skfolio

skfolio is a Python library for portfolio optimization, factor model construction, and risk management built on top of scikit-learn. It offers a unified interface and tools compatible with scikit-learn to build, fine-tune, cross-validate, and stress-test portfolio models.

It is distributed under the open-source 3-Clause BSD license.

skfolio is backed by Skfolio Labs, which provides enterprise support and SLAs for institutions.

Important links

Featured in

Portfolio Optimization: Theory and Application by Daniel P. Palomar, includes Python code examples using skfolio.

Installation

skfolio requires Python 3.10 or later and can be installed with:

pip install -U skfolio

See the installation guide for the full dependency list, for conda-forge and for the mixed-integer solvers.

LLM-friendly documentation

The documentation follows the llms.txt convention and provides token-efficient Markdown alongside the HTML site:

Start with llms.txt to find relevant pages.
Read only the Markdown pages needed by appending .md to their HTML URLs, for example factor_models.html.md.
Use llms-full.txt only when the complete documentation is required in a single file.

Contribution

We welcome contributions of all kinds. Whether it’s reporting a bug, suggesting an improvement, or submitting code, your input helps make skfolio better. See the contributing guide to get started.

Key Concepts

Since the development of modern portfolio theory by Markowitz (1952), mean-variance optimization (MVO) has received considerable attention.

Unfortunately, it faces a number of shortcomings, including high sensitivity to the input parameters (expected returns and covariance), weight concentration, high turnover, and poor out-of-sample performance.

It is well-known that naive allocation (1/N, inverse-vol, etc.) tends to outperform MVO out-of-sample (DeMiguel, 2007).

Numerous approaches have been developed to alleviate these shortcomings (shrinkage, additional constraints, regularization, uncertainty set, higher moments, Bayesian approaches, coherent risk measures, left-tail risk optimization, distributionally robust optimization, factor model, risk-parity, hierarchical clustering, ensemble methods, pre-selection, etc.).

Given the large number of methods, and the fact that they can be combined, there is a need for a unified framework with a machine-learning approach to perform model selection, validation, and parameter tuning while mitigating the risk of data leakage and overfitting.

This framework is built on scikit-learn’s API.

Available models

Portfolio Optimization:
- Naive:
  
  Equal-Weighted
  
  Inverse-Volatility
  
  Random (Dirichlet)
- Convex:
  
  Mean-Risk
  
  Risk Budgeting
  
  Maximum Diversification
  
  Distributionally Robust CVaR
  
  Benchmark Tracker
- Clustering:
  
  Hierarchical Risk Parity
  
  Hierarchical Equal Risk Contribution
  
  Schur Complementary Allocation
  
  Nested Clusters Optimization
- Ensemble Methods:
  
  Stacking Optimization
Prior Estimator:
- Empirical
- Characteristics-Based Cross-Sectional Factor Model:
  
  46 descriptors across 17 families (e.g. value, size, momentum, profitability)
  
  Factor Exposures
  
  Cross-Sectional Regression
  
  Alpha Estimators
  
  Forecast Evaluation
  
  Ex-post and Ex-ante Attribution
- Time-Series Factor Model
- Black & Litterman
- Synthetic Data (Stress Test, Factor Stress Test)
- Entropy Pooling
- Opinion Pooling
Expected Returns Estimator:
- Empirical
- Exponentially Weighted
- Equilibrium
- Shrinkage
Covariance Estimator:
- Empirical
- Gerber
- Denoising
- Detoning
- Exponentially Weighted
- Regime-Adjusted Exponentially Weighted
- Ledoit-Wolf
- Oracle Approximating Shrinkage
- Shrunk Covariance
- Geodesic Shrinkage Covariance
- Graphical Lasso CV
- Implied Covariance
Variance Estimator:
- Empirical
- Exponentially Weighted
- Regime-Adjusted Exponentially Weighted
Distance Estimator:
- Pearson Distance
- Kendall Distance
- Spearman Distance
- Covariance Distance (based on any of the above covariance estimators)
- Distance Correlation
- Variation of Information
Seriation Estimator:
- Hierarchical Seriation
- Spectral Seriation
Distribution Estimator:
- Univariate:
  
  Gaussian
  
  Student’s t
  
  Johnson Su
  
  Normal Inverse Gaussian
- Bivariate Copula
  
  Gaussian Copula
  
  Student’s t Copula
  
  Clayton Copula
  
  Gumbel Copula
  
  Joe Copula
  
  Independent Copula
- Multivariate
  
  Vine Copula (Regular, Centered, Clustered, Conditional Sampling)
Uncertainty Set Estimator:
- On Expected Returns:
  
