EQUITY & FIXED INCOME STRATEGIES — CHEAT SHEET

EQUITY PORTFOLIO STRATEGIES

Passive vs. Active Management

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Passive Replication Methods

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Rule: Full replication of broad indices (>1000 securities) → prohibitive transaction costs; use stratified sampling instead.

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Active Management Metrics

Information Ratio (IR) $$\text{IR} = \frac{\alpha}{\text{Active Risk (TE)}}$$

Benchmarks:

• IR > 0.75 → excellent

• IR 0.5–0.75 → good

• IR < 0.3 → underperforming

Active Share = fraction of portfolio holdings that differ from benchmark

• >70% → true active manager

• 20–70% → mixed

• <20% → closet indexer (replicates index while charging active fees)

⚠️ Trap: High tracking error ≠ high active share. A manager can deviate from benchmark (high TE) without changing many holdings (low active share) by overweighting high-volatility sectors.

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Long-Short & Extension Strategies

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Mechanics of 130/30: Initial capital $100M → short $30M → reinvest proceeds → long $130M, short $30M, net $100M.

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FACTOR MODELS IN ASSET ALLOCATION

Factor Model Types

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Fama-French Models

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PORTFOLIO CONSTRUCTION & RISK BUDGETING

Smart Beta / Factor Tilting

Definition: Systematic tilt toward factors expected to earn premiums (value, quality, momentum, low volatility) while maintaining low cost and staying approximately long-only.

Advantage over passive: Captures factor premiums; higher cost than full passive but lower than fundamental active.

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Risk Factor Budgeting

Equal Risk Contribution (ERC)

• Weight each asset so it contributes equally to total portfolio variance.

• Formula: $w_i \propto \frac{1}{\sigma_i}$ (inverse volatility weighting; refined for correlation).

• Benefit: More balanced risk across assets than cap-weight; especially useful when asset classes have very different volatilities (equities vs. bonds).

Risk Contribution by Factor $$\text{Risk Contribution}_{\text{factor}} = \beta_{\text{factor}} \times \sigma_{\text{factor}} \times w_{\text{factor}}$$

Budget total portfolio risk among factors rather than capital weights → often produces more diversified, stable allocations.

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HIGH-YIELD DECISION RULES

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Dimension	Passive	Active
Objective	Replicate benchmark return	Generate alpha (excess risk-adjusted return)
Primary Risk Metric	Tracking error (TE)	Active risk = tracking error
Performance Measure	Minimized TE	Information Ratio (IR) = α / active risk
Cost Trade-off	Low costs, low TE	Higher costs, targeting positive IR
Method	Holdings	Tracking Error	Use Case
Full replication	All index securities at index weights	Minimal	Small, liquid indices
Stratified sampling	Representative subset by cell (sector, cap, country)	Low-moderate	Large, broad indices (cost-efficient)
Optimization-based	Subset chosen via factor model to minimize TE	Low-moderate	Highly customized, factor-aware tracking
Strategy	Structure	Net Exposure	Purpose
Long-only	100% long, 0% short	+100%	Traditional equity
Market-neutral	Equal long/short (e.g., $100M L, $100M S)	$0	Pure alpha; β = 0
130/30	130% long, 30% short	+100%	Long-biased + enhanced alpha
150/50	150% long, 50% short	+100%	Higher leverage, higher alpha ambition
Type	Factors	Estimation	Advantage
Macroeconomic	GDP growth, inflation, rates, spreads, liquidity	Regression on economic variables	Interpretable economic story
Fundamental	Size, value, momentum, profitability, investment	Firm characteristics; Fama-French examples	Economically motivated; stable
Statistical (PCA)	Latent factors from return covariance	Principal component analysis	Data-driven; no theory needed
Model	Factors	Use
CAPM (1-factor)	Market (MKT-RF)	Baseline; underexplains cross-section
FF3	MKT + SMB (size) + HML (value)	Standard equity model
Carhart 4	FF3 + UMD (momentum)	Adds price momentum
FF5	FF3 + RMW (profitability) + CMA (investment)	State-of-art; reduces anomalies
Scenario	Decision
Tracking broad index, >1000 securities, cost-conscious	Use stratified sampling
Active share <20%, tracking error >2%	Likely closet indexer → question fees
α = 2%, TE = 2.5%	IR = 0.80 (excellent)
Portfolio 90% long, 30% short	Net +60% exposure; not 130/30
Need stable correlation inputs for optimization	Use factor model rather than direct asset correlations
Want pure alpha, eliminate market risk	Construct market-neutral long-short (L = S)
Asset classes have very different volatilities	Use ERC weighting instead of cap-weight

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COMMON TRAPS

• Confuse "active" with "systematic": Systematic