Factor-based return attribution offers a powerful way to analyze the sources of a portfolio’s active returns. While traditional models like the Brinson model focus on allocation and security selection, factor-based models provide a deeper understanding by decomposing returns into exposures to specific risk factors. The Carhart model is one such framework that attributes returns to four key factors: market index (RMRF), market capitalization (SMB), book-to-price ratio (HML), and momentum (WML).
This article explores the Carhart model, its components, and a practical example of its application, showcasing how it helps in evaluating active management strategies.
The Carhart Four-Factor Model
The Carhart model extends traditional attribution analysis by incorporating specific market factors that influence portfolio returns. The model is expressed as:
This model quantifies the portfolio’s tilt toward specific factors relative to its benchmark and calculates the contribution of each tilt to active returns.
Understanding the Factors
- Market Index (RMRF):
Captures the general market risk premium. A portfolio’s sensitivity to RMRF indicates its exposure to systematic market risk. - Size (SMB):
Measures the performance difference between small-cap and large-cap stocks. Portfolios tilted toward small-cap stocks will have positive sensitivity to SMB. - Value (HML):
Reflects the difference between high and low book-to-market stocks. Positive sensitivity indicates a value tilt, while negative sensitivity suggests growth. - Momentum (WML):
Represents the difference in returns between stocks with strong past performance (“winners”) and poor performers (“losers”). Portfolios with momentum-driven strategies will have higher sensitivity to WML.
Practical Example: Attribution Analysis Using the Carhart Model
Sample Attribution Data
| Factor | Portfolio Sensitivity | Benchmark Sensitivity | Difference | Factor Return | Contribution to Active Return | Proportion of Total Active Return |
|---|---|---|---|---|---|---|
| RMRF | 0.98 | 1.00 | –0.02 | 4.62% | –0.09% | –5.59% |
| SMB | –1.10 | –1.00 | –0.10 | –2.06% | 0.21% | 12.46% |
| HML | 0.30 | 0.00 | 0.30 | 4.30% | 1.29% | 78.01% |
| WML | 0.09 | 0.05 | 0.04 | 8.75% | 0.35% | 21.17% |
| Security Selection | –0.10% | –6.05% |
Analysis
- Benchmark Characteristics:
The benchmark’s sensitivity to RMRF (1.00) indicates it represents a broad market index. Its negative SMB sensitivity suggests a large-cap bias, while zero sensitivity to HML and WML implies no value or momentum tilts. - Portfolio Characteristics:
- RMRF Sensitivity (0.98): Slightly lower market exposure than the benchmark.
- SMB Sensitivity (–1.10): A stronger large-cap bias compared to the benchmark.
- HML Sensitivity (0.30): A clear tilt toward value stocks.
- WML Sensitivity (0.09): Modest momentum exposure exceeding the benchmark.
- Factor Contributions:
- HML (Value Tilt): The largest driver of active returns, contributing 1.29% (78% of total active return).
- WML (Momentum Tilt): Added 0.35% (21.17% of active return).
- SMB (Size Tilt): A smaller but positive contribution of 0.21%.
- RMRF (Market Exposure): Detracted slightly from active returns (–0.09%).
- Security Selection:
The manager’s stock-picking underperformed, detracting 0.10% from active returns.
Total Active Return:
Factor tilts contributed 1.75%, but security selection detracted 0.10%, resulting in a net active return of 1.65%.
Key Insights from Factor-Based Attribution
- The portfolio manager’s value tilt was the dominant source of excess returns, consistent with a value-oriented strategy.
- Momentum and size tilts also contributed positively, though to a lesser extent.
- Security selection slightly detracted, suggesting the manager’s stock-picking could improve.
- The results align well if the manager’s prospectus highlights a value-driven approach. However, misalignment between stated and actual strategies warrants further investigation.
Advantages of the Carhart Model
- Granular Analysis: Breaks down returns into specific factors, providing deep insights into portfolio strategy.
- Quantifies Manager Skill: Separates returns due to market factors from those driven by active management decisions.
- Transparency: Helps clients and stakeholders understand the sources of portfolio performance.
Conclusion
Factor-based return attribution, especially using the Carhart model, is an essential tool for evaluating the effectiveness of active portfolio management. By isolating contributions from market exposure, size, value, and momentum, it provides actionable insights into a manager’s investment decisions. For fund sponsors, institutional investors, and portfolio managers, understanding these dynamics is crucial for aligning strategies with objectives and maintaining transparency with clients.
