skfolio.measures.fourth_lower_partial_moment

skfolio.measures.fourth_lower_partial_moment(returns, min_acceptable_return=None, sample_weight=None)

Compute the fourth lower partial moment.

The Fourth Lower Partial Moment is a measure of the heaviness of the downside tail of the returns below a minimum acceptable return. Higher Fourth Lower Partial Moment corresponds to greater extremity of downside deviations (downside fat tail).

Parameters:

returnsndarray of shape (n_observations,) or (n_observations, n_assets)

Array of return values.

min_acceptable_returnfloat or ndarray of shape (n_assets,), optional

Minimum acceptable return. It is the return target to distinguish “downside” and “upside” returns. The default (None) is to use the returns mean.

sample_weightndarray of shape (n_observations,), optional

Relative observation weights. Must be finite and nonnegative. If None, equal weights are assumed.

Returns:

valuefloat or ndarray of shape (n_assets,)

Fourth lower partial moment. If returns is a 1D-array, the result is a float. If returns is a 2D-array, the result is a ndarray of shape (n_assets,).

Notes

NaN handling: NaN returns are excluded from each column’s calculation. Remaining sample weights are rescaled to sum to one. The result is NaN if no observations or no positive weight remain.