skfolio.optimization.HierarchicalRiskParity#

class skfolio.optimization.HierarchicalRiskParity(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, fallback=None, raise_on_failure=True, *, seriation_estimator=None, distance_from_prior=True)[source]#

Hierarchical Risk Parity estimator.

Hierarchical Risk Parity is a portfolio optimization method developed by Marcos Lopez de Prado [1].

This algorithm uses a distance matrix to compute hierarchical clusters using the Hierarchical Tree Clustering algorithm. It then employs seriation to rearrange the assets in the dendrogram, minimizing the distance between leaves.

The final step is the recursive bisection where each cluster is split between two sub-clusters by starting with the topmost cluster and traversing in a top-down manner. For each sub-cluster, we compute the total cluster risk of an inverse-risk allocation. A weighting factor is then computed from these two sub-cluster risks, which is used to update the cluster weight.

Note

The original paper uses the variance as the risk measure and the single-linkage method for the Hierarchical Tree Clustering algorithm. Here we generalize it to multiple risk measures and linkage methods. The default linkage method is set to the Ward variance minimization algorithm, which is more stable and has better properties than the single-linkage method [2].

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 ReturnDistribution containing estimates of expected asset 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 used by the seriation estimator. The default (None) is to use PearsonDistance.

hierarchical_clustering_estimatorHierarchicalClustering, optional

Deprecated. Use seriation_estimator=HierarchicalSeriation( hierarchical_clustering_estimator=...). Supplying both parameters is an error. Will be removed in version 2.0.

seriation_estimatorBaseSeriation, optional

Asset ordering estimator. The default is HierarchicalSeriation with Ward linkage and optimal leaf ordering. Use SpectralSeriation for spectral ordering with orientation carried across online updates.

distance_from_priorbool, default=True

If True, fit the distance estimator on the return scenarios produced by the prior. With CovarianceDistance(covariance_estimator="precomputed"), use the prior’s covariance instead.

If False, use the X argument supplied to this optimizer’s fit(X) or partial_fit(X), before the prior processes it. In a pipeline, X is the output of the preceding steps. Precomputed covariance distances require True.

During online learning, True refits the distance estimator on the prior’s current scenarios or covariance at each update. False updates it from the new observations in X and requires support for partial_fit. Portfolio allocation always uses the prior’s moments and return scenarios. See Seriation for HRP and Schur.

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

Minimum assets weights (weights lower bounds). The default is 0.0 (no short selling). Negative weights are not allowed. If a float is provided, it is applied to each asset. None is equivalent to the default 0.0. If a dictionary is provided, its (key/value) pair must be the (asset name/asset minimum weight) and the input X of the fit methods must be a DataFrame with the asset names in columns. When using a dictionary, assets values that are not provided are assigned the default minimum weight of 0.0.

Example:

min_weights = 0.0 –> long only portfolio (default).

min_weights = {"SX5E": 0.1, "SPX": 0.2}

min_weights = [0.1, 0.2]

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

Maximum assets weights (weights upper bounds). The default is 1.0 (each asset is below 100%). Weights above 1.0 are not allowed. If a float is provided, it is applied to each asset. None is equivalent to the default 1.0. 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 asset names in columns. When using a dictionary, assets values that are not provided are assigned the default maximum weight of 1.0.

Example:

max_weights = 1.0 –> each weight must be below 100% (default).

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

max_weights = {"SX5E": 0.8, "SPX": 0.9}

max_weights = [0.8, 0.9]

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 of 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 asset names in columns. The default value is 0.0.

Warning

Based on the above formula, the periodicity of the transaction costs must match 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. A transaction cost is paid once per rebalancing while a position earns its expected return on every period it is held, so the one-off cost is converted by dividing it by the expected investment duration (e.g. 0.001 / 21 for a 10 bps cost with daily returns and a one-month expected holding period). (See Periodicity Convention)

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 of 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 asset names in columns. The default value is 0.0.

