6.5 Factor models

Types of Factor Models

Factor models decompose asset returns into components driven by broad, systematic forces and components unique to individual assets. This decomposition is central to portfolio optimization, risk management, and performance evaluation.

Several types of factor models exist, each with different assumptions about where the factors come from and how they're identified.

Single-Factor Models

The simplest factor model uses one explanatory variable to describe asset returns. The most well-known example is the Capital Asset Pricing Model (CAPM), which uses the market return as the sole factor.

The equation for a single-factor model:

$R_i = \alpha_i + \beta_i R_m + \epsilon_i$

• $R_i$: return of asset $i$
• $\alpha_i$: asset-specific intercept (the return not explained by the market)
• $\beta_i$: sensitivity to the market factor
• $R_m$: market return
• $\epsilon_i$: idiosyncratic (asset-specific) return

Single-factor models are easy to interpret and estimate, but they assume one factor captures all systematic risk. That's a strong assumption, and in practice, multiple sources of systematic risk exist.

Multi-Factor Models

Multi-factor models extend the single-factor framework by incorporating several explanatory variables. Common factors include market, size, value, momentum, and industry-specific variables.

The general form:

$R_i = \alpha_i + \beta_{i1}F_1 + \beta_{i2}F_2 + ... + \beta_{iK}F_K + \epsilon_i$

• $F_1, F_2, ..., F_K$: the $K$ factors
• $\beta_{i1}, \beta_{i2}, ..., \beta_{iK}$: the asset's sensitivity (loading) on each factor

By including multiple factors, these models provide more comprehensive risk decomposition and better explanatory power. The Fama-French Three-Factor Model (market, size, value) and the Carhart Four-Factor Model (adds momentum) are the most widely referenced examples.

Fundamental Factor Models

Fundamental factor models use observable company characteristics as factors. These characteristics are drawn from financial statements, market data, and economic indicators.

Common fundamental factors include:

• Price-to-earnings ratio: measures how expensive a stock is relative to its earnings
• Book-to-market ratio: compares accounting value to market value
• Debt-to-equity ratio: captures financial leverage
• Earnings growth: reflects profitability trends

Because the factors map directly to company attributes, the results are intuitive to interpret. Portfolio managers use these models extensively in equity risk analysis. One practical consideration: factor exposures need regular updating as company fundamentals change over time.

Statistical Factor Models

Statistical factor models extract factors directly from historical return data using statistical techniques, rather than specifying factors in advance. The two most common methods are Principal Component Analysis (PCA) and Factor Analysis.

The advantage is that these models are purely data-driven and can capture latent (hidden) sources of risk that you might not think to include. The disadvantage is that the resulting factors often lack clear economic interpretation. A "Factor 1" that explains 40% of return variance might be hard to label as "market risk" or "inflation risk" without further analysis.

Statistical models are often used alongside fundamental models to cross-check results and identify factors that fundamental approaches might miss.

Components of Factor Models

Every factor model has three core components that work together to explain asset returns. Understanding each one is essential for interpreting model output and applying it to investment decisions.

Factor Exposures

Factor exposures (also called factor loadings or betas) measure how sensitive an asset's return is to a given factor. A beta of 1.3 on the market factor means the asset's return tends to move 1.3% for every 1% move in the market.

Factor exposures can be estimated through:

• Regression analysis: regressing asset returns on factor returns over a historical window
• Fundamental characteristic mapping: assigning exposures based on company attributes (e.g., a small-cap stock gets high exposure to the size factor)
• Statistical techniques: extracting loadings through PCA or factor analysis

Depending on the model, exposures may be treated as constant or allowed to vary over time. The interpretation depends on the factor type: a high market beta means high market sensitivity, while a positive value tilt means the asset behaves more like a value stock.

Factor Returns

Factor returns represent how each factor performed over a given period. For the market factor, this is straightforward: it's the return on a broad market index. For other factors like size or value, factor returns are typically constructed as the return difference between two portfolios (e.g., small-cap minus large-cap for the size factor).

Time series of factor returns are used to:

• Estimate factor risk premia (the average compensation for bearing factor risk)
• Analyze how factors behave across different market environments (e.g., does value underperform during growth rallies?)
• Construct factor-mimicking portfolios that replicate factor exposures

Factor returns are key inputs for both portfolio construction and risk management.

