<a id="skfolio-optimization-distributionallyrobustcvar"></a>

# skfolio.optimization.DistributionallyRobustCVaR

<a id="skfolio.optimization.DistributionallyRobustCVaR"></a>

### *class* skfolio.optimization.DistributionallyRobustCVaR(risk_aversion=1.0, cvar_beta=0.95, wasserstein_ball_radius=0.02, prior_estimator=None, min_weights=0.0, max_weights=1.0, budget=1, min_budget=None, max_budget=None, max_short=None, max_long=None, groups=None, linear_constraints=None, left_inequality=None, right_inequality=None, risk_free_rate=0.0, solver='CLARABEL', solver_params=None, scale_objective=None, scale_constraints=None, save_problem=False, add_objective=None, add_constraints=None, overwrite_expected_return=None, portfolio_params=None, fallback=None, previous_weights=None, raise_on_failure=True)

Distributionally Robust CVaR.

The Distributionally Robust CVaR model constructs a Wasserstein ball in the space of
multivariate and non-discrete probability distributions centered at the uniform
distribution on the training samples and finds the allocation that minimizes the
CVaR of the worst-case distribution within this Wasserstein ball.
Esfahani and Kuhn [[1]](#r75a2f8fbeddd-1) proved that for piecewise linear objective functions,
which is the case of CVaR [[2]](#r75a2f8fbeddd-2), the distributionally robust optimization problem
over a Wasserstein ball can be reformulated as finite convex programs.

Only piecewise linear functions are supported, which means that transaction costs
and regularization are not permitted.

A solver like `Mosek` that can handle a high number of constraints is preferred.

* **Parameters:**
  **cvar_beta** *float, default=0.95*
  : CVaR (Conditional Value at Risk) confidence level.

  **risk_aversion** *float, default=1.0*
  : Risk aversion factor of the utility function: return - risk_aversion \* cvar.

  **wasserstein_ball_radius: float, default=0.02**
  : Radius of the Wasserstein ball.

  **prior_estimator** *BasePrior, optional*
  : [Prior estimator](https://skfolio.org/user_guide/prior.html.md#prior).
    The prior estimator is used to estimate the [`ReturnDistribution`](https://skfolio.org/generated/skfolio.prior.ReturnDistribution.html.md#skfolio.prior.ReturnDistribution)
    containing estimates of expected asset returns, covariance matrix,
    returns and Cholesky decomposition of the covariance.
    The default (`None`) is to use [`EmpiricalPrior`](https://skfolio.org/generated/skfolio.prior.EmpiricalPrior.html.md#skfolio.prior.EmpiricalPrior).

  **min_weights** *float | dict[str, float] | array-like of shape (n_assets, ) | None, default=0.0*
  : Minimum assets weights (weights lower bounds).
    If a float is provided, it is applied to each asset.
    `None` is equivalent to `-np.Inf` (no lower bound).
    If a dictionary is provided, its (key/value) pair must be the
    (asset name/asset minimum 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 `0.0`.
    The default value is `0.0` (no short selling).
    <br/>
    Example:
    > * `min_weights = 0` –> long only portfolio (no short selling).
    > * `min_weights = None` –> no lower bound (same as `-np.Inf`).
    > * `min_weights = -2` –> each weight must be above -200%.
    > * `min_weights = {"SX5E": 0, "SPX": -2}`
    > * `min_weights = [0, -2]`

  **max_weights** *float | dict[str, float] | array-like of shape (n_assets, ) | None, default=1.0*
  : Maximum assets weights (weights upper bounds).
    If a float is provided, it is applied to each asset.
    `None` is equivalent to `+np.Inf` (no upper bound).
    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 value is `1.0` (each asset is below 100%).
    <br/>
    Example:
    > * `max_weights = 0` –> no long position (short only portfolio).
    > * `max_weights = None` –> no upper bound.
    > * `max_weights = 2` –> each weight must be below 200%.
    > * `max_weights = {"SX5E": 1, "SPX": 2}`
    > * `max_weights = [1, 2]`

  **budget** *float | None, default=1.0*
  : Investment budget. It is the sum of long positions and short positions (sum of
    all weights). `None` means no budget constraints.
    The default value is `1.0` (fully invested portfolio).
    <br/>
    For example:
    > * `budget = 1` –> fully invested portfolio.
    > * `budget = 0` –> market neutral portfolio.
    > * `budget = None` –> no constraints on the sum of weights.

