skfolio.optimization.BaseHierarchicalOptimization#

class skfolio.optimization.BaseHierarchicalOptimization(risk_measure=Variance, prior_estimator=None, distance_estimator=None, hierarchical_clustering_estimator=None, min_weights=0.0, max_weights=1.0, transaction_costs=0.0, management_fees=0.0, previous_weights=None, portfolio_params=None)[source]#

Base Hierarchical Clustering Optimization estimator.

Parameters:
risk_measureRiskMeasure or ExtraRiskMeasure, default=RiskMeasure.VARIANCE

RiskMeasure or ExtraRiskMeasure of the optimization. Can be any of:

  • MEAN_ABSOLUTE_DEVIATION

  • FIRST_LOWER_PARTIAL_MOMENT

  • VARIANCE

  • SEMI_VARIANCE

  • CVAR

  • EVAR

  • WORST_REALIZATION

  • CDAR

  • MAX_DRAWDOWN

  • AVERAGE_DRAWDOWN

  • EDAR

  • ULCER_INDEX

  • GINI_MEAN_DIFFERENCE_RATIO

  • VALUE_AT_RISK

  • DRAWDOWN_AT_RISK

  • ENTROPIC_RISK_MEASURE

  • FOURTH_CENTRAL_MOMENT

  • FOURTH_LOWER_PARTIAL_MOMENT

The default is RiskMeasure.VARIANCE.

prior_estimatorBasePrior, optional

Prior estimator. The prior estimator is used to estimate the PriorModel containing the estimation of assets expected returns, covariance matrix and returns. The moments and returns estimations are used for the risk computation and the returns estimation are used by the distance matrix estimator. The default (None) is to use EmpiricalPrior.

distance_estimatorBaseDistance, optional

Distance estimator. The distance estimator is used to estimate the codependence and the distance matrix needed for the computation of the linkage matrix. The default (None) is to use PearsonDistance.

hierarchical_clustering_estimatorHierarchicalClustering, optional

Hierarchical Clustering estimator. The hierarchical clustering estimator is used to compute the linkage matrix and the hierarchical clustering of the assets based on the distance matrix. The default (None) is to use HierarchicalClustering.

min_weightsfloat | dict[str, float] | array-like of shape (n_assets, ), default=0.0

Minimum assets weights (weights lower bounds). Negative weights are not allowed. If a float is provided, it is applied to each asset. If a dictionary is provided, its (key/value) pair must be the (asset name/asset minium weight) and the input X of the fit methods must be a DataFrame with the assets names in columns. When using a dictionary, assets values that are not provided are assigned a minimum weight of 0.0. The default is 0.0 (no short selling).

Example:

  • min_weights = 0 –> long only portfolio (no short selling).

  • min_weights = None –> no lower bound (same as -np.Inf).

  • min_weights = {“SX5E”: 0, “SPX”: 0.1}

  • min_weights = [0, 0.1]

max_weightsfloat | dict[str, float] | array-like of shape (n_assets, ), default=1.0

Maximum assets weights (weights upper bounds). Weights above 1.0 are not allowed. If a float is provided, it is applied to each asset. If a dictionary is provided, its (key/value) pair must be the (asset name/asset maximum weight) and the input X of the fit method must be a DataFrame with the assets names in columns. When using a dictionary, assets values that are not provided are assigned a minimum weight of 1.0. The default is 1.0 (each asset is below 100%).

Example:

  • max_weights = 0 –> no long position (short only portfolio).

  • max_weights = 0.5 –> each weight must be below 50%.

  • max_weights = {“SX5E”: 1, “SPX”: 0.25}

  • max_weights = [1, 0.25]

transaction_costsfloat | dict[str, float] | array-like of shape (n_assets, ), default=0.0

Transaction costs of the assets. It is used to add linear transaction costs to the optimization problem:

\[total\_cost = \sum_{i=1}^{N} c_{i} \times |w_{i} - w\_prev_{i}|\]

with \(c_{i}\) the transaction cost of asset i, \(w_{i}\) its weight and \(w\_prev_{i}\) its previous weight (defined in previous_weights). The float \(total\_cost\) is impacting the portfolio expected return in the optimization:

\[expected\_return = \mu^{T} \cdot w - total\_cost\]

with \(\mu\) the vector af assets’ expected returns and \(w\) the vector of assets weights.

If a float is provided, it is applied to each asset. If a dictionary is provided, its (key/value) pair must be the (asset name/asset cost) and the input X of the fit method must be a DataFrame with the assets names in columns. The default value is 0.0.

