About FactorsToday

About the Creator

FactorsToday was created by Lukasz Tomicki, Founder and Managing Partner of LRT Capital Management, an investment firm based in Austin, Texas. Founded in 2012, LRT Capital employs a proprietary systematic long-short investment strategy focused on companies with durable economic moats.

Lukasz also teaches finance at The University of Texas at Austin's McCombs School of Business and has been featured in Bloomberg, BNN Bloomberg, and Schwab Network discussing quantitative investment strategies and market analysis.

Contact: Lukasz R. Tomicki — ltomicki@lrtcapital.com

⚠ Important Disclaimer

FactorsToday is provided for informational and educational purposes only. The data, analysis, and tools on this site do not constitute investment advice, recommendations, or solicitations to buy or sell any securities. Past performance does not guarantee future results. Factor exposures and model fits are statistical estimates and may not accurately represent future relationships; no guarantee is made regarding the accuracy or reliability of any particular model fit. Always conduct your own research and consult with a qualified financial advisor before making investment decisions. The creators of FactorsToday are not liable for any losses incurred from using this information.

What is Factor Investing?

Factor investing is a systematic approach to understanding and decomposing investment returns. Rather than viewing a stock's return as a single number, factor analysis breaks it down into components attributable to various systematic risk exposures—such as market risk, size, value, momentum, and others.

By understanding a stock's factor exposures, investors can:

• Attribute Performance: Understand why a stock or portfolio performed the way it did
• Manage Risk: Identify hidden risk concentrations and diversify more effectively
• Build Portfolios: Construct portfolios with desired factor tilts
• Generate Alpha: Identify stocks with attractive characteristics after controlling for known factors

Factor Construction Methodology

FactorsToday uses a rigorous quantitative methodology to construct pure factor returns. Each factor is designed to isolate a specific risk premium or market characteristic while removing exposure to other known factors. This "purification" process ensures that when you see exposure to the Value factor, it represents pure value exposure—not value mixed with market beta or size effects.

The Problem with Raw Factor Returns

Consider a simple "Value" factor constructed by going long value stocks and short growth stocks. This raw return stream will contain contamination from other factors: value stocks tend to be smaller (size effect), may have different market betas, and may have sector tilts. Without purification, you cannot cleanly attribute returns to the "value" characteristic alone.

Core Methodology: Factor Purification

Our factors undergo a rigorous multi-step purification process:

Key Hyperparameters Summary

Factor Types

FactorsToday constructs six categories of factors, each serving different analytical purposes. Factors are computed in a specific order to ensure proper dependency resolution—standard factors first, then dependent factors that use the standard factors for stripping, followed by sector, industry, country, and custom factors.

1. Standard Factors

Core risk factors constructed from liquid ETFs. These form the foundation of the factor model and are used to strip other factors. Each factor captures a well-documented risk premium:

2. Dependent Factors

These factors are computed after standard factors and are fully orthogonalized against all of them. This means their returns represent pure exposure to the named characteristic with zero correlation to Market, Size, Value, etc.

• Buybacks: Buyback premium (DIVB - VYM), stripped of all standard factors. Captures the return attributable to share repurchases after controlling for other factors.
• USDividends: US dividend exposure (VYM), fully orthogonalized. Pure dividend yield exposure independent of value, quality, or other characteristics.
• GlobalDividends: Global dividend exposure (SDIV), fully orthogonalized. International high-yield equity exposure, purified of US factor effects.

3. Sector Factors

Broad sector-level factors derived from Select Sector SPDR ETFs (XLF, XLK, XLE, XLV, XLB, XLI, XLY, XLP, XLU, XLRE, XLC). These capture exposure to the 11 GICS sectors. The construction process:

1. Source: Daily returns from Sector SPDR ETFs with at least 756 days (~3 years) of trading history
2. Purification: Regressed against all standard factors using the full factor stripping methodology
3. Result: Pure sector-specific return—the portion of sector performance not explained by broad market factors like beta, size, or value

For example, the "Sector: Technology" factor captures pure tech sector exposure at the broadest level. A stock with high exposure to this factor moves with the overall tech sector in ways not explained by its market beta or other characteristics.

4. Industry Factors

Granular industry-level factors derived from specialized iShares and other thematic ETFs. These provide more targeted exposure than broad sector factors, capturing specific sub-industries and investment themes. The construction process is identical to sector factors: daily returns are purified against all standard factors.