  **min_budget** *float, optional*
  : Minimum budget. It is the lower bound of the sum of long and short positions
    (sum of all weights). If provided, you must set `budget=None`.
    The default (`None`) means no minimum budget constraint.

  **max_short** *float, optional*
  : Maximum short position. The short position is defined as the sum of negative
    weights (in absolute term).
    The default (`None`) means no maximum short position.

  **max_long** *float, optional*
  : Maximum long position. The long position is defined as the sum of positive
    weights.
    The default (`None`) means no maximum long position.

  **max_budget** *float, optional*
  : Maximum budget. It is the upper bound of the sum of long and short positions
    (sum of all weights). If provided, you must set `budget=None`.
    The default (`None`) means no maximum budget constraint.

  **linear_constraints** *array-like of shape (n_constraints,), optional*
  : Linear constraints on portfolio weights or factor exposures.
    <br/>
    Constraint names can reference:
    > * Asset names: individual asset weights (e.g. `"SPX"`, `"AAPL"`)
    > * Group names: sums of weights in groups defined by `groups`
    > * Factor names: portfolio factor exposure (requires factor model prior)
    > * Factor families: sum of portfolio exposures to all factors in one family
    <br/>
    Supported equation patterns include:
    > * `"name <= value"` or `"name >= value"`
    > * `"name == value"`
    > * `"a * name1 + b * name2 <= c * name3 + d"`
    <br/>
    For example:
    > * `"SPX >= 0.10"` –> SPX weight >= 10%
    > * `"SX5E + SPX >= 0.2"` –> sum of SX5E and SPX weights >= 20%
    > * `"US == 0.7"` –> sum of weights in US group == 70%
    > * `"Equity == 3 * Bond"` –> sum of weights in Equity group == 3x sum of weights in Bond group
    > * `"Momentum <= 0.30"` –> portfolio Momentum exposure <= 30%
    > * `"style <= 0.50"` –> sum of all style factor exposures (Momentum, Value, Size, etc.) <= 50%
    <br/>
    Factor constraints require a prior estimator (e.g.
    [`TimeSeriesFactorModel`](https://skfolio.org/generated/skfolio.prior.TimeSeriesFactorModel.html.md#skfolio.prior.TimeSeriesFactorModel),
    [`CharacteristicsFactorModel`](https://skfolio.org/generated/skfolio.prior.CharacteristicsFactorModel.html.md#skfolio.prior.CharacteristicsFactorModel))
    that provides `loading_matrix`, `factor_names` and optionally `factor_families`
    in its [`FactorModel`](https://skfolio.org/generated/skfolio.prior.FactorModel.html.md#skfolio.prior.FactorModel).
    <br/>
    Asset, group, factor, and factor family names must be unique.

  **groups** *dict[str, list[str]] or array-like of shape (n_groups, n_assets), optional*
  : The assets groups referenced in `linear_constraints`.
    If a dictionary is provided, its (key/value) pair must be the
    (asset name/asset groups) and the input `X` of the `fit` method must be a
    DataFrame with the assets names in columns.
    <br/>
    For example:
    > * `groups = {"SX5E": ["Equity", "Europe"], "SPX": ["Equity", "US"], "TLT": ["Bond", "US"]}`
    > * `groups = [["Equity", "Equity", "Bond"], ["Europe", "US", "US"]]`

  **left_inequality** *array-like of shape (n_constraints, n_assets), optional*
  : Left inequality matrix $A$ of the linear
    constraint $A \cdot w \leq b$.

  **right_inequality** *array-like of shape (n_constraints, ), optional*
  : Right inequality vector $b$ of the linear
    constraint $A \cdot w \leq b$.