Idiosyncratic Returns

Idiosyncratic returns (also called residual or asset-specific returns) are whatever is left over after the factor model has done its work. They represent the portion of an asset's return not explained by any of the included factors.

$\epsilon_i = R_i - (\alpha_i + \beta_{i1}F_1 + ... + \beta_{iK}F_K)$

A critical assumption in most factor models is that idiosyncratic returns are uncorrelated across assets and uncorrelated with the factors themselves. This assumption is what makes the risk decomposition clean.

Idiosyncratic returns matter for several reasons:

• Model fit: large residuals suggest the model is missing important factors
• Alpha identification: persistent positive residuals may indicate genuine stock-picking skill
• Diversification: idiosyncratic risk can be reduced by holding many assets, while factor risk cannot

Factor Model Applications

Factor models are used across many areas of investment management. The three most important applications are risk analysis, performance attribution, and asset pricing.

Portfolio Risk Analysis

Factor models let you decompose portfolio risk into its sources. Instead of just knowing your portfolio has 15% annualized volatility, you can identify how much of that risk comes from market exposure, how much from a value tilt, and how much from stock-specific bets.

This decomposition enables you to:

• Quantify exposure to each risk factor (market, size, value, momentum, etc.)
• Calculate each factor's contribution to total portfolio volatility
• Spot unintended factor concentrations (e.g., a portfolio that looks diversified across sectors but is heavily loaded on the momentum factor)
• Run stress tests by shocking individual factors and observing the impact on portfolio value
• Implement risk budgeting, where you allocate a target amount of risk to each factor

Performance Attribution

Performance attribution uses factor models to answer: where did the returns come from?

You can break portfolio returns into:

• Factor-driven returns: the portion explained by the portfolio's factor exposures
• Security selection returns: the portion from picking individual stocks that outperformed (or underperformed) what the factor model predicted

This distinction is critical for evaluating investment managers. A manager who claims skill but whose returns are entirely explained by a persistent value tilt isn't adding much beyond what a cheap factor ETF could deliver. True alpha shows up in the residual after accounting for factor exposures.

Asset Pricing

Factor models provide a framework for explaining why different assets have different expected returns. The core idea: assets with higher exposure to systematic risk factors should earn higher expected returns as compensation.

Applications in asset pricing include:

• Testing whether specific factors (size, value, momentum) carry statistically significant risk premia
• Estimating a firm's cost of capital based on its factor exposures
• Identifying market anomalies where assets appear mispriced relative to their factor risk
• Informing the construction of smart beta strategies that systematically target factor premia

Statistical Techniques

The statistical methods behind factor models determine how factors are identified, how exposures are estimated, and how models are tested.

Principal Component Analysis

Principal Component Analysis (PCA) is a dimensionality reduction technique that transforms a set of correlated asset returns into uncorrelated components, ordered by how much variance each explains.

Steps in PCA for factor model construction:

1. Compute the covariance (or correlation) matrix of asset returns
2. Calculate the eigenvectors and eigenvalues of that matrix
3. Rank eigenvectors by eigenvalue size; the top eigenvectors become your factors
4. Project the original return data onto the new factor space

The first principal component typically captures the most variance and often corresponds roughly to the market factor. Subsequent components capture progressively less variance. PCA is useful because it's entirely data-driven and guarantees that factors are uncorrelated. The main challenge is that the resulting components may not have obvious economic meaning.

Factor Analysis

Factor analysis is related to PCA but differs in an important way: it explicitly models measurement error and focuses on the shared variance among assets rather than total variance.

Steps in factor analysis:

1. Estimate factor loadings using maximum likelihood or principal factor methods
2. Determine the number of factors using scree plots or information criteria (like BIC)
3. Apply factor rotation (e.g., varimax or oblimin) to improve interpretability
4. Compute factor scores for each observation

Factor rotation is a key step. Raw statistical factors are often hard to interpret, but rotating them can align them more closely with recognizable economic concepts. Factor analysis is particularly useful when you believe there are common risk drivers but don't want to specify them in advance.

Regression Methods

Regression is the workhorse technique for estimating factor exposures and testing whether factors are priced.