Warning

Based on the above formula, the periodicity of the transaction costs needs to be homogenous to the periodicity of \(\mu\). For example, if the input X is composed of daily returns, the transaction_costs need to be expressed as daily costs. (See Transaction Costs)

management_feesfloat | dict[str, float] | array-like of shape (n_assets, ), default=0.0

Management fees of the assets. It is used to add linear management fees to the optimization problem:

\[total\_fee = \sum_{i=1}^{N} f_{i} \times w_{i}\]

with \(f_{i}\) the management fee of asset i and \(w_{i}\) its weight. The float \(total\_fee\) is impacting the portfolio expected return in the optimization:

\[expected\_return = \mu^{T} \cdot w - total\_fee\]

with \(\mu\) the vector af assets expected returns and \(w\) the vector of assets weights.

If a float is provided, it is applied to each asset. If a dictionary is provided, its (key/value) pair must be the (asset name/asset fee) and the input X of the fit method must be a DataFrame with the assets names in columns. The default value is 0.0.

Warning

Based on the above formula, the periodicity of the management fees needs to be homogenous to the periodicity of \(\mu\). For example, if the input X is composed of daily returns, the management_fees need to be expressed in daily fees.

Note

Another approach is to directly impact the management fees to the input X in order to express the returns net of fees. However, when estimating the \(\mu\) parameter using for example Shrinkage estimators, this approach would mix a deterministic value with an uncertain one leading to unwanted bias in the management fees.

previous_weightsfloat | dict[str, float] | array-like of shape (n_assets, ), optional

Previous weights of the assets. Previous weights are used to compute the portfolio total cost. If a float is provided, it is applied to each asset. If a dictionary is provided, its (key/value) pair must be the (asset name/asset previous weight) and the input X of the fit method must be a DataFrame with the assets names in columns. The default (None) means no previous weights.

portfolio_paramsdict, optional

Portfolio parameters passed to the portfolio evaluated by the predict and score methods. If not provided, the name, transaction_costs, management_fees, previous_weights and risk_free_rate are copied from the optimization model and passed to the portfolio.

Attributes:
weights_ndarray of shape (n_assets,)

Weights of the assets.

prior_estimator_BasePrior

Fitted prior_estimator.

distance_estimator_BaseDistance

Fitted distance_estimator.

hierarchical_clustering_estimator_HierarchicalClustering

Fitted hierarchical_clustering_estimator.

Methods

fit_predict(X)

Perform fit on X and returns the predicted Portfolio or Population of Portfolio on X based on the fitted weights.

get_metadata_routing()

Get metadata routing of this object.

get_params([deep])

Get parameters for this estimator.

predict(X)

Predict the Portfolio or Population of Portfolio on X based on the fitted weights.

score(X[, y])

Prediction score.

set_params(**params)

Set the parameters of this estimator.

fit
fit_predict(X)#

Perform fit on X and returns the predicted Portfolio or Population of Portfolio on X based on the fitted weights. For factor models, use fit(X, y) then predict(X) separately.

Parameters:
Xarray-like of shape (n_observations, n_assets)

Price returns of the assets.

Returns:
predictionPortfolio | Population

Portfolio or Population of Portfolio estimated on X based on the fitted weights.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:
routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)#

Get parameters for this estimator.

Parameters:
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:
paramsdict

Parameter names mapped to their values.

predict(X)#

Predict the Portfolio or Population of Portfolio on X based on the fitted weights.

Optimization estimators can return a 1D or a 2D array of weights. For a 1D array, the prediction returns a Portfolio. For a 2D array, the prediction returns a Population of Portfolio.

If name is not provided in the portfolio arguments, we use the first 500 characters of the estimator name.

Parameters:
Xarray-like of shape (n_observations, n_assets)

Price returns of the assets.

Returns:
predictionPortfolio | Population

Portfolio or Population of Portfolio estimated on X based on the fitted weights.

score(X, y=None)#

Prediction score. If the prediction is a single Portfolio, the score is the Sharpe Ratio. If the prediction is a Population of Portfolio, the score is the mean of all the portfolios Sharpe Ratios in the population.

Parameters:
Xarray-like of shape (n_observations, n_assets)

Price returns of the assets.

yIgnored

Not used, present here for API consistency by convention.

Returns:
scorefloat

The Sharpe Ratio of the portfolio if the prediction is a single Portfolio or the mean of all the portfolios Sharpe Ratios if the prediction is a Population of Portfolio.

set_params(**params)#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:
**paramsdict

Estimator parameters.

Returns:
selfestimator instance

Estimator instance.