API Reference

This is the class and function reference of skfolio. Please refer to the full user guide for further details, as the class and function raw specifications may not be enough to give full guidelines on their uses.

skfolio.measures: Measures

Module that includes all Measures functions used across skfolio.

Base Class

measures.BaseMeasure

Base Enum of measures.

Classes

measures.PerfMeasure	Enumeration of performance measures.
measures.RiskMeasure	Enumeration of risk measures.
measures.ExtraRiskMeasure	Enumeration of other risk measures not used in convex optimization.
measures.RatioMeasure	Enumeration of ratio measures.

Functions

measures.mean(returns[, sample_weight])	Compute the mean.
measures.get_cumulative_returns(returns[, ...])	Compute the cumulative returns from a series of returns.
measures.get_drawdowns(returns[, compounded])	Compute the drawdowns' series from the returns.
measures.variance(returns[, biased, ...])	Compute the variance (second moment).
measures.semi_variance(returns[, ...])	Compute the semi-variance (second lower partial moment).
measures.standard_deviation(returns[, ...])	Compute the standard-deviation (square root of the second moment).
measures.semi_deviation(returns[, ...])	Compute the semi deviation (square root of the second lower partial moment).
measures.third_central_moment(returns[, ...])	Compute the third central moment.
measures.fourth_central_moment(returns[, ...])	Compute the Fourth central moment.
measures.fourth_lower_partial_moment(returns)	Compute the fourth lower partial moment.
measures.cvar(returns[, beta, sample_weight])	Compute the historical CVaR (conditional value at risk).
measures.mean_absolute_deviation(returns[, ...])	Compute the mean absolute deviation (MAD).
measures.value_at_risk(returns[, beta, ...])	Compute the historical value at risk (VaR).
measures.worst_realization(returns)	Compute the worst realization (worst return).
measures.first_lower_partial_moment(returns)	Compute the first lower partial moment.
measures.entropic_risk_measure(returns[, ...])	Compute the entropic risk measure.
measures.evar(returns[, beta])	Compute the EVaR (entropic value at risk) and its associated risk aversion.
measures.drawdown_at_risk(drawdowns[, beta])	Compute the Drawdown at risk.
measures.cdar(drawdowns[, beta])	Compute the historical CDaR (conditional drawdown at risk).
measures.max_drawdown(drawdowns)	Compute the maximum drawdown.
measures.average_drawdown(drawdowns)	Compute the average drawdown.
measures.edar(drawdowns[, beta])	Compute the EDaR (entropic drawdown at risk).
measures.ulcer_index(drawdowns)	Compute the Ulcer index.
measures.gini_mean_difference(returns)	Compute the Gini mean difference (GMD).
measures.owa_gmd_weights(n_observations)	Compute the OWA weights used for the Gini mean difference (GMD) computation.
measures.effective_number_assets(weights)	Compute the effective number of assets, defined as the inverse of the Herfindahl index.
measures.correlation(X[, sample_weight])	Compute the correlation matrix.

skfolio.portfolio: Portfolio

Portfolio module. Portfolio and MultiPeriodPortfolio objects are returned by the predict method of Optimization estimators. They need to be homogeneous to the convex optimization problems meaning that Portfolio is the dot product of the assets weights with the assets returns and MultiPeriodPortfolio is a list of Portfolio.

Base Class

portfolio.BasePortfolio

Base Portfolio class for all portfolios in skfolio.

Classes

portfolio.Portfolio	Portfolio class.
portfolio.FailedPortfolio	Portfolio object returned when an optimization step fails.
portfolio.MultiPeriodPortfolio	Multi-Period Portfolio class.

skfolio.population: Population

Population module.

Classes

population.Population

Population Class.

skfolio.optimization.base: Base Optimization Estimator

Optimization module.

Classes

optimization.BaseOptimization

Base class for all portfolio optimizations in skfolio.

skfolio.optimization.naive: Naive Optimization Estimators

Naive Optimization module.

Classes

optimization.EqualWeighted	Equally Weighted estimator.
optimization.InverseVolatility	Inverse Volatility estimator.
optimization.Random	Random weight estimator.

skfolio.optimization.convex: Convex Optimization Estimators

Convex Optimization module.

Enum

optimization.ObjectiveFunction

Enumeration of objective functions.