Time series regression estimates an individual asset's factor exposures:

$R_{it} = \alpha_i + \beta_{i1}F_{1t} + \beta_{i2}F_{2t} + ... + \beta_{iK}F_{Kt} + \epsilon_{it}$

Cross-sectional regression tests whether factor exposures explain differences in expected returns across assets:

$E[R_i] = \lambda_0 + \lambda_1\beta_{i1} + \lambda_2\beta_{i2} + ... + \lambda_K\beta_{iK}$

Here, the $\lambda$ coefficients represent the estimated factor risk premia.

Beyond ordinary least squares (OLS), more advanced techniques address specific issues:

• Generalized Least Squares (GLS): corrects for heteroscedasticity (non-constant error variance)
• Panel regression: combines time series and cross-sectional data for more efficient estimation
• Quantile regression: examines how factor effects differ across the return distribution (e.g., do factors matter more in the tails?)

Common Factors in Finance

Empirical research has identified several systematic factors that persistently explain variation in asset returns. These are the building blocks of most multi-factor models used in practice.

Market Factor

The market factor captures the overall movement of the equity market, typically proxied by a broad index like the S&P 500 or MSCI World.

In the CAPM framework:

$R_i = R_f + \beta_i(R_m - R_f) + \epsilon_i$

• $R_f$: risk-free rate
• $R_m - R_f$: the market risk premium (excess return of the market over the risk-free rate)

Market beta measures an asset's sensitivity to market movements. A beta of 1.0 means the asset moves in line with the market; above 1.0 indicates amplified sensitivity; below 1.0 indicates dampened sensitivity. The market factor serves as the baseline in virtually all multi-factor models.

Size Factor

The size factor captures the historical tendency of smaller companies to outperform larger ones, known as the size premium. It was introduced in the Fama-French Three-Factor Model and is typically calculated as the return of small-cap stocks minus the return of large-cap stocks (SMB: "Small Minus Big").

Explanations for the size premium include:

• Small firms carry more risk (less diversified revenue, higher default probability)
• Small firms have greater growth potential
• Small-cap stocks may be less efficiently priced due to lower analyst coverage

The size factor is an important consideration in portfolio diversification and style analysis, though the magnitude of the size premium has been debated in recent decades.

Value Factor

The value factor reflects the historical outperformance of stocks that are cheap relative to their fundamentals. Common metrics for identifying value stocks include price-to-book ratio, price-to-earnings ratio, and dividend yield.

In the Fama-French model, the value factor is constructed as the return of high book-to-market stocks minus low book-to-market stocks (HML: "High Minus Low").

Explanations for the value premium:

• Risk-based: value stocks tend to be financially distressed, so higher returns compensate for higher risk
• Behavioral: investors systematically overreact to bad news, pushing prices below fundamental value
• Mean reversion: extreme valuations tend to revert toward historical averages

Value is often paired with growth in style analysis, and value strategies aim to systematically capture this premium.

Momentum Factor

The momentum factor captures the tendency of recent winners to keep winning and recent losers to keep losing over horizons of roughly 3 to 12 months. Jegadeesh and Titman documented this effect, and Carhart incorporated it as the fourth factor in his model.

The factor is constructed as the return of high-momentum stocks minus low-momentum stocks (WML: "Winners Minus Losers"), typically excluding the most recent month to avoid short-term reversal effects.

Explanations for momentum include:

• Underreaction: investors are slow to incorporate new information into prices
• Herding: trend-following behavior amplifies price movements
• Disposition effect: investors hold losers too long and sell winners too early, delaying price adjustment

Momentum is widely used in quantitative strategies, though it's known for occasional sharp reversals (momentum crashes), particularly during market recoveries.

Factor Model Limitations

Factor models are useful but imperfect. Being aware of their limitations helps you use them more carefully and avoid overconfidence in model outputs.

Model Specification Errors

Specification errors occur when the model includes the wrong factors, omits important ones, or assumes the wrong functional form.

Types of specification errors:

• Omitted variable bias: leaving out a relevant factor causes the remaining betas to absorb its effect, biasing estimates
• Irrelevant factors: including factors that don't actually matter introduces noise and reduces estimation precision
• Nonlinearity: assuming linear relationships when the true relationship is nonlinear leads to systematic errors

The consequences are real: inaccurate risk assessments, misleading performance attributions, and suboptimal portfolio allocations. Mitigation involves grounding factor selection in economic theory, testing for omitted variables, and considering nonlinear specifications when warranted.

Estimation Risk

Even with the right factors, parameter estimates are uncertain because they're based on finite historical data.