Industry factors require at least 504 trading days (~2 years) of history. The full list of industry factors includes:

The distinction between Sector and Industry factors is important: Sector factors capture broad exposure to major economic sectors, while Industry factors capture more specific sub-industry themes. For example, a semiconductor company will have exposure to both "Sector: Technology" (broad tech sector) and "Industry: Semiconductors" (specific chip industry).

5. Country Factors

Geographic factors derived from iShares and other country-specific ETFs. Each country factor captures pure country-specific exposure after removing all standard factor exposures (Market, Size, Value, etc.) as well as sector and industry factor exposures. This isolates the true geographic risk premium. Country factors require at least 756 trading days (~3 years) of history. Supported countries include:

Each country factor captures the idiosyncratic return component specific to that nation's equity market—things like local economic conditions, political risk, currency effects, and domestic market sentiment that cannot be explained by global factors. This allows investors to understand and manage geographic risk concentrations in their portfolios. For example, a US multinational with significant operations in Brazil will show exposure to the "Country: Brazil" factor even if traded on US exchanges.

6. Custom Factors (AI-Discovered)

Thematic factors automatically discovered through correlation analysis. This innovative approach identifies groups of stocks that move together for reasons not captured by traditional factors—often representing emerging themes, supply chain relationships, or shared business characteristics.

Discovery Algorithm: Recursive Correlation Clustering

1. Build Correlation Graph: Compute pairwise return correlations for all common stocks. Create edges between stocks with correlation ≥ 0.50 (base threshold).
2. Find Connected Components: Use breadth-first search to identify groups of interconnected stocks.
3. Evaluate Group Size:
   • If group has 8-30 stocks: Accept as valid custom factor
   • If group has < 8 stocks: Discard (too small for meaningful diversification)
   • If group has > 30 stocks: Recursively split at higher correlation threshold
4. Recursive Refinement: For oversized groups, increment correlation threshold by 0.01 and repeat clustering. Continue until all groups are 8-30 stocks or threshold reaches 0.99.
5. AI Naming: Send each group's tickers to Google's Gemini AI with the prompt: "Analyze their common industry, sector, or theme. Generate a short, catchy name (max 6 words) for this investment basket."
6. Factor Construction: Create an equal-weighted basket of group members and apply the full factor purification methodology.

Example discoveries: The algorithm might identify groups like "Semiconductor Equipment" (ASML, LRCX, AMAT, KLAC...), "Streaming Media" (NFLX, SPOT, ROKU...), or "EV Supply Chain" (TSLA, LI, RIVN, LCID...). These represent thematic exposures that transcend traditional sector classifications.

Factor Equations & Replication

A key feature of our methodology is that every factor's returns can be expressed as a linear combination of tradeable instruments. The system stores "factor equations" that represent the current weights needed to replicate each factor.

The Factor Equation

Where:

• L = Leverage scalar for volatility targeting (from most recent calculation)
• R_basket = Return of the underlying basket (ETF or equal-weighted stocks)
• β_i = Regression coefficients from the most recent calibration window
• R_Factori = Returns of the factors being stripped out

Example: Quality Factor Equation

Dependency Resolution

Factor equations can reference other factors, creating dependencies. The system uses topological sorting (Kahn's algorithm) to determine the correct calculation order. Factors that only depend on tickers are computed first, followed by factors that depend on those, and so on. This ensures that when a factor equation references another factor, that factor's returns are already available.

Finding Factor Equations

The complete equation for any factor can be found on that factor's dedicated page:

1. Navigate to the Factor History page
2. Click on any factor name to view its detail page
3. Click the ▼ button next to the live return to expand the equation details
4. View the full equation with all component weights and live contribution breakdowns

Alternatively, use the /api/factor-equation/:factorNameEncoded endpoint to programmatically fetch the equation data. See the API Documentation for details.

Stock Factor Analysis

For individual stocks, FactorsToday computes factor exposures (betas) using ElasticNet regression with cross-validation. For each stock, the system also calculates R² and Adjusted R² to measure how well the factor model explains that stock's returns. This approach provides several advantages over ordinary least squares:

• Regularization: Prevents overfitting when many factors are considered
• Sparsity: L1 penalty encourages sparse solutions, setting weak exposures to exactly zero
• Stability: More robust estimates when factors are correlated

Four Nested Factor Models

Each stock is analyzed against four progressively more comprehensive factor models:

Return Decomposition

On each stock's detail page, you can view a live return decomposition that breaks down the stock's intraday return into factor contributions. This shows exactly how much of today's move is attributable to:

• Factor Contributions: Beta × Factor Return for each factor in the model
• Idiosyncratic Return: The unexplained portion (stock-specific news, earnings, etc.)
• Total Stock Return: Sum of all factor contributions plus idiosyncratic

You can switch between the four models to see how the decomposition changes. A high idiosyncratic return suggests stock-specific news; a return dominated by factor contributions suggests the stock is simply moving with the market.