Classes

optimization.ConvexOptimization	Base class for all convex optimization estimators in skfolio.
optimization.MeanRisk	Mean-Risk Optimization estimator.
optimization.BenchmarkTracker	Benchmark Tracker Optimization estimator.
optimization.RiskBudgeting	Risk Budgeting Optimization estimator.
optimization.MaximumDiversification	Maximum Diversification Optimization estimator.
optimization.DistributionallyRobustCVaR	Distributionally Robust CVaR.

skfolio.optimization.cluster: Clustering Optimization Estimators

Cluster Optimization module.

Classes

optimization.BaseHierarchicalOptimization	Base Hierarchical Clustering Optimization estimator.
optimization.HierarchicalRiskParity	Hierarchical Risk Parity estimator.
optimization.HierarchicalEqualRiskContribution	Hierarchical Equal Risk Contribution estimator.
optimization.SchurComplementary	Schur Complementary Allocation estimator.
optimization.NestedClustersOptimization	Nested Clusters Optimization estimator.

skfolio.optimization.ensemble: Ensemble Optimization Estimators

Ensemble Optimization module.

Classes

optimization.BaseComposition	Handles parameter management for ensemble estimators.
optimization.StackingOptimization	Stack of optimizations with a final optimization.

skfolio.prior: Prior Estimators

Prior module.

Model Dataclass

prior.ReturnDistribution

Return Distribution dataclass used by the optimization estimators.

Base Class

prior.BasePrior

Base class for all prior estimators in skfolio.

Classes

prior.EmpiricalPrior	Empirical Prior estimator.
prior.BlackLitterman	Black & Litterman estimator.
prior.TimeSeriesFactorModel	Time-series factor model estimator.
prior.SyntheticData	Synthetic Data Estimator.
prior.EntropyPooling	Entropy Pooling estimator.
prior.OpinionPooling	Opinion Pooling estimator.

Loading Matrix Classes for Factor Models

prior.BaseLoadingMatrix	Base class for all Loading Matrix estimators.
prior.LoadingMatrixRegression	Loading Matrix Regression estimator.

skfolio.moments.expected_returns: Expected Returns Estimators

Expected returns module.

Base Class

moments.BaseMu

Base class for all expected returns estimators in skfolio.

Classes

moments.EmpiricalMu	Empirical Expected Returns (Mu) estimator.
moments.EWMu	Exponentially Weighted Expected Returns (Mu) estimator.
moments.ShrunkMu	Shrinkage Expected Returns (Mu) estimator.
moments.EquilibriumMu	Equilibrium Expected Returns (Mu) estimator.
moments.ShrunkMuMethods	Shrinkage methods for the ShrunkMu estimator.

skfolio.moments.variance: Variance Estimators

Variance module.

Base Class

moments.BaseVariance

Base class for all variance estimators in skfolio.

Classes

moments.EmpiricalVariance	Empirical Variance estimator.
moments.EWVariance	Exponentially Weighted Variance estimator.
moments.RegimeAdjustedEWVariance	Exponentially weighted variance estimator with regime adjustment via the Short-Term Volatility Update (STVU) [R1cff04c74aab-1].

skfolio.moments.covariance: Covariance Estimators

Covariance module.

Base Class

moments.BaseCovariance

Base class for all covariance estimators in skfolio.

Enum

moments.RegimeAdjustmentMethod	Transformation used to map the STVU statistic to the volatility multiplier.
moments.RegimeAdjustmentTarget	Target dimension used to calibrate the short-term volatility update (STVU).

Classes

moments.EmpiricalCovariance	Empirical Covariance estimator.
moments.EWCovariance	Exponentially Weighted Covariance estimator with NaN-aware pairwise updates.
moments.GerberCovariance	Gerber Covariance estimator.
moments.DenoiseCovariance	Covariance Denoising estimator.
moments.DetoneCovariance	Covariance Detoning estimator.
moments.LedoitWolf	LedoitWolf Covariance Estimator.
moments.OAS	Oracle Approximating Shrinkage Estimator as proposed in [Re9a22b087643-1].
moments.ShrunkCovariance	Covariance estimator with shrinkage.
moments.GraphicalLassoCV	Sparse inverse covariance with cross-validated choice of the l1 penalty.
moments.ImpliedCovariance	Implied Covariance estimator.
moments.RegimeAdjustedEWCovariance	Exponentially weighted covariance estimator with regime adjustment via the Short-Term Volatility Update (STVU) [R9fdb90a74052-1].

skfolio.distance: Distance Estimators

Distance Estimators.