Sources of estimation risk:

• Sampling error: limited data means estimated betas and expected returns are noisy
• Instability: factor relationships can shift over time, so historical estimates may not reflect current dynamics
• Outliers: extreme market events can distort estimates

Estimation risk is particularly problematic in mean-variance optimization, where small errors in expected returns can lead to large swings in optimal portfolio weights. Techniques to manage this include shrinkage estimators (which pull extreme estimates toward a central value), Bayesian methods (which blend prior beliefs with data), and explicitly incorporating estimation uncertainty into the optimization process.

Time-Varying Factor Exposures

Factor exposures are not static. A company's beta can change as its business evolves, as market conditions shift, or as investor preferences change. A tech startup might have a high growth loading that decreases as it matures into a large, stable firm.

This creates challenges for static factor models:

• Historical estimates may not reflect current exposures
• Forecasting future exposures adds another layer of uncertainty
• Risk management and rebalancing become more complex

Methods for handling time variation include rolling window estimation (re-estimating betas over a moving window of data), conditional factor models (where betas are functions of observable state variables), and regime-switching models (which allow for discrete shifts in factor relationships). Regular model monitoring is essential.

Factor Model Implementation

Building a factor model that works in practice requires careful attention to data quality, factor selection, and validation. Each step introduces potential errors that compound if not handled properly.

Data Collection and Cleaning

Reliable data is the foundation. You need comprehensive financial data from trustworthy sources: stock prices, accounting data, and economic indicators.

Key data preparation steps:

1. Ensure consistency across time periods and asset classes
2. Handle missing data through imputation or careful exclusion
3. Adjust for corporate actions (stock splits, dividends, mergers) so returns are comparable
4. Identify and treat outliers using methods like winsorization (capping extreme values at a percentile threshold) or trimming
5. Normalize variables to account for different scales
6. Build a data pipeline that supports regular updates

Dirty data leads to unreliable estimates, so this step deserves more attention than it typically gets.

Factor Selection Criteria

Choosing factors involves balancing theory, empirical evidence, and practical constraints.

Evaluate potential factors based on:

• Economic rationale: does the factor have a plausible explanation for why it should earn a premium?
• Persistence: has the premium been stable over long time periods?
• Independence: is the factor capturing something distinct from existing factors, or is it redundant?
• Robustness: does the factor work across different markets, time periods, and asset classes?

Statistical tools for factor selection include stepwise regression, information criteria (AIC, BIC) for comparing model specifications, and cross-validation to test out-of-sample stability. There's always a trade-off between parsimony (fewer factors, simpler model) and explanatory power (more factors, better fit but higher risk of overfitting).

Model Validation Techniques

Validation determines whether your model actually works or just fits historical noise.

1. In-sample vs. out-of-sample testing: a model that fits historical data well but fails on new data is overfit

2. Statistical significance tests:

   • T-tests for individual factor coefficients
   • F-tests for overall model significance
   • $R^2$ and adjusted $R^2$ for explanatory power

3. Residual diagnostics:

   • Normality checks (Q-Q plots, Jarque-Bera test)
   • Homoscedasticity (White's test)
   • Autocorrelation (Durbin-Watson test)

4. Sensitivity analysis: Monte Carlo simulations and bootstrap resampling to assess how stable results are

5. Forecast accuracy: compare predictions to realized returns using mean absolute error (MAE) and root mean squared error (RMSE)

6. Backtesting: evaluate model performance across different market regimes

Risk Decomposition

One of the most valuable applications of factor models is breaking total portfolio risk into its component parts. This tells you not just how much risk you have, but where it's coming from.

Systematic vs. Idiosyncratic Risk

Total portfolio variance can be decomposed as:

$\sigma_p^2 = \beta_p'\Omega\beta_p + \sigma_\epsilon^2$

• $\beta_p$: vector of portfolio factor exposures
• $\Omega$: factor covariance matrix
• $\sigma_\epsilon^2$: idiosyncratic variance

The first term ($\beta_p'\Omega\beta_p$) is systematic risk, driven by factor exposures. The second term ($\sigma_\epsilon^2$) is idiosyncratic risk, driven by asset-specific events.

In a well-diversified portfolio, systematic risk dominates because idiosyncratic risk gets diversified away as you add more holdings. In a concentrated portfolio (say, 10-15 stocks), idiosyncratic risk can be a large share of total risk. This distinction matters because you can diversify away idiosyncratic risk, but systematic risk requires you to reduce factor exposures.