Model Quality Metrics: R² and Adjusted R²

To measure how well the factor model explains a stock's returns, FactorsToday calculates two key metrics for each stock:

Both R² and Adjusted R² are displayed on each stock's detail page as badges next to the model name. They are also available in the Stock Screener, where you can filter and sort stocks by model fit quality. This is useful for:

• Finding Factor-Driven Stocks: High R² stocks move predictably with factors—useful for factor-based strategies
• Finding Alpha Opportunities: Low R² stocks have more idiosyncratic risk—potentially under-researched or with unique catalysts
• Model Comparison: See which model best explains a stock's behavior by comparing Adjusted R² across the four models

Portfolio Analysis

The Portfolio Analysis tool allows you to analyze the factor exposures and risk characteristics of a custom portfolio of stocks. This powerful feature helps you understand what's really driving your portfolio's returns and identify hidden risk concentrations that may not be apparent from sector classifications alone.

How to Use Portfolio Analysis

To analyze a portfolio, navigate to the Portfolio page and enter your holdings using one of three methods:

Portfolio Factor Exposure Calculation

Portfolio factor exposures are calculated as the weighted average of individual stock exposures:

Where w_i is the weight of stock i in the portfolio and β_i,factor is that stock's exposure to the given factor. This aggregation reveals the portfolio's net exposure to each systematic risk factor, accounting for offsetting positions and diversification effects.

Four Model Views

Portfolio analysis uses the same four nested factor models as stock analysis:

• Base: Core macro factors only - reveals fundamental risk exposures (market, size, value, momentum, quality, etc.)
• Base + Sector: Adds 11 GICS sector exposures - shows broad sector tilts in the portfolio
• Base + Sector + Industry: Adds ~50 industry factors - reveals granular industry concentrations
• All Factors: Adds country and custom thematic factors - uncovers geographic risks and thematic exposures

You can switch between models using the tab selector to see how factor exposures change as more factors are included. Generally, as you move to more comprehensive models, absolute beta values for individual factors decrease (as variance is explained by additional factors), but R² increases (as the model captures more of the portfolio's behavior).

Key Portfolio Metrics

Historical Performance Chart

The portfolio page displays a cumulative return chart showing your portfolio's historical performance. This chart requires historical returns data for each holding. The system:

1. Fetches daily price history for all tickers in the portfolio (up to 10 years of data)
2. Calculates daily returns for each holding
3. Computes portfolio daily returns as the weighted average of constituent returns
4. Compounds returns to show cumulative performance over time
5. Optionally overlays SPY (S&P 500) for comparison if the checkbox is enabled

You can use the timeframe buttons (1M, 3M, 6M, 1Y, 3Y, 5Y, 10Y, ALL) to zoom into different periods, and the chart supports pan and zoom interactions for detailed examination of specific time windows. The chart also displays key metrics like total return, annualized return, max drawdown, and Sharpe ratio (if sufficient history is available).

Practical Applications

Portfolio factor analysis enables several powerful use cases:

• Risk Management: Identify unintended concentrations (e.g., high exposure to "Industry: Semiconductors" despite diversification across sectors)
• Factor Tilts: Verify that your portfolio has the intended factor exposures (e.g., value, momentum, quality tilts)
• Geographic Exposure: Using the "All Factors" model, see hidden country risk (e.g., multinational US stocks with high "Country: China" exposure)
• Thematic Analysis: Discover unexpected thematic exposures through AI-discovered custom factors
• Diversification Diagnostics: Low active factor count suggests potential concentration risk; high R² with few factors suggests you could achieve similar exposure more efficiently
• Alpha Attribution: Compare alpha across models to determine if outperformance is true skill (persists in "All Factors") or just exposure to overlooked factors

Example Interpretation

Performance Attribution Analysis

The Attribution page provides sophisticated performance attribution analysis for individual stocks or custom return streams using a rolling-window regression methodology. Unlike the static factor exposures shown on stock detail pages, attribution analysis decomposes historical returns into factor contributions using time-varying betas that adapt to changing market conditions.