Base Class

distance.BaseDistance

Base class for all distance estimators in skfolio.

Classes

distance.PearsonDistance	Pearson Distance estimator.
distance.KendallDistance	Kendall Distance estimator.
distance.SpearmanDistance	Spearman Distance estimator.
distance.CovarianceDistance	Covariance Distance estimator.
distance.DistanceCorrelation	Distance Correlation estimator.
distance.MutualInformation	Mutual Information estimator.

skfolio.cluster: Cluster Estimators

Hierarchical Clustering estimators.

Classes

cluster.HierarchicalClustering	Hierarchical Clustering.
cluster.LinkageMethod	Methods for calculating the distance between clusters in the linkage matrix.

skfolio.uncertainty_set: Uncertainty set Estimators

Uncertainty Set module.

Model Dataclass

uncertainty_set.UncertaintySet

Ellipsoidal uncertainty set dataclass.

Base Classes

uncertainty_set.BaseMuUncertaintySet	Base class for all Mu Uncertainty Set estimators in skfolio.
uncertainty_set.BaseCovarianceUncertaintySet	Base class for all Covariance Uncertainty Set estimators in skfolio.

Classes

uncertainty_set.EmpiricalMuUncertaintySet	Empirical Mu Uncertainty Set.
uncertainty_set.EmpiricalCovarianceUncertaintySet	Empirical Covariance Uncertainty set.
uncertainty_set.BootstrapMuUncertaintySet	Bootstrap Mu Uncertainty set.
uncertainty_set.BootstrapCovarianceUncertaintySet	Bootstrap Covariance Uncertainty set.

skfolio.pre_selection: Pre-selection Transformers

Pre Selection module.

Classes

pre_selection.DropCorrelated	Transformer for dropping highly correlated assets.
pre_selection.DropZeroVariance	Transformer for dropping assets with near-zero variance.
pre_selection.SelectKExtremes	Transformer for selecting the k best or worst assets.
pre_selection.SelectNonDominated	Transformer for selecting non dominated assets.
pre_selection.SelectComplete	Transformer to select assets with complete data across the entire observation period.
pre_selection.SelectNonExpiring	Transformer to select assets that do not expire within a specified lookahead period after the end of the observation period.

skfolio.linear_model: Cross-sectional linear models

Linear model module.

Base Class

linear_model.BaseCSLinearModel

Base class for all cross-sectional linear model estimators.

Classes

linear_model.CSLinearRegression	Cross-sectional weighted least squares regression.
linear_model.CSLinearRegressorWrapper	Cross-sectional regression based on a scikit-learn regressor.

skfolio.model_selection: Model Selection

Model selection module.

Base Classes

model_selection.BaseCombinatorialCV

Base class for all combinatorial cross-validators.

Classes

model_selection.WalkForward	Walk Forward Cross-Validator.
model_selection.CombinatorialPurgedCV	Combinatorial Purged Cross-Validation.
model_selection.MultipleRandomizedCV	Multiple Randomized Cross-Validation.
model_selection.OnlineGridSearch	Online exhaustive hyperparameter search over a parameter grid.
model_selection.OnlineRandomizedSearch	Online randomized search on hyper parameters.
model_selection.CovarianceForecastEvaluation	Out-of-sample covariance forecast evaluation.
model_selection.CovarianceForecastComparison	Side-by-side comparison of covariance forecast evaluations.

Functions

model_selection.cross_val_predict(estimator, X)	Generate cross-validated Portfolios estimates.
model_selection.online_predict(estimator, X)	Generate out-of-sample portfolios using online learning.
model_selection.online_score(estimator, X[, ...])	Score an online estimator using walk-forward evaluation.
model_selection.online_covariance_forecast_evaluation(...)	Evaluate out-of-sample covariance forecast quality.
model_selection.covariance_forecast_evaluation(...)	Evaluate out-of-sample covariance forecast quality using walk-forward cross-validation.
model_selection.optimal_folds_number(...[, ...])	Find the optimal number of folds (total folds and test folds) for a target training size and a target number of test paths.

skfolio.metrics: Metrics

Metrics module.

