skfolio.moments.EquilibriumMu#

class skfolio.moments.EquilibriumMu(risk_aversion=1, weights=None, covariance_estimator=None)[source]#

Equilibrium Expected Returns (Mu) estimator.

The Equilibrium is defined as:

\[risk\_aversion \times \Sigma \cdot w^T\]

For Market Cap Equilibrium, the weights are the assets Market Caps. For Equal-weighted Equilibrium, the weights are equal-weighted (1/N).

Parameters:

risk_aversionfloat, default=1.0

Risk aversion factor. The default value is 1.0.

weightsarray-like of shape (n_assets,), optional

Reference portfolio weights used to compute the implied excess returns. Supplied weights are used as given, without normalization. They may contain negative values and need not sum to one. Their scale is preserved, so changing the portfolio exposure changes the estimated returns.

For a market-cap-weighted equilibrium, provide normalized market capitalizations: market_caps / market_caps.sum().

Other weights define a reverse-optimization prior for the chosen reference portfolio, which may be leveraged, long-short, or market-neutral.

The default (None) is to use equal weights (1/N).

covariance_estimatorBaseCovariance, optional

Covariance estimator used to estimate the covariance in the equilibrium formula. The default (None) is to use EmpiricalCovariance.

Attributes:

mu_ndarray of shape (n_assets,): Estimated expected returns of the assets.
covariance_estimator_BaseCovariance: Fitted covariance_estimator.
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 assets names that are all strings.

Methods

`fit`(X[, y])	Fit the EquilibriumMu estimator model.
`get_metadata_routing`()	Get metadata routing for this estimator.
`get_params`([deep])	Get parameters for this estimator.
`set_params`(**params)	Set the parameters of this estimator.

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

Fit the EquilibriumMu estimator model.

Parameters:

Xarray-like of shape (n_observations, n_assets): Price returns of the assets.
yIgnored: Not used, present for API consistency by convention.
**fit_paramsdict: Parameters to pass to the underlying estimators. Only available if enable_metadata_routing=True, which can be set by using sklearn.set_config(enable_metadata_routing=True). See Metadata Routing User Guide for more details.

Returns:

selfEquilibriumMu: Fitted estimator.

get_metadata_routing()[source]#

Get metadata routing for this estimator.

Routes metadata passed to fit to the fit method of covariance_estimator.

Returns:

routingMetadataRouter: Metadata routing configuration.

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.

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.