What is Performance Attribution?

Performance attribution answers the question: "Why did this asset generate the return it did?" Rather than simply showing factor exposures (betas), attribution breaks down realized returns into contributions from each factor, allowing you to see exactly how much of your total return came from market exposure, size effects, sector tilts, and idiosyncratic (stock-specific) performance.

For example, if a stock returned +50% over a year, attribution might reveal that +30% came from market (beta), +10% from the technology sector, +5% from momentum, and +5% was alpha (unexplained by factors). This insight is crucial for understanding whether performance was due to systematic factor exposure (replicable, predictable) or idiosyncratic factors (harder to predict, potentially unsustainable).

How to Use the Attribution Page

You can analyze returns using several input methods:

Attribution Methodology: Rolling Window OLS Regression

The attribution engine uses a sophisticated rolling-window approach that captures how factor exposures evolve over time:

Return Frequency Selection

The attribution page supports analysis at three different return frequencies:

Key Attribution Parameters

Attribution Output Metrics

Excel Export with Daily Factor Loadings

The attribution page includes a "Download as Excel" feature that exports comprehensive attribution results including:

• Summary Tab: Total return, factor return, annualized alpha, R², and observation count
• Factor Attribution Tab: Table of all factors with average beta, factor return, and contribution to portfolio return
• Daily Returns Tab: Time series of actual vs. fitted returns and cumulative performance
• Daily Factor Loadings Tab: Complete history of factor betas over time, showing how exposures evolved during the period

The daily factor loadings are particularly valuable for understanding regime changes, examining when factor exposures shifted, and validating the stability of beta estimates. Due to the large size of this data (potentially thousands of rows × dozens of factors), it is stored in a temporary database table rather than being passed via JSON, with automatic cleanup after 24 hours.

Example Use Cases

Update Pipeline

Factor returns are updated through a two-tier system designed to balance freshness with computational efficiency:

Daily Incremental Updates

Each trading day, new factor returns are calculated using saved factor equations. This process:

• Loads the most recent factor equations from the database
• Fetches new price data for all underlying tickers
• Computes returns using the stored weights (no regression required)
• Appends new returns to the factor_return table

Weekly Full Recalibration

Every 7 days, the entire factor model is rebuilt from scratch:

1. Initialize Market Factor: Set Market = 100% IVV as the foundation
2. Process Standard Factors: Calculate all core factors (Market, Size, Value, Momentum, Quality, LowVolatility, CreditRisk, InterestRate, OilPrice, GoldPrice) with fresh regression coefficients
3. Process Dependent Factors: Calculate factors that depend on standard factors (Buybacks, USDividends, GlobalDividends)
4. Process Sector Factors: Recalculate all broad sector factors from Sector SPDR ETFs (11 GICS sectors)
5. Process Industry Factors: Recalculate all granular industry factors from iShares and thematic ETFs (~50 sub-industries)
6. Process Country Factors: Recalculate all country ETF-based factors (42 countries)
7. Rediscover Custom Factors: Run correlation clustering to find new thematic stock groups
8. Process Custom Factors: Calculate factor returns for AI-discovered groups
9. Store Equations: Save all new factor equations for daily incremental updates

This weekly recalibration allows the model to adapt to changing market regimes, evolving factor correlations, and emerging thematic groups, while daily updates ensure factor returns are always current. The pipeline is carefully ordered to ensure proper dependency resolution—each factor type is stripped against all previously computed factors, creating a hierarchical structure where industry factors are orthogonal to sector factors, which are in turn orthogonal to standard factors.

Factor Diagnostics

FactorsToday runs statistical diagnostics on each factor to characterize its time series properties:

• Augmented Dickey-Fuller Test: Tests for stationarity (mean reversion vs. random walk)
• Hurst Exponent: Measures long-term memory (H < 0.5 = mean-reverting, H > 0.5 = trending)
• Variance Ratio Test: Compares variances at different time scales to detect momentum or mean reversion
• Runs Test: Detects non-random clustering of up/down moves
• Ljung-Box Test: Tests for significant autocorrelation in returns
• Durbin-Watson Statistic: Measures lag-1 autocorrelation in residuals

These diagnostics help identify factors with predictable behavior (momentum or mean reversion) versus those that follow a random walk, informing factor timing and portfolio construction decisions.