Functions

metrics.make_scorer(score_func[, ...])	Make a scorer from a measure, a portfolio score function, or a non-predictor estimator score function.
metrics.diagonal_calibration_loss(estimator, ...)	Diagonal calibration loss.
metrics.diagonal_calibration_ratio(...[, y])	Diagonal calibration ratio based on marginal variances.
metrics.exceedance_rate(squared_distances, ...)	Exceedance rate for chi-squared calibration statistics.
metrics.mahalanobis_calibration_loss(...[, y])	Mahalanobis calibration loss.
metrics.mahalanobis_calibration_ratio(...[, y])	Mahalanobis calibration ratio.
metrics.portfolio_variance_calibration_loss(...)	Portfolio variance calibration loss.
metrics.portfolio_variance_calibration_ratio(...)	Portfolio variance calibration ratio.
metrics.portfolio_variance_qlike_loss(...[, ...])	QLIKE loss for a projected portfolio variance forecast [R7dedfcdc36e0-1].
metrics.qlike_loss(returns, forecast_variance)	QLIKE loss for univariate variance forecasts.

skfolio.datasets: Datasets

Functions

datasets.load_sp500_dataset()	Load the prices of 20 assets from the S&P 500 Index.
datasets.load_sp500_index()	Load the prices of the S&P 500 Index.
datasets.load_factors_dataset()	Load the prices of 5 factor ETFs.
datasets.load_ftse100_dataset([data_home, ...])	Load the prices of 64 assets from the FTSE 100 Index composition.
datasets.load_nasdaq_dataset([data_home, ...])	Load the prices of 1455 assets from the NASDAQ Composite Index.
datasets.load_sp500_implied_vol_dataset([...])	Load the 3 months ATM implied volatility of the 20 assets from the SP500 dataset.

skfolio.preprocessing: Preprocessing

Functions

preprocessing.prices_to_returns(X[, y, ...])

Transform a DataFrame of prices to linear or logarithmic returns.

skfolio.utils.tools: Tools

Classes

tools.AutoEnum	Base Enum class used in skfolio.
tools.cached_property_slots	Cached property decorator for slots.

Functions

tools.apply_window_size(X, window_size)	Return the last window_size observations from the array X.
tools.args_names(func)	Returns the argument names of a function.
tools.bisection(x)	Generator to bisect a list of array.
tools.cache_method(cache_name)	Decorator that caches class methods results into a class dictionary.
tools.check_estimator(estimator, default, ...)	Check the estimator type and returns its cloned version it provided, otherwise
tools.deduplicate_names(names)	Rename duplicated names by appending "_{duplicate_nb}" at the end.
tools.default_asset_names(n_assets)	Default asset names are ["x0", "x1", ..., "x(n_assets - 1)"].
tools.fit_and_predict(estimator, X, y, ...)	Fit the estimator and predict values for a given dataset split.
tools.fit_single_estimator(estimator, X, y, ...)	Fit (or partial-fit) an estimator on a subset of the data.
tools.format_measure(x[, percent])	Format a measure number into a user-friendly string.
tools.get_feature_names(X)	Get feature names from X.
tools.half_life_to_decay_factor(half_life)	Convert half-life to exponential decay factor.
tools.input_to_array(items, n_assets, ...[, ...])	Convert a collection of items (array-like or dictionary) into a numpy array and verify its shape.
tools.optimal_rounding_decimals(x)	Return the optimal rounding decimal number for a user-friendly formatting.
tools.safe_indexing(X, indices[, axis])	Return rows, items or columns of X using indices.
tools.safe_split(X[, y, indices, axis])	Create subset of dataset.
tools.validate_input_list(items, n_assets, ...)	Convert a list of items (asset indices or asset names) into a list of validated asset indices.

skfolio.utils.stats: Stats

Enum

stats.NBinsMethod

Enumeration of the Number of Bins Methods.