  Empirical
  
  Circular Bootstrap
- On Covariance:
  
  Empirical
  
  Circular Bootstrap
Pre-Selection Transformers:
- Non-Dominated Selection
- Select K Extremes (Best or Worst)
- Drop Highly Correlated Assets
- Select Non-Expiring Assets
- Select Complete Assets (handle late inception, delisting, etc.)
- Drop Zero Variance
Cross-Sectional Transformers:
- Standard Scaler (z-score)
- Percentile Rank Scaler
- Gaussian Rank Scaler (rank gaussianization)
- Winsorizer (percentile clipping)
- Tanh Shrinker (smooth outlier shrinkage)
Cross-Validation and Model Selection:
- Compatible with all sklearn methods (KFold, etc.)
- Walk Forward
- Combinatorial Purged Cross-Validation
- Multiple Randomized Cross-Validation
- Covariance Forecast Evaluation
- Online Predict and Online Score
Hyper-Parameter Tuning:
- Compatible with all sklearn methods (GridSearchCV, RandomizedSearchCV)
- Online Grid Search and Online Randomized Search
Risk Measures:
- Variance
- Semi-Variance
- Mean Absolute Deviation
- First Lower Partial Moment
- CVaR (Conditional Value at Risk)
- EVaR (Entropic Value at Risk)
- Worst Realization
- CDaR (Conditional Drawdown at Risk)
- Maximum Drawdown
- Average Drawdown
- EDaR (Entropic Drawdown at Risk)
- Ulcer Index
- Gini Mean Difference
- Value at Risk
- Drawdown at Risk
- Entropic Risk Measure
- Fourth Central Moment
- Fourth Lower Partial Moment
- Skew
- Kurtosis
Optimization Features:
- Minimize Risk
- Maximize Returns
- Maximize Utility
- Maximize Ratio
- Transaction Costs
- Management Fees
- L1 and L2 Regularization
- Weight Constraints
- Group Constraints
- Budget Constraints
- Tracking Error Constraints
- Turnover Constraints
- Cardinality and Group Cardinality Constraints
- Threshold (Long and Short) Constraints

Quickstart

The code snippets below are designed to introduce the functionality of skfolio so you can start using it quickly. It follows the same API as scikit-learn.

Imports

from sklearn import set_config
from sklearn.model_selection import (
    GridSearchCV,
    KFold,
    RandomizedSearchCV,
    train_test_split,
)
from sklearn.pipeline import Pipeline
from scipy.stats import loguniform

from skfolio import RatioMeasure, RiskMeasure
from skfolio.datasets import (
    load_factors_dataset,
    load_sp500_dataset,
    make_synthetic_characteristics,
)
from skfolio.descriptor import (
    BookToPrice,
    CashFlowToPrice,
    EWMarketBeta,
    EWMomentum,
    EWResidualVolatility,
    EWVolatility,
    LogMarketCap,
    SalesToPrice,
)
from skfolio.distribution import VineCopula
from skfolio.factor_exposure import (
    DerivedFactor,
    FixedWeightedFactor,
    GlobalFactor,
    OneHotCategoricalFactors,
)
from skfolio.model_selection import (
    CombinatorialPurgedCV,
    WalkForward,
    cross_val_predict,
)
from skfolio.moments import (
    DenoiseCovariance,
    DetoneCovariance,
    EWMu,
    GerberCovariance,
    ShrunkMu,
)
from skfolio.optimization import (
    MeanRisk,
    HierarchicalRiskParity,
    NestedClustersOptimization,
    ObjectiveFunction,
    RiskBudgeting,
)
from skfolio.pre_selection import SelectKExtremes
from skfolio.preprocessing import prices_to_returns
from skfolio.prior import (
    BlackLitterman,
    CharacteristicsFactorModel,
    EmpiricalPrior,
    EntropyPooling,
    TimeSeriesFactorModel,
    OpinionPooling,
    SyntheticData,
)
from skfolio.uncertainty_set import BootstrapMuUncertaintySet

Load Dataset

prices = load_sp500_dataset()

Train/Test split

X = prices_to_returns(prices)
X_train, X_test = train_test_split(X, test_size=0.33, shuffle=False)

Minimum Variance

model = MeanRisk()

Fit on Training Set

model.fit(X_train)

print(model.weights_)

Predict on Test Set

portfolio = model.predict(X_test)

print(portfolio.annualized_sharpe_ratio)
print(portfolio.summary())