Factor Contribution to Risk

Beyond the systematic/idiosyncratic split, you can measure how much each individual factor contributes to portfolio risk.

Marginal contribution to risk (MCR) for factor $i$:

$MCR_i = \frac{(\Omega\beta_p)_i}{\sigma_p}$

This tells you how much total portfolio risk changes for a small increase in exposure to factor $i$.

Percentage contribution to risk (PCR) for factor $i$:

$PCR_i = \frac{\beta_{p,i} \cdot MCR_i}{\sigma_p}$

PCR values sum to the systematic portion of total risk and reveal which factors are the dominant risk drivers. If 60% of your portfolio risk comes from the market factor and 25% from a value tilt, you know exactly where to look if you want to reduce risk.

Risk Budgeting with Factors

Risk budgeting takes factor risk decomposition and turns it into a portfolio construction tool. Instead of allocating capital to assets, you allocate risk to factors.

Steps in factor-based risk budgeting:

1. Set target risk contributions for each factor (e.g., 40% market, 20% value, 20% momentum, 20% size)
2. Solve for portfolio weights that achieve the target risk allocation
3. Implement the portfolio and monitor actual risk contributions over time

The equal risk contribution (ERC) approach assigns the same risk budget to each factor, ensuring no single factor dominates. You can also tilt risk budgets based on views about which factors will be compensated going forward.

Challenges include dealing with time-varying factor correlations, balancing risk allocation with return objectives, and implementing risk budgets when there are real-world constraints (position limits, liquidity, etc.).

Factor Investing Strategies

Factor investing translates the insights from factor models into actual portfolio strategies that aim to capture factor premia systematically.

Smart Beta Approaches

Smart beta strategies sit between pure passive indexing and active management. They follow transparent, rules-based methodologies but deviate from market-cap weighting to target specific factor exposures.

Common smart beta strategies:

• Value-weighted: overweight stocks with low price-to-book or price-to-earnings ratios
• Equal-weighted: assign equal weight to all index constituents, which implicitly tilts toward smaller stocks
• Low volatility: select stocks with lower historical volatility, aiming for better risk-adjusted returns
• Quality: select stocks based on profitability, earnings stability, and balance sheet strength

Smart beta offers potential for improved risk-adjusted returns at lower cost than traditional active management. The main risks are factor crowding (too many investors chasing the same factor, compressing the premium) and the cyclicality of factor performance (every factor goes through periods of underperformance).

Factor Timing

Factor timing attempts to dynamically adjust factor exposures based on predictions about which factors will perform well in the near future.

Signals used for factor timing include:

• Valuation spreads: when the gap between cheap and expensive stocks is wide, the value premium may be larger going forward
• Macroeconomic variables: interest rates, GDP growth, and inflation can signal which factors are likely to benefit
• Technical indicators: recent factor momentum or mean reversion patterns

Factor timing can potentially improve risk-adjusted returns and provide downside protection, but it's difficult to execute consistently. The challenges are significant: factor returns are hard to predict, timing strategies increase turnover and transaction costs, and there's always the risk of data mining (finding patterns in historical data that don't persist).

Factor Rotation

Factor rotation systematically shifts allocations among factors over time, based on the premise that factor performance is cyclical and linked to economic conditions.

Common rotation approaches:

• Business cycle-based: favor value and small-cap in economic recoveries, quality and low volatility in recessions
• Momentum-based: allocate more to factors that have recently outperformed
• Valuation-based: tilt toward factors that appear cheap relative to historical norms

Implementation can be done through sector rotation (gaining indirect factor exposure), factor-based ETFs, long-short factor portfolios, or risk parity approaches with dynamic rebalancing. Transaction costs and tax implications need careful consideration, as frequent rotation can erode returns.

Regulatory Considerations

Financial institutions using factor models must operate within regulatory frameworks that govern risk measurement, capital requirements, and model governance.