  **risk_free_rate** *float, default=0.0*
  : Risk-free interest rate.
    The default value is `0.0`.

  **add_constraints** *Callable[[cp.Variable], cp.Expression | list[cp.Expression]], optional*
  : Add a custom constraint or a list of constraints to the existing constraints.
    It must be a function taking the CVXPY weight variable `w` as its first
    positional argument and, optionally, the estimator instance as its second.
    It must return a CVXPY expression or a list of CVXPY expressions, evaluated
    when `fit` is called.
    <br/>
    For example, to require an effective number of assets of at least 20:
    ```pycon
    >>> import cvxpy as cp
    >>> from skfolio.optimization import DistributionallyRobustCVaR
    >>> model = DistributionallyRobustCVaR(
    ...     add_constraints=lambda w: cp.sum_squares(w) <= 1 / 20
    ... )
    ```
    <br/>
    The optional second argument gives access to the estimator’s attributes,
    including quantities estimated during `fit`. For example, to cap each
    position size in risk units at 20 bps, using the volatilities estimated
    by the prior:
    ```pycon
    >>> import numpy as np
    >>> def position_risk_cap(w, model):
    ...     covariance = model.prior_estimator_.return_distribution_.covariance
    ...     vols = np.sqrt(np.diag(covariance))
    ...     return cp.multiply(vols, w) <= 0.002
    >>> model = DistributionallyRobustCVaR(add_constraints=position_risk_cap)
    ```

  **overwrite_expected_return** *Callable[[cp.Variable], cp.Expression], optional*
  : Overwrite the expected return $\mu \cdot w$ with a custom CVXPY
    expression. It must be a function taking the CVXPY weight variable `w` as
    its first positional argument and, optionally, the estimator instance as
    its second. It must return a concave CVXPY expression, evaluated when
    `fit` is called. The custom expression replaces the expected return in the
    objective function and in the constraints where the expected return is
    used.
    <br/>
    For example, to adjust the expected return for volatility drag,
    approximating the portfolio geometric mean return:
    ```pycon
    >>> import cvxpy as cp
    >>> from skfolio.optimization import DistributionallyRobustCVaR
    >>> def geometric_expected_return(w, model):
    ...     dist = model.prior_estimator_.return_distribution_
    ...     return dist.mu @ w - 0.5 * cp.quad_form(w, dist.covariance)
    >>> model = DistributionallyRobustCVaR(
    ...     overwrite_expected_return=geometric_expected_return
    ... )
    ```

  **solver** *str, default=”CLARABEL”*
  : The solver to use. The default is “CLARABEL” which is written in Rust and has
    better numerical stability and performance than ECOS and SCS. Cvxpy will replace
    its default solver “ECOS” by “CLARABEL” in future releases.
    For more details about available solvers, check the CVXPY documentation:
    [https://www.cvxpy.org/tutorial/advanced/index.html#choosing-a-solver](https://www.cvxpy.org/tutorial/advanced/index.html#choosing-a-solver)

  **solver_params** *dict, optional*
  : Solver parameters. For example, `solver_params=dict(verbose=True)`.
    The default (`None`) is to use `{"tol_gap_abs": 1e-9, "tol_gap_rel": 1e-9}`
    for the solver “CLARABEL” and the CVXPY default otherwise.
    For more details about solver arguments, check the CVXPY documentation:
    [https://www.cvxpy.org/tutorial/advanced/index.html#setting-solver-options](https://www.cvxpy.org/tutorial/advanced/index.html#setting-solver-options)

  **scale_objective** *float, optional*
  : Scale each objective element by this value.
    It can be used to increase the optimization accuracies in specific cases.
    The default (`None`) is set depending on the problem.

  **scale_constraints** *float, optional*
  : Scale each constraint element by this value.
    It can be used to increase the optimization accuracies in specific cases.
    The default (`None`) is set depending on the problem.

  **save_problem** *bool, default=False*
  : If this is set to True, the CVXPY Problem is saved in `problem_`.
    The default is `False`.

  **portfolio_params** *dict, 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`.

  **fallback** *BaseOptimization | “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.

  **previous_weights** *float | dict[str, float] | array-like of shape (n_assets,), optional*
  : When `fallback="previous_weights"`, failures will fall back to these weights if
    provided.

  **raise_on_failure** *bool, default=True*
  : Controls error handling when fitting fails.
    If True, any failure during `fit` is raised immediately, no `weights_` are
    set and subsequent calls to `predict` will raise a `NotFittedError`.
    If False, errors are not raised; instead, a warning is emitted, `weights_`
    is set to `None` and subsequent calls to `predict` will return a
    `FailedPortfolio`. When fallbacks are specified, this behavior applies only
    after all fallbacks have been exhausted.
* **Attributes:**
  **weights_** *ndarray of shape (n_assets,) or (n_optimizations, n_assets)*
  : Weights of the assets.

  **problem_values_** *dict[str, float] | list[dict[str, float]] of size n_optimizations*
  : Expression values retrieved from the CVXPY problem.