Maximum Sortino Ratio

model = MeanRisk(
    objective_function=ObjectiveFunction.MAXIMIZE_RATIO,
    risk_measure=RiskMeasure.SEMI_VARIANCE,
)

Denoised Covariance & Shrunk Expected Returns

model = MeanRisk(
    objective_function=ObjectiveFunction.MAXIMIZE_RATIO,
    prior_estimator=EmpiricalPrior(
        mu_estimator=ShrunkMu(), covariance_estimator=DenoiseCovariance()
    ),
)

Uncertainty Set on Expected Returns

model = MeanRisk(
    objective_function=ObjectiveFunction.MAXIMIZE_RATIO,
    mu_uncertainty_set_estimator=BootstrapMuUncertaintySet(),
)

Weight Constraints & Transaction Costs

model = MeanRisk(
    min_weights={"AAPL": 0.10, "JPM": 0.05},
    max_weights=0.8,
    transaction_costs={"AAPL": 0.0001, "RRC": 0.0002},
    groups=[
        ["Equity"] * 3 + ["Fund"] * 5 + ["Bond"] * 12,
        ["US"] * 2 + ["Europe"] * 8 + ["Japan"] * 10,
    ],
    linear_constraints=[
        "Equity <= 0.5 * Bond",
        "US >= 0.1",
        "Europe >= 0.5 * Fund",
        "Japan <= 1",
    ],
)
model.fit(X_train)

Risk Parity on CVaR

model = RiskBudgeting(risk_measure=RiskMeasure.CVAR)

Risk Parity & Gerber Covariance

model = RiskBudgeting(
    prior_estimator=EmpiricalPrior(covariance_estimator=GerberCovariance())
)

Nested Cluster Optimization with Cross-Validation and Parallelization

model = NestedClustersOptimization(
    inner_estimator=MeanRisk(risk_measure=RiskMeasure.CVAR),
    outer_estimator=RiskBudgeting(risk_measure=RiskMeasure.VARIANCE),
    cv=KFold(),
    n_jobs=-1,
)

Randomized Search of the L2 Norm

randomized_search = RandomizedSearchCV(
    estimator=MeanRisk(),
    cv=WalkForward(train_size=252, test_size=60),
    param_distributions={
        "l2_coef": loguniform(1e-3, 1e-1),
    },
)
randomized_search.fit(X_train)

best_model = randomized_search.best_estimator_

print(best_model.weights_)

Grid Search on Embedded Parameters

model = MeanRisk(
    objective_function=ObjectiveFunction.MAXIMIZE_RATIO,
    risk_measure=RiskMeasure.VARIANCE,
    prior_estimator=EmpiricalPrior(mu_estimator=EWMu(half_life=40)),
)

print(model.get_params(deep=True))

gs = GridSearchCV(
    estimator=model,
    cv=WalkForward(train_size=252, test_size=60),
    n_jobs=-1,
    param_grid={
        "risk_measure": [
            RiskMeasure.VARIANCE,
            RiskMeasure.CVAR,
            RiskMeasure.CDAR,
        ],
        "prior_estimator__mu_estimator__half_life": [10, 20, 30, 40],
    },
)
gs.fit(X_train)

best_model = gs.best_estimator_

print(best_model.weights_)

portfolio = best_model.predict(X_test)
print(portfolio.summary())

Black & Litterman Model

views = ["AAPL - BBY == 0.03 ", "CVX - KO == 0.04", "MSFT == 0.06 "]
model = MeanRisk(
    objective_function=ObjectiveFunction.MAXIMIZE_RATIO,
    prior_estimator=BlackLitterman(views=views),
)

Characteristics-Based Factor Model

month = 21
quarter = 3 * month
half_year = 6 * month
year = 12 * month

characteristics = make_synthetic_characteristics(
    n_assets=500,
    n_observations=2000,
    random_state=0,
)

# Global factor
market_factor = GlobalFactor(family="market")

# Industry factors
industry_factors = OneHotCategoricalFactors(
    category="industry",
    family="industry",
)

# Style factors
beta_factor = FixedWeightedFactor(
    descriptors=[
        ("market_beta", EWMarketBeta(half_life=year)),
    ],
    transform_by_group="industry",
)

momentum_factor = FixedWeightedFactor(
    descriptors=[
        ("momentum", EWMomentum(half_life=half_year, skip=month)),
    ],
    transform_by_group="industry",
)

size_factor = FixedWeightedFactor(
    descriptors=[("log_market_cap", LogMarketCap())],
    transform_by_group="industry",
)

non_linear_size_factor = DerivedFactor(
    source="size",
    func=lambda x: x**3,
    transform_by_group="industry",
)

value_factor = FixedWeightedFactor(
    descriptors=[
        ("book_to_price", BookToPrice()),
        ("sales_to_price", SalesToPrice()),
        ("cash_flow_to_price", CashFlowToPrice()),
    ],
    weights=[0.8, 0.1, 0.1],
    transform_by_group="industry",
)

volatility_factor = FixedWeightedFactor(
    descriptors=[
        ("vol", EWVolatility(half_life=quarter)),
        (
            "residual_vol",
            EWResidualVolatility(
                half_life=quarter,
                beta_half_life=quarter,
            ),
        ),
    ],
    transform_by_group="industry",
)

