<a id="skfolio-descriptor-ewdownsidevolatility"></a>

# skfolio.descriptor.EWDownsideVolatility

<a id="skfolio.descriptor.EWDownsideVolatility"></a>

### *class* skfolio.descriptor.EWDownsideVolatility(half_life=40.0, min_acceptable_return=0.0, min_periods=None)

Exponentially weighted downside return volatility descriptor.

Computes the downside semi-deviation of asset returns using EWMA estimation [[1]](#r598f00014148-1).
Only returns below the `min_acceptable_return` threshold contribute to the variance
estimate:

$$
\[
\begin{aligned}
D_i(t)
    &= \min(r_i(t) - \text{mar},\; 0) \\[0.75em]
S_{\text{down},i}(t)
    &= \lambda \cdot S_{\text{down},i}(t-1)
       + (1 - \lambda) \cdot D_i(t)^2 \\[0.75em]
\text{output}_i(t)
    &= \sqrt{\frac{S_{\text{down},i}(t)}
                 {1 - \lambda^{n_i(t)}}}
\end{aligned}
\]
$$

where $\lambda = \exp(-\ln(2)/\text{half\_life})$ and $n_i(t)$ is the
number of valid returns for asset $i$.

* **Parameters:**
  **half_life** *float, default=40.0*
  : EWMA half-life in observations.

  **min_acceptable_return** *float, default=0.0*
  : Threshold below which returns are considered “downside”. The default of `0.0`
    defines downside as negative returns (losses).

  **min_periods** *int, optional*
  : Minimum number of valid returns required for each asset. Until an asset reaches
    this count, its output is NaN. This warm-up period avoids exposing early EWMA
    values before the downside volatility estimate has sufficiently converged from
    its zero initialization. If `None`, defaults to
    $\lceil\text{half\_life}\rceil$, with a minimum of 1.
* **Attributes:**
  **n_assets_** *int*
  : Number of assets seen during fitting.

  **asset_names_** *ndarray of shape (n_assets,)*
  : Asset names seen during fitting.

  **volatility_** *ndarray of shape (n_assets,)*
  : Last computed EWMA downside volatility. Contains NaN for inactive assets and
    assets that have not reached `min_periods` valid returns.

### Methods

| [`fit_transform`](#skfolio.descriptor.EWDownsideVolatility.fit_transform)(X[, y])         | Compute exponentially weighted return volatility.       |
|--------------------------------------------------------------------------------|---------------------------------------------------------|
| [`get_metadata_routing`](#skfolio.descriptor.EWDownsideVolatility.get_metadata_routing)()        | Get metadata routing of this object.                    |
| [`get_params`](#skfolio.descriptor.EWDownsideVolatility.get_params)([deep])            | Get parameters for this estimator.                      |
| [`partial_fit_transform`](#skfolio.descriptor.EWDownsideVolatility.partial_fit_transform)(X[, y]) | Update EWMA state and return volatility for this batch. |
| [`set_params`](#skfolio.descriptor.EWDownsideVolatility.set_params)(\*\*params)        | Set the parameters of this estimator.                   |

#### SEE ALSO
[`EWVolatility`](https://skfolio.org/generated/skfolio.descriptor.EWVolatility.html.md#skfolio.descriptor.EWVolatility)
: Total (non-downside) variant.

[`EWResidualDownsideVolatility`](https://skfolio.org/generated/skfolio.descriptor.EWResidualDownsideVolatility.html.md#skfolio.descriptor.EWResidualDownsideVolatility)
: Downside CAPM residual volatility.

### Notes

The EWMA variance accumulator is initialized to zero and bias-corrected at output
time using each asset’s valid observation count, matching
[`EWVariance`](https://skfolio.org/generated/skfolio.moments.EWVariance.html.md#skfolio.moments.EWVariance).

NaNs are treated as missing observations. Active assets with missing returns keep
their previous EWMA state and inactive assets output NaN and restart their warm-up
period when they become active again. Non-missing returns must be finite.

### References

* <a id='r598f00014148-1'>**[1]**</a> “The cross-section of volatility and expected returns” The Journal of Finance. Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006).

### Examples

```pycon
>>> from skfolio.datasets import make_synthetic_characteristics
>>> from skfolio.descriptor import EWDownsideVolatility
>>>
>>> X = make_synthetic_characteristics()
>>>
>>> descriptor = EWDownsideVolatility()
>>> downside_volatility = descriptor.fit_transform(X)
>>>
>>> # Custom threshold
>>> descriptor = EWDownsideVolatility(min_acceptable_return=-0.01)
>>> downside_volatility = descriptor.fit_transform(X)
```

<a id="skfolio.descriptor.EWDownsideVolatility.fit_transform"></a>

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

Compute exponentially weighted return volatility.

* **Parameters:**
  **X** *AssetPanel*
  : Input panel containing `returns`.

  **y** *None*
  : Ignored. Present for compatibility with scikit-learn’s API.

  **\*\*fit_params** *dict*
  : Additional fit parameters. Ignored.
* **Returns:**
  **volatility** *ndarray of shape (n_observations, n_assets)*
  : EWMA volatility (or downside volatility) for each observation and asset.

<a id="skfolio.descriptor.EWDownsideVolatility.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.descriptor.EWDownsideVolatility.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.descriptor.EWDownsideVolatility.partial_fit_transform"></a>

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

Update EWMA state and return volatility for this batch.

This method supports online updates by continuing from the current fitted state.
Use `fit_transform` to start from a clean state.

* **Parameters:**
  **X** *AssetPanel*
  : Input panel containing `returns`.

  **y** *None*
  : Ignored. Present for compatibility with scikit-learn’s API.

  **\*\*fit_params** *dict*
  : Additional fit parameters. Ignored.
* **Returns:**
  **volatility** *ndarray of shape (n_observations, n_assets)*
  : EWMA volatility (or downside volatility) for each observation and asset.

<a id="skfolio.descriptor.EWDownsideVolatility.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.