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# skfolio.moments.EquilibriumMu

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### *class* skfolio.moments.EquilibriumMu(risk_aversion=1, weights=None, covariance_estimator=None)

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_aversion** *float, default=1.0*
  : Risk aversion factor.
    The default value is `1.0`.

  **weights** *array-like of shape (n_assets,), optional*
  : Asset weights used to compute the Expected Return Equilibrium.
    The default is to use the equal-weighted equilibrium (1/N).
    For a Market Cap weighted equilibrium, you must provide the asset Market Caps.

  **covariance_estimator** *BaseCovariance, optional*
  : [Covariance estimator](https://skfolio.org/user_guide/covariance.html.md#covariance-estimator) used to estimate the
    covariance in the equilibrium formula.
    The default (`None`) is to use [`EmpiricalCovariance`](https://skfolio.org/generated/skfolio.moments.EmpiricalCovariance.html.md#skfolio.moments.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`](#skfolio.moments.EquilibriumMu.fit)(X[, y])            | Fit the EquilibriumMu estimator model.   |
|-------------------------------------------------------------------------|------------------------------------------|
| [`get_metadata_routing`](#skfolio.moments.EquilibriumMu.get_metadata_routing)() | Get metadata routing of this object.     |
| [`get_params`](#skfolio.moments.EquilibriumMu.get_params)([deep])     | Get parameters for this estimator.       |
| [`set_params`](#skfolio.moments.EquilibriumMu.set_params)(\*\*params) | Set the parameters of this estimator.    |

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#### fit(X, y=None, \*\*fit_params)

Fit the EquilibriumMu estimator model.

* **Parameters:**
  **X** *array-like of shape (n_observations, n_assets)*
  : Price returns of the assets.

  **y** *Ignored*
  : Not used, present for API consistency by convention.

  **\*\*fit_params** *dict*
  : 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](https://skfolio.org/user_guide/metadata_routing.html.md#metadata-routing) for
    more details.
* **Returns:**
  **self** *EquilibriumMu*
  : Fitted estimator.

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#### get_metadata_routing()

Get metadata routing of this object.

Please check [User Guide](https://skfolio.org/user_guide/metadata_routing.html.md#metadata-routing) on how the routing
mechanism works.

* **Returns:**
  **routing** *MetadataRequest*
  : A `MetadataRequest` encapsulating
    routing information.

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#### get_params(deep=True)

Get parameters for this estimator.

* **Parameters:**
  **deep** *bool, default=True*
  : If True, will return the parameters for this estimator and
    contained subobjects that are estimators.
* **Returns:**
  **params** *dict*
  : Parameter names mapped to their values.

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#### 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:**
  **\*\*params** *dict*
  : Estimator parameters.
* **Returns:**
  **self** *estimator instance*
  : Estimator instance.