# Characteristics factor model
model = CharacteristicsFactorModel(
    factors=[
        ("market", market_factor),
        ("industry", industry_factors),
        ("beta", beta_factor),
        ("momentum", momentum_factor),
        ("size", size_factor),
        ("non_linear_size", non_linear_size_factor),
        ("value", value_factor),
        ("volatility", volatility_factor),
    ],
    neutralize_against={
        "volatility": ["beta"],
        "non_linear_size": ["size"],
    },
    constrained_families=[("industry", None)],
    exposure_lag=1,
    inv_idio_variance_weight_shrinkage=0.5,
    n_jobs=-1,
)

model.fit(characteristics=characteristics)

factor_model = model.factor_model_
print(factor_model.summary())

For complete workflows, see the Factor Models user guide and the Factor Models tutorials.

Time-Series Factor Model

factor_prices = load_factors_dataset()

X, factors = prices_to_returns(prices, factor_prices)
X_train, X_test, factors_train, factors_test = train_test_split(
    X, factors, test_size=0.33, shuffle=False
)

model = MeanRisk(prior_estimator=TimeSeriesFactorModel())
model.fit(X_train, factors=factors_train)

print(model.weights_)

portfolio = model.predict(X_test)

print(portfolio.calmar_ratio)
print(portfolio.summary())

Time-Series Factor Model & Covariance Detoning

model = MeanRisk(
    prior_estimator=TimeSeriesFactorModel(
        factor_prior_estimator=EmpiricalPrior(covariance_estimator=DetoneCovariance())
    )
)

Black & Litterman Time-Series Factor Model

factor_views = ["MTUM - QUAL == 0.03 ", "VLUE == 0.06"]
model = MeanRisk(
    objective_function=ObjectiveFunction.MAXIMIZE_RATIO,
    prior_estimator=TimeSeriesFactorModel(
        factor_prior_estimator=BlackLitterman(views=factor_views),
    ),
)

Pre-Selection Pipeline

set_config(transform_output="pandas")
model = Pipeline(
    [
        ("pre_selection", SelectKExtremes(k=10, highest=True)),
        ("optimization", MeanRisk()),
    ]
)
model.fit(X_train)

portfolio = model.predict(X_test)

K-fold Cross-Validation

model = MeanRisk()
mpp = cross_val_predict(model, X_test, cv=KFold(n_splits=5))
# mpp is the predicted MultiPeriodPortfolio object composed of 5 Portfolios (1 per testing fold)

mpp.plot_cumulative_returns()
print(mpp.summary())

Combinatorial Purged Cross-Validation

model = MeanRisk()

cv = CombinatorialPurgedCV(n_folds=10, n_test_folds=2)

print(cv.summary(X_test))

population = cross_val_predict(model, X_test, cv=cv)

population.plot_distribution(
    measure_list=[RatioMeasure.SHARPE_RATIO, RatioMeasure.SORTINO_RATIO]
)
population.plot_cumulative_returns()
print(population.summary())

Minimum CVaR Optimization on Synthetic Returns

vine = VineCopula(log_transform=True, n_jobs=-1)
prior = SyntheticData(distribution_estimator=vine, n_samples=2000)
model = MeanRisk(risk_measure=RiskMeasure.CVAR, prior_estimator=prior)
model.fit(X)
print(model.weights_)

Stress Test

vine = VineCopula(log_transform=True, central_assets=["BAC"], n_jobs=-1)
vine.fit(X)
X_stressed = vine.sample(n_samples=10_000, conditioning = {"BAC": -0.2})
ptf_stressed = model.predict(X_stressed)

Minimum CVaR Optimization on Synthetic Factors

vine = VineCopula(central_assets=["QUAL"], log_transform=True, n_jobs=-1)
factor_prior = SyntheticData(
    distribution_estimator=vine,
    n_samples=10_000,
    sample_args=dict(conditioning={"QUAL": -0.2}),
)
factor_model = TimeSeriesFactorModel(factor_prior_estimator=factor_prior)
model = MeanRisk(risk_measure=RiskMeasure.CVAR, prior_estimator=factor_model)
model.fit(X, factors=factors)
print(model.weights_)