Warning

Based on the above formula, the periodicity of the management fees must match 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. Unlike transaction costs, management fees accrue with holding time, so a stated annual fee converts directly to the return periodicity (e.g. 0.02 / 252 for a 2% annual fee on daily returns).

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 asset names in columns. The default (None) means no previous weights. Additionally, when fallback="previous_weights", failures will fall back to these weights if provided.

portfolio_paramsdict, optional

Portfolio parameters forwarded to the resulting Portfolio in predict. If not provided and if available on the estimator, the following attributes are propagated to the portfolio by default: name, transaction_costs, management_fees, previous_weights and risk_free_rate.

fallbackBaseOptimization | “previous_weights” | list[BaseOptimization | “previous_weights”], optional

Fallback estimator or a list of estimators to try, in order, when the primary optimization raises during fit. Alternatively, use "previous_weights" (alone or in a list) to fall back to the estimator’s previous_weights. When a fallback succeeds, its fitted weights_ are copied back to the primary estimator so that fit still returns the original instance. For traceability, fallback_ stores the successful estimator (or the string "previous_weights") and fallback_chain_ stores each attempt with the associated outcome. With partial_fit, only None or "previous_weights" is supported because fallback estimators have not accumulated the primary model’s online history. See Fallbacks.

raise_on_failurebool, default=True

Controls error handling when fitting fails and no fallback succeeds. If True, the estimator raises the final error. If False, the estimator emits a warning and sets weights_ to None, so subsequent calls to predict return a FailedPortfolio. During fit, raise_on_failure applies to any fitting error, including errors raised by the prior estimator. During partial_fit, raise_on_failure applies only to optimization failures after learning completes. Input validation failures and errors from the prior or other learning estimators are always raised. See Failure Handling for batch recovery and Updates and Failure Handling for online continuation and restart rules.

Attributes:

weights_ndarray of shape (n_assets,): Weights of the assets.
distance_estimator_BaseDistance or None: Fitted distance_estimator. None when distance_from_prior=True and fewer than two assets are investable.
seriation_estimator_BaseSeriation: Fitted ordering estimator. Its ordering_ contains positions in the full input schema. Hierarchical linkage diagnostics are available through seriation_estimator_.hierarchical_clustering_estimator_.
hierarchical_clustering_estimator_HierarchicalClustering or None: Deprecated alias for seriation_estimator_.hierarchical_clustering_estimator_.
investable_mask_ndarray of shape (n_assets,) or None: Mask of investable assets from the fitted prior. None when all assets are investable. May be absent after batch fallback if fitting failed before the prior’s investable mask was determined.
n_features_in_int: Number of assets seen during fit.
feature_names_in_ndarray of shape (n_features_in_,): Names of assets seen during fit. Defined only when X has asset names that are all strings.
fallback_BaseOptimization | “previous_weights” | None: The fallback estimator instance, or the string "previous_weights", that produced the final result. None if no fallback was used.
fallback_chain_list[tuple[str, str]] | None: Sequence describing the optimization fallback attempts. Each element is a pair (estimator_repr, outcome) where estimator_repr is the string representation of the primary estimator or a fallback (e.g. "EqualWeighted()", "previous_weights"), and outcome is "success" if that step produced a valid solution, otherwise the stringified error message. For successful fits without any fallback, this is None.
error_str | list[str | None] | None: For a single portfolio, this is the recorded error message, or None after a successful allocation or fallback. For multiple portfolios, it is a list with one entry per row of weights_, containing an error message for each failed portfolio and None for each successful portfolio.

Methods

`fit`(X[, y])	Fit the Hierarchical Risk Parity Optimization estimator.
`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 for the prior, distance and seriation estimators.
`get_params`([deep])	Get parameters for this estimator.
`partial_fit`(X[, y])	Update the prior, distances and seriation, then compute portfolio weights.
`predict`(X)	Predict the `Portfolio` or a `Population` of portfolios on `X`.
`score`(X[, y])	Prediction score using the Sharpe Ratio.
`set_params`(**params)	Set the parameters of this estimator.

