The Three Building Blocks of Portfolio Construction: 1. Rewarded Factor Weightings: Overweighting or underweighting factors with associated long-term premiums (e.g., Market, Size, Value, Momentum). 2. Alpha Skills: The manager’s ability to generate excess returns unrelated to factor exposures (e.g., through factor timing or selecting specific mispriced securities). 3. Position Sizing: Allocating capital to specific ideas to balance return potential against risk.
Breadth of Expertise: * A fourth critical component. A manager’s ability to outperform is linked to the number of independent investment decisions (bets) they make.
Active Return (\(R_A\)) Calculation: * The difference between the portfolio return and benchmark return. * Formula: \(R_A = \sum_{i=1}^{N} \Delta W_i R_i\) * Where \(\Delta W_i\) is the active weight (\(W_{portfolio} - W_{benchmark}\)). * Decomposition: \(R_A = \sum (\beta_{pk} - \beta_{bk}) \times F_k + (\alpha + \epsilon)\) * Active return comes from: Factor Tilts (difference in beta to factors) + Alpha (skill) + Luck/Noise (\(\epsilon\)).
Systematic (Quantitative) vs. Discretionary (Fundamental) * Systematic: Rules-based, automated, typically looks at a broad universe of securities, manages risk at the portfolio level. * Discretionary: Judgment-based, relies on in-depth analysis of a smaller subset of stocks, manages risk at the company level.
Bottom-Up vs. Top-Down * Bottom-Up: Starts with individual security valuation. Aggregating these picks results in incidental sector/country exposures. * Top-Down: Starts with macro/market environment to set sector/country weights, then selects securities to fulfill those quotas.
Risk Budgeting: * The process of allocating the total risk appetite of the portfolio among various components (e.g., factors, specific securities). * Absolute Risk: Total volatility (\(\sigma_p\)). Appropriate for absolute return mandates. * Relative Risk: Active risk/Tracking error (\(\sigma_{R_p - R_b}\)). Appropriate for benchmark-relative mandates. * Contribution to Variance: * A manager can decompose risk to see how much comes from the Market factor vs. Style factors vs. Idiosyncratic risk. * Formula for contribution of asset \(i\) to active variance: \(CAV_i = (x_i - b_i) \times RC_{ip}\) (where \(RC\) is covariance of relative returns).
Constraints: 1. Heuristic Constraints: Rules of thumb based on experience. * Examples: “Max 3% in any single stock,” “Sector weights within +/- 5% of benchmark,” “No cash > 5%.” * Pros: Easy to communicate and implement; prevents hubris. * Cons: May inefficiently constrain managers with genuine skill. 2. Formal Risk Constraints: Statistical limits based on return distribution models. * Examples: “Predicted Tracking Error < 4%,” “VaR (5%) < 2%.” * Cons: Estimation error (historical correlations may not hold in crises).
Risk Measures: * Value at Risk (VaR): Minimum expected loss at a given probability (e.g., 5%) over a specific time. * Conditional VaR (CVaR): Expected loss given that the loss exceeds the VaR (measures the tail). * Incremental VaR (IVaR): Change in VaR from adding a new position. * Marginal VaR (MVaR): Impact of a small change in position size on portfolio VaR.
Market Impact Cost: * Buying large positions pushes prices up; selling pushes them down. * Slippage: The difference between the decision price and the execution price. * Relationship: Higher AUM \(\rightarrow\) Larger trade sizes \(\rightarrow\) Higher market impact.
The Implementation Shortfall: * Managers with large AUM in illiquid stocks face a trade-off: * Trade Fast: High market impact costs. * Trade Slow: High opportunity cost (alpha decays while waiting). * Cap Limits: Managers may close funds to new investors (soft close or hard close) to preserve performance when AUM becomes too large to trade efficiently.
The “Well-Constructed” Portfolio: * Characteristics: 1. Clear investment philosophy and consistent process. 2. Risk exposures match the manager’s promises (e.g., a stock picker should have high Active Share). 3. Low unexplained (idiosyncratic) risk unless the manager is a discretionary stock picker targeting alpha. 4. Cost-efficient delivery (fees and trading costs are justified by expected alpha). * Structural Mismatches: * A “Diversified Factor” manager should not have high idiosyncratic risk. * A “Sector Rotator” should typically have high active risk.
1. Long-Only: * Constraint: Cannot sell what you don’t own. * Limitation: Hard to underweight small-cap stocks (if a stock is 0.05% of index, max underweight is 0.05%). This limits the ability to exploit negative views.
2. Long/Short: * Structure: Can hold long positions and short positions. * Gross Exposure: Longs + |Shorts|. (Often > 100%). * Net Exposure: Longs - |Shorts|. (Market directional bias). * Pros: Can fully exploit negative views; better risk management (hedging). * Cons: Unlimited loss potential on shorts; borrowing costs; regulatory constraints; operational complexity (prime brokerage).
3. Long Extension (e.g., 130/30): * Structure: 130% Long, 30% Short. Net exposure = 100% (beta \(\approx\) 1). * Goal: Maintain market exposure while leveraging stock selection skills (using proceeds from shorts to buy more longs). * Benefit: Allows the manager to underweight stocks by more than their index weight (e.g., shorting a stock by 2%).
4. Market Neutral: * Structure: \(\beta \approx 0\). Longs roughly equal Shorts. * Goal: Generate pure alpha uncorrelated with the market. * Equitized Market Neutral: Taking a cash-neutral long/short alpha portfolio and overlaying it with equity futures to gain market beta.