Factor Stress Test

factor_model.set_params(factor_prior_estimator__sample_args=dict(
    conditioning={"QUAL": -0.5}
))
factor_model.fit(X, factors=factors)
stressed_dist = factor_model.return_distribution_
stressed_ptf = model.predict(stressed_dist)

Entropy Pooling

entropy_pooling = EntropyPooling(
    mean_views=[
        "JPM == -0.002",
        "PG >= LLY",
        "BAC >= prior(BAC) * 1.2",
    ],
    cvar_views=[
        "GE == 0.08",
    ],
)
entropy_pooling.fit(X)
print(entropy_pooling.relative_entropy_)
print(entropy_pooling.effective_number_of_scenarios_)
print(entropy_pooling.return_distribution_.sample_weight)

CVaR Hierarchical Risk Parity optimization on Entropy Pooling

entropy_pooling = EntropyPooling(cvar_views=["GE == 0.08"])
model = HierarchicalRiskParity(
    risk_measure=RiskMeasure.CVAR,
    prior_estimator=entropy_pooling
)
model.fit(X)
print(model.weights_)

Stress Test with Entropy Pooling on Factor Synthetic Data

# Regular Vine Copula and sampling of 100,000 synthetic factor returns
factor_synth = SyntheticData(
    n_samples=100_000,
    distribution_estimator=VineCopula(log_transform=True, n_jobs=-1, random_state=0)
)

# Entropy Pooling by imposing a CVaR-95% of 10% on the Quality factor
factor_entropy_pooling = EntropyPooling(
    prior_estimator=factor_synth,
    cvar_views=["QUAL == 0.10"],
)

factor_model = TimeSeriesFactorModel(factor_prior_estimator=factor_entropy_pooling)
factor_model.fit(X, factors=factors)

# We retrieve the stressed distribution:
stressed_dist = factor_model.return_distribution_

# We stress-test our portfolio:
stressed_ptf = model.predict(stressed_dist)

Opinion Pooling

# We consider two expert opinions, each generated via Entropy Pooling with
# user-defined views.
# We assign probabilities of 40% to Expert 1, 50% to Expert 2, and by default
# the remaining 10% is allocated to the prior distribution:
opinion_1 = EntropyPooling(cvar_views=["AMD == 0.10"])
opinion_2 = EntropyPooling(
    mean_views=["AMD >= BAC", "JPM <= prior(JPM) * 0.8"],
    cvar_views=["GE == 0.12"],
)

opinion_pooling = OpinionPooling(
    estimators=[("opinion_1", opinion_1), ("opinion_2", opinion_2)],
    opinion_probabilities=[0.4, 0.5],
)

opinion_pooling.fit(X)

Recognition

We would like to thank all contributors to our direct dependencies, such as scikit-learn and cvxpy, as well as the contributors of the following resources:

PyPortfolioOpt

Riskfolio-Lib

scikit-portfolio

statsmodels

rsome

Microprediction (Peter Cotton)

Portfolio Optimization Book (Daniel P. Palomar)

The Elements of Quantitative Investing (Giuseppe Paleologo)

quantresearch.org (Marcos López de Prado)

gautier.marti.ai (Gautier Marti)

Citation

If you use skfolio in a scientific publication, we would appreciate citations:

The library:

@software{skfolio,
  title     = {skfolio},
  author    = {Delatte, Hugo and Nicolini, Carlo and Manzi, Matteo},
  year      = {2026},
  doi       = {10.5281/zenodo.16148630},
  url       = {https://doi.org/10.5281/zenodo.16148630}
}

The citation above refers to skfolio across all versions. Its concept DOI resolves to the latest version archived on Zenodo.

For reproducible research, we recommend citing the specific release you used. Visit the Zenodo project page, select that release, and use its citation so that the DOI, version, and publication date correspond to the same release.

The paper:

@article{nicolini2025skfolio,
  title         = {skfolio: Portfolio Optimization in Python},
  author        = {Nicolini, Carlo and Manzi, Matteo and Delatte, Hugo},
  journal       = {arXiv preprint arXiv:2507.04176},
  year          = {2025},
  eprint        = {2507.04176},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2507.04176}
}

Repository mirror

The project is also mirrored on AtomGit. GitHub remains the primary repository for development and contributions.

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Subject: skfolio-1.9.12.tar.gz
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