skfolio

skfolio is a Python library for portfolio optimization 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.

Installation

skfolio is available on PyPI and can be installed with:

$ pip install skfolio

Contribution

We welcome contributions of all kinds. To get started, please visit our GitHub repository.

Whether it’s reporting a bug, suggesting an improvement, or submitting code, your input helps make skfolio better.

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

  • Clustering:

    • Hierarchical Risk Parity

    • Hierarchical Equal Risk Contribution

    • Nested Clusters Optimization

  • Ensemble Methods:

    • Stacking Optimization

• Expected Returns Estimator:

  • Empirical

  • Exponentially Weighted

  • Equilibrium

  • Shrinkage

• Covariance Estimator:

  • Empirical

  • Gerber

  • Denoising

  • Detoning

  • Exponentially Weighted

  • Ledoit-Wolf

  • Oracle Approximating Shrinkage

  • Shrunk Covariance

  • Graphical Lasso CV

  • Implied Covariance

• Distance Estimator:

  • Pearson Distance

  • Kendall Distance

  • Spearman Distance

  • Covariance Distance (based on any of the above covariance estimators)

  • Distance Correlation

  • Variation of Information

• 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)

• Prior Estimator:

  • Empirical

  • Black & Litterman

  • Factor Model

  • Synthetic Data (Stress Test, Factor Stress Test)

  • Entropy Pooling

  • Opinion Pooling

• Uncertainty Set Estimator:

  • On Expected Returns:

    • Empirical

    • Circular Bootstrap

  • On Covariance:

    • Empirical

    • Circular Bootstrap

• Pre-Selection Transformer:

  • 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-Validation and Model Selection:

  • Compatible with all sklearn methods (KFold, etc.)

  • Walk Forward

  • Combinatorial Purged Cross-Validation

  • Multiple Randomized Cross-Validation

• Hyper-Parameter Tuning:

  • Compatible with all sklearn methods (GridSearchCV, RandomizedSearchCV)

• 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.

For more detailed information see the Examples, User Guide and API Reference .

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
from skfolio.distribution import VineCopula
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,
    EmpiricalPrior,
    EntropyPooling,
    FactorModel,
    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(alpha=0.2)),
)

print(model.get_params(deep=True))

gs = GridSearchCV(
    estimator=model,
    cv=KFold(n_splits=5, shuffle=False),
    n_jobs=-1,
    param_grid={
        "risk_measure": [
            RiskMeasure.VARIANCE,
            RiskMeasure.CVAR,
            RiskMeasure.VARIANCE.CDAR,
        ],
        "prior_estimator__mu_estimator__alpha": [0.05, 0.1, 0.2, 0.5],
    },
)
gs.fit(X)

best_model = gs.best_estimator_

print(best_model.weights_)

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),
)

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=FactorModel())
model.fit(X_train, factors_train)

print(model.weights_)

portfolio = model.predict(X_test)

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

Factor Model & Covariance Detoning

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

Black & Litterman Factor Model

factor_views = ["MTUM - QUAL == 0.03 ", "SIZE - TLT == 0.04", "VLUE == 0.06"]
model = MeanRisk(
    objective_function=ObjectiveFunction.MAXIMIZE_RATIO,
    prior_estimator=FactorModel(
        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()
mmp = cross_val_predict(model, X_test, cv=KFold(n_splits=5))
# mmp is the predicted MultiPeriodPortfolio object composed of 5 Portfolios (1 per testing fold)

mmp.plot_cumulative_returns()
print(mmp.summary()

Combinatorial Purged Cross-Validation

model = MeanRisk()

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

print(cv.summary(X_train))

population = cross_val_predict(model, X_train, 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 = FactorModel(factor_prior_estimator=factor_prior)
model = MeanRisk(risk_measure=RiskMeasure.CVAR, prior_estimator=factor_model)
model.fit(X, 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)
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_entropy_pooling.fit(X, 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 that served as sources of inspiration:

* PyPortfolioOpt
* Riskfolio-Lib
* scikit-portfolio
* microprediction
* statsmodels
* rsome
* danielppalomar.com
* gautier.marti.ai

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      = {2024},
  doi       = {10.5281/zenodo.16148630},
  url       = {https://doi.org/10.5281/zenodo.16148630}
}

The above uses the concept DOI, which always resolves to the latest release. If you need precise reproducibility, especially for journals or conferences that require it, you can cite the version-specific DOI for the exact release you used. To find it, go to our Zenodo project page, locate the release you wish to reference (e.g. “v0.10.2”), and copy the DOI listed next to that version.

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}
}