  **prior_estimator_** *BasePrior*
  : Fitted `prior_estimator`.

  **problem_: cvxpy.Problem**
  : CVXPY problem used for the optimization. Only when `save_problem` is set to
    `True`.

  **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.

  **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*
  : Captured error message(s) when `fit` fails. For multi-portfolio outputs
    (`weights_` is 2D), this is a list aligned with portfolios.

### Methods

| [`fit`](#skfolio.optimization.DistributionallyRobustCVaR.fit)(X[, y])            | Fit the Distributionally Robust CVaR Optimization estimator.                                                                    |
|-------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------|
| [`fit_predict`](#skfolio.optimization.DistributionallyRobustCVaR.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`](#skfolio.optimization.DistributionallyRobustCVaR.get_metadata_routing)() | Get metadata routing of this object.                                                                                            |
| [`get_params`](#skfolio.optimization.DistributionallyRobustCVaR.get_params)([deep])     | Get parameters for this estimator.                                                                                              |
| [`predict`](#skfolio.optimization.DistributionallyRobustCVaR.predict)(X)             | Predict the `Portfolio` or a `Population` of portfolios on `X`.                                                                 |
| [`score`](#skfolio.optimization.DistributionallyRobustCVaR.score)(X[, y])          | Prediction score using the Sharpe Ratio.                                                                                        |
| [`set_params`](#skfolio.optimization.DistributionallyRobustCVaR.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

* <a id='r75a2f8fbeddd-1'>**[1]**</a> “Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations”. Esfahani and Kuhn (2018).
* <a id='r75a2f8fbeddd-2'>**[2]**</a> “Optimization of conditional value-at-risk”. Rockafellar and Uryasev (2000).

### Examples

For a complete tutorial on distributionally robust CVaR optimization, see the
[Distributionally Robust CVaR](https://skfolio.org/auto_examples/distributionally_robust_cvar/index.html.md#distributionally-robust-examples) gallery.

```pycon
>>> from skfolio.datasets import load_sp500_dataset
>>> from skfolio.optimization import DistributionallyRobustCVaR
>>> from skfolio.preprocessing import prices_to_returns
>>>
>>> # Use the most recent 252 daily returns
>>> prices = load_sp500_dataset()
>>> X = prices_to_returns(prices).tail(252)
>>>
>>> # Distributionally robust CVaR optimization
>>> model = DistributionallyRobustCVaR(wasserstein_ball_radius=0.01)
>>> model.fit(X)
DistributionallyRobustCVaR(wasserstein_ball_radius=0.01)
>>> print(model.weights_)
[0.     0.     0.0706 ... 0.0706 0.0706 0.0706]
>>>
>>> # Increasing the radius increases the uncertainty around the distribution,
>>> # which brings the weights closer to equal weighting
>>> model = DistributionallyRobustCVaR(wasserstein_ball_radius=0.10)
>>> model.fit(X)
DistributionallyRobustCVaR(wasserstein_ball_radius=0.1)
>>> print(model.weights_)
[0.05 0.05 0.05 ... 0.05 0.05 0.05]
```

<a id="skfolio.optimization.DistributionallyRobustCVaR.fit"></a>

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

Fit the Distributionally Robust CVaR Optimization estimator.

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

  **y** *array-like of shape (n_observations, n_factors), optional*
  : Price returns of factors.
    The default is `None`.

  **\*\*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** *DistributionallyRobustCVaR*
  : Fitted estimator.

<a id="skfolio.optimization.DistributionallyRobustCVaR.fit_predict"></a>

#### 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:**
  **X** *array-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`.

<a id="skfolio.optimization.DistributionallyRobustCVaR.get_metadata_routing"></a>

#### 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.

<a id="skfolio.optimization.DistributionallyRobustCVaR.get_params"></a>

#### 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.

<a id="skfolio.optimization.DistributionallyRobustCVaR.needs_previous_weights"></a>

#### *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.

<a id="skfolio.optimization.DistributionallyRobustCVaR.predict"></a>

#### 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:**
  **X** *array-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`.

<a id="skfolio.optimization.DistributionallyRobustCVaR.score"></a>

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

  **y** *Ignored*
  : Not used, present here for API consistency by convention.
* **Returns:**
  **score** *float*
  : 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`.

<a id="skfolio.optimization.DistributionallyRobustCVaR.set_params"></a>

#### 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.