on short proceeds − borrowing costs − fees; Short contribution is positive when shorted stocks fall. Include stated costs only when given.
Active return: Active return = Portfolio return − Benchmark return; Measured per period. Net of fees when judging a manager.
Tracking error (active risk): TE = standard deviation of active returns; Usually annualized. Higher TE means a wider range of outcomes versus the benchmark.
Information ratio: IR = Average active return ÷ Tracking error; Return per unit of active risk. Use net-of-fee active return for selection.
Combined tracking error of two sleeves: TE_p = √(w1² × TE1² + w2² × TE2² + 2 × w1 × w2 × ρ × TE1 × TE2); w are weights of each sleeve, ρ is the correlation of the sleeves' active returns. Lower ρ gives lower combined TE.
Core-satellite active risk (core with no active risk): TE_p = w_satellite × TE_satellite; Holds only if the core is a pure index with zero tracking error. Simple scaling of active risk.
Active share: Active share = ½ × Σ |w_portfolio,i − w_benchmark,i|; Ranges from 0% (index) to 100% (no overlap). Helps spot closet indexers.

Quick revision

Active management deliberately departs from the benchmark to seek excess return.
Top-down starts with markets or sectors; bottom-up starts with individual companies.
Value managers buy stocks they judge cheap relative to fundamentals.
Growth managers look for above-average earnings or revenue growth.
Value and growth each have sub-types, and the sub-type changes the risks.
Style drift is a move away from the manager's stated style over time.
Active share measures how much portfolio holdings differ from benchmark holdings.
Tracking risk measures the variability of returns relative to the benchmark.
A high active share does not by itself prove skill.
Activist strategies seek to improve a company through engagement.
Match manager choice to the client's objectives and constraints.
Answer the command word first, then give one clear reason.

Common mistakes

Treating bottom-up and top-down as the same as value and growth. Fix: Bottom-up and top-down describe the order of decisions. Value and growth describe the type of stock sought. A bottom-up manager can be either value or growth.
Saying active management always beats passive in inefficient markets. Fix: Inefficiency gives more opportunity, not a guarantee. Skill and costs still decide the net result. Use words like 'greater scope'.
Treating any low multiple as proof a stock is undervalued. Fix: Ask why the multiple is low. If earnings are expected to fall, it may be a value trap.
Confusing contrarian with deep value. Fix: Contrarian is defined by trading against sentiment and overreaction. Deep value is defined by very low price relative to assets or normalized earnings, often with distress.
Treating GARP as the same as value investing. Fix: GARP still requires above-average growth. Value does not. GARP limits what you pay for growth.
Saying momentum investing relies on intrinsic value. Fix: Momentum follows price or earnings trends. It does not need a valuation view.
Using a returns-based method when holdings are supplied, or the reverse. Fix: Start every question by asking what data is available and match the method to it.
Saying returns-based analysis needs holdings data. Fix: Remember returns-based needs only portfolio and index returns. Its weakness is the long history and index choice.
Forgetting the ½ in the active share formula Fix: Write ½ × Σ|…| first, then fill in. The result must not exceed 100% for a long-only portfolio.
Leaving out securities held only in the benchmark Fix: Include every benchmark constituent. A stock the manager does not own has portfolio weight 0% and still adds to the difference.

Exam tips

Answer the classification first, then give the reason. Short, direct responses earn the points.
Always link your choice of approach to a named client objective or constraint from the vignette.
Show each step of any IR or active return calculation, though a correct number on its own earns full credit.
Read command words in bold. 'Justify' needs a reason, while 'identify' needs only the name.
Expect this topic to appear inside the Portfolio Management pathway mixed with item sets and essays, so be ready for both formats.
Match the style to the evidence in the vignette. Name the style in the first few words of your answer.
When asked for a risk, give the one specific to that style, then add one phrase on why it applies here.
Show formulas and working for yields and P/E. A correct number alone earns credit, but working protects you if the setup is wrong.