Notes

All estimators should specify all parameters as explicit keyword arguments in __init__ (no *args or **kwargs), following scikit-learn conventions.

References

[1]

“A robust estimator of the efficient frontier”, SSRN Electronic Journal, Marcos López de Prado (2019).

[2]

“A review of two decades of correlations, hierarchies, networks and clustering in financial markets”, Gautier Marti, Frank Nielsen, Mikołaj Bińkowski, Philippe Donnat (2020).

[3]

“Portfolio Optimization: Theory and Application”, Chapter 12, Daniel P. Palomar (2025)

[4]

“Building diversified portfolios that outperform out of sample”, The Journal of Portfolio Management, Marcos López de Prado (2016).

[5]

“Machine Learning for Asset Managers”, Elements in Quantitative Finance. Cambridge University Press, Marcos López de Prado (2020).

Examples

For online updates with late listings, delistings, holidays and asset warm-up, see Online Schur Allocation with a Changing Universe. That example uses Schur, and the same online setup applies to HRP.

fit(X, y=None, **fit_params)[source]#

Fit the Hierarchical Risk Parity Optimization estimator.

Parameters:

Xarray-like of shape (n_observations, n_assets): Price returns of the assets.
yarray-like, optional: Targets passed to the prior and, when distance_from_prior=False, to the distance estimator. Prior scenarios do not receive this target.
**fit_paramsdict: Metadata routed to the underlying estimators. Metadata supplied to a distance fitted on prior scenarios must align with those scenarios.

Returns:

selfHierarchicalRiskParity: Fitted estimator.

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, factors=...) then predict(X) separately.

If fitting fails and raise_on_failure=False, this returns a FailedPortfolio.

Parameters:

Xarray-like of shape (n_observations, n_assets): Price returns of the assets.

Returns:

Portfolio | Population: The predicted Portfolio or Population based on the fitted weights.

get_metadata_routing()#: Get metadata routing for the prior, distance and seriation estimators.

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.

property hierarchical_clustering_estimator_#: Deprecated alias for seriation_estimator_.hierarchical_clustering_estimator_.

property needs_previous_weights#

Whether previous_weights must be propagated between folds/rebalances.

Used by cross_val_predict and online_predict to decide whether to run sequentially and pass the weights from the previous rebalancing to the next. This is True when portfolio_params sets weight_drift=True, or when transaction costs, a maximum turnover, or a fallback depending on previous_weights are present.

partial_fit(X, y=None, **fit_params)[source]#

Update the prior, distances and seriation, then compute portfolio weights.

The prior must support incremental learning. With distance_from_prior=False, the distance must also support it. Supply only new observations on each call. See Updates and Failure Handling for failure handling and restarts.

Parameters:

Xarray-like of shape (n_observations, n_assets): New returns with the same full asset schema as previous calls.
yarray-like, optional: Targets passed to the prior and, when distance_from_prior=False, to the distance estimator.
**fit_paramsdict: Metadata routed to the underlying estimators. Requires metadata routing to be enabled. Observation metadata is not forwarded to distances fitted on the prior’s return scenarios or covariance.

Returns:

selfHierarchicalRiskParity: Updated estimator.

Raises:

OptimizationError: If optimization fails with raise_on_failure=True and fallback=None.

predict(X)#

Predict the Portfolio or a Population of portfolios on X.

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

If name is not provided in the portfolio parameters, the estimator class name is used.

Parameters:

Xarray-like of shape (n_observations, n_assets) | ReturnDistribution: Asset returns or a ReturnDistribution carrying returns and optional sample weights.

Returns:

Portfolio | Population: The predicted Portfolio or Population based on the fitted weights.

score(X, y=None)#

Prediction score using the Sharpe Ratio. If the prediction is a single Portfolio, the score is its Sharpe Ratio. If the prediction is a Population, the score is the mean Sharpe Ratio across portfolios.

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 portfolio 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.