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 (>= 1.3.2)
• joblib (>= 1.3.2)
• plotly (>= 5.15.0)

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.).

With this large number of methods, added to the fact that they can be composed together, there is a need for a unified framework with a machine learning approach to perform model selection, validation, and parameter tuning while reducing 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

• 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

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 behind our direct dependencies, such as scikit-learn and cvxpy, but also the contributors of the following resources that were a source 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}
}