Functions

stats.assert_is_distance(x)	Raises an error if the matrix is not a distance matrix.
stats.assert_is_square(x)	Raises an error if the matrix is not square.
stats.assert_is_symmetric(x)	Raises an error if the matrix is not symmetric.
stats.combination_by_index(idx, n, k)	Retrieve the k-combination at a given lexicographic position without enumerating all combinations.
stats.commutation_matrix(x)	Compute the commutation matrix.
stats.compute_optimal_n_clusters(distance, ...)	Compute the optimal number of clusters based on Two-Order Difference to Gap Statistic [Re0e718a4c413-1].
stats.corr_to_cov(corr, std)	Convert a correlation matrix to a covariance matrix given its standard-deviation vector.
stats.cov_nearest(cov[, higham, ...])	Compute the nearest covariance matrix that is positive definite and with a cholesky decomposition than can be computed.
stats.cov_to_corr(cov)	Convert a covariance matrix to a correlation matrix.
stats.cs_rank(a[, axis])	Cross-sectional rank along an axis.
stats.cs_rank_correlation(a, b[, axis, ...])	Cross-sectional Spearman rank correlation.
stats.cs_weighted_correlation(a, b[, ...])	Weighted cross-sectional Pearson correlation.
stats.inverse_multiply(a, b)	Multiply the inverse of matrix a by matrix b.
stats.inverse_volatility_weights(covariance)	Inverse-volatility portfolio weights from a covariance matrix.
stats.safe_cholesky(covariance[, ...])	Compute a Cholesky factor \(L\) from covariance \(\Sigma\).
stats.is_cholesky_dec(x)	Returns True if Cholesky decomposition can be computed.
stats.minimize_relative_weight_deviation(...)	Apply weight constraints to an initial array of weights by minimizing the relative weight deviation of the final weights from the initial weights.
stats.multiply_by_inverse(a, b)	Multiply matrix a by the inverse of matrix b.
stats.n_bins_freedman(x)	Compute the optimal histogram bin size using the Freedman-Diaconis rule [R8d5b646da1d1-1].
stats.n_bins_knuth(x)	Compute the optimal histogram bin size using Knuth's rule [R8c3fe88ee915-1].
stats.rand_weights(n[, zeros, seed])	Produces n random weights that sum to one from a uniform distribution (non-uniform distribution over a simplex).
stats.rand_weights_dirichlet(n)	Produces n random weights that sum to one from a dirichlet distribution (uniform distribution over a simplex).
stats.sample_unique_subsets(n, k, n_subsets)	Generate unique k-element subsets from a universe of size n using combinatorial unranking.
stats.squared_mahalanobis_dist(X, covariance)	Squared Mahalanobis distance via Cholesky decomposition.
stats.squared_standardized_euclidean_dist(...)	Squared standardized Euclidean distance.
stats.symmetric_step_up_matrix(n1, n2)	Compute the Symmetric step-up matrix M such that M @ np.ones(n2) = np.ones(n1).
stats.symmetrize(matrix[, where])	In-place symmetrization: \(M \leftarrow (M + M^T) / 2\).

skfolio.distribution.univariate: Univariate Distribution Estimators

Univariate Distribution module.

Base Class

distribution.BaseUnivariateDist

Base Univariate Distribution Estimator.

Classes

distribution.Gaussian	Gaussian Distribution Estimation.
distribution.StudentT	Student's t Distribution Estimation.
distribution.JohnsonSU	Johnson SU Distribution Estimation.
distribution.NormalInverseGaussian	Normal Inverse Gaussian Distribution Estimation.

Functions

distribution.select_univariate_dist(X[, ...])

Select the optimal univariate distribution estimator based on an information criterion.

skfolio.distribution.multivariate: Multivariate Distribution Estimators

Multivariate Distribution module.

Classes

distribution.VineCopula

Regular Vine Copula Estimator.

Enum

distribution.DependenceMethod

Enumeration of methods to measure bivariate dependence.

skfolio.distribution.copula: Bivariate Copula Estimators

Copula module.

Base Class

distribution.BaseBivariateCopula

Base class for Bivariate Copula Estimators.

Classes

distribution.GaussianCopula	Bivariate Gaussian Copula Estimation.
distribution.StudentTCopula	Bivariate Student's t Copula Estimation.
distribution.ClaytonCopula	Bivariate Clayton Copula Estimation.
distribution.GumbelCopula	Bivariate Gumbel Copula Estimation.
distribution.JoeCopula	Bivariate Joe Copula Estimation.
distribution.IndependentCopula	Bivariate Independent Copula (also called the product copula).

Functions

distribution.compute_pseudo_observations(X)	Compute pseudo-observations by ranking each column of the data and scaling the ranks.
distribution.empirical_tail_concentration(X, ...)	Compute empirical tail concentration for the two variables in X.
distribution.plot_tail_concentration(...[, ...])	Plot the empirical tail concentration curves.
distribution.select_bivariate_copula(X[, ...])	Select the best bivariate copula from a list of candidates using an information criterion.

Enum

distribution.CopulaRotation

Enum representing the rotation (in degrees) to apply to a bivariate copula.