skfolio

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

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

Important links

• Documentation: https://skfolio.org/
• Examples: https://skfolio.org/auto_examples/
• User Guide: https://skfolio.org/user_guide/
• GitHub Repo: https://github.com/skfolio/skfolio/

Installation

skfolio is available on PyPI and can be installed with:

pip install -U skfolio

Dependencies

skfolio requires:

• python (>= 3.10)
• numpy (>= 1.23.4)
• scipy (>= 1.8.0)
• pandas (>= 1.4.1)
• cvxpy (>= 1.4.1)
• scikit-learn (>= 1.6.0)
• joblib (>= 1.3.2)
• plotly (>= 5.22.0)

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

• Prior Estimator:

  • Empirical
  • Black & Litterman
  • Factor Model

• 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.)

• Cross-Validation and Model Selection:

  • Compatible with all sklearn methods (KFold, etc.)
  • Walk Forward
  • Combinatorial Purged 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.

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.model_selection import (
    CombinatorialPurgedCV,
    WalkForward,
    cross_val_predict,
)
from skfolio.moments import (
    DenoiseCovariance,
    DetoneCovariance,
    EWMu,
    GerberCovariance,
    ShrunkMu,
)
from skfolio.optimization import (
    MeanRisk,
    NestedClustersOptimization,
    ObjectiveFunction,
    RiskBudgeting,
)
from skfolio.pre_selection import SelectKExtremes
from skfolio.preprocessing import prices_to_returns
from skfolio.prior import BlackLitterman, EmpiricalPrior, FactorModel
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, y = prices_to_returns(prices, factor_prices)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, shuffle=False)

model = MeanRisk(prior_estimator=FactorModel())
model.fit(X_train, y_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 ", "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.get_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())

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
• gautier.marti.ai

Citation

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

Bibtex entry:

@misc{skfolio,
  author = {Delatte, Hugo and Nicolini, Carlo},
  title = {skfolio},
  year  = {2023},
  url   = {https://github.com/skfolio/skfolio}
}