Basel Framework

The Basel framework sets international standards for bank regulation. Its three pillars are directly relevant to factor model use:

• Pillar 1 (Minimum Capital Requirements): banks must hold capital proportional to risk-weighted assets, and factor models feed into internal risk calculations
• Pillar 2 (Supervisory Review): regulators assess the adequacy of banks' internal models, including factor models used for risk measurement
• Pillar 3 (Market Discipline): banks must disclose their risk management practices and model methodologies

Banks choosing to use internal models (rather than standardized regulatory approaches) for risk calculation face higher validation requirements but may benefit from more accurate, and potentially lower, capital charges. Factor models must align with regulatory capital calculations.

Stress Testing Requirements

Regulatory stress tests evaluate whether banks can withstand severe economic downturns. Factor models play a central role by:

• Projecting asset returns and portfolio losses under adverse scenarios
• Estimating how factors behave during crises (e.g., do correlations spike?)
• Assessing how sensitive risk measures are to changes in factor exposures

Regulators expect comprehensive coverage of material risks, multiple scenarios (including severe but plausible ones), and integration of stress test results into capital planning. The main challenges are modeling factor behavior in unprecedented scenarios, capturing nonlinear relationships and tail dependencies, and ensuring consistency between factor projections and the macroeconomic narrative of the stress scenario.

Model Risk Management

Regulators require institutions to manage the risks that arise from relying on quantitative models. For factor models, this means:

• Development: thorough documentation of assumptions, limitations, and intended use
• Validation: independent review of methodology, data, and performance by a team separate from the developers
• Ongoing monitoring: regular assessment of model accuracy, checking whether factor relationships have shifted
• Governance: clear roles and responsibilities for model oversight, with senior management accountability

Key regulatory guidance includes OCC 2011-12 and SR 11-7 in the U.S. Institutions must maintain a model inventory, assess each model's materiality, and balance model complexity with interpretability. A model that's statistically sophisticated but impossible for risk managers to understand and challenge creates its own form of risk.

Advanced Factor Model Topics

These topics extend traditional factor models to address their limitations and incorporate more sophisticated methodologies.

Conditional Factor Models

Standard factor models assume constant factor exposures, but conditional factor models allow exposures to vary with observable state variables.

The general form:

$R_{it} = \alpha_i(Z_t) + \beta_i(Z_t)'F_t + \epsilon_{it}$

• $Z_t$: vector of conditioning variables (e.g., term spread, default spread, dividend yield, volatility index)
• $\alpha_i(Z_t)$ and $\beta_i(Z_t)$: intercept and factor exposures that are functions of the conditioning variables

For example, a stock's market beta might increase during high-volatility regimes and decrease during calm markets. Conditional models capture this dynamic.

Implementation approaches range from parametric (specifying $\beta_i(Z_t) = b_0 + b_1 Z_t$) to non-parametric methods (kernel regression, local linear regression). The trade-off is between flexibility and the risk of overfitting, especially with limited data.

Bayesian Factor Models

Bayesian factor models apply Bayesian inference to incorporate prior beliefs about factor structure alongside observed data.

The framework involves:

• Prior distributions for factor loadings and returns (encoding beliefs before seeing data)
• Likelihood function based on observed asset returns
• Posterior distributions obtained via Bayes' theorem, combining priors with data

The Bayesian approach naturally handles parameter uncertainty, which is a major advantage for portfolio optimization. Instead of treating estimated betas as known quantities, you work with distributions of possible values, leading to more robust portfolio decisions.

Estimation typically uses Markov Chain Monte Carlo (MCMC) methods or variational inference for larger-scale problems. Bayesian factor models are particularly valuable when data is limited or when you have strong economic priors about factor structure.

Machine Learning in Factor Models

Machine learning techniques are increasingly applied to factor model development, offering tools to handle nonlinearity, high dimensionality, and complex interactions.

Applications include:

• Factor construction: using dimensionality reduction techniques (t-SNE, UMAP, autoencoders) to discover new factors from large datasets
• Nonlinear factor models: neural networks or support vector machines that capture relationships linear models miss
• Ensemble methods: combining multiple factor models using random forests or gradient boosting to improve prediction accuracy

Machine learning can capture complex patterns and adapt to changing market conditions, but it comes with significant challenges. Model interpretability is a major concern: a neural network might predict returns well but offer no insight into why. Overfitting is another persistent risk, especially in finance where the signal-to-noise ratio is low and datasets are relatively small compared to other ML domains.

The most effective approaches tend to combine machine learning's statistical power with traditional financial theory, using economic intuition to constrain and guide the models rather than letting the algorithms operate in a purely data-driven vacuum.