diversification_ratio not tested

[ricardoV94]

The helper is not tested directly (_covariance_matrix is). It's unclear how a user was supposed to use as part of an optimization cost because it requires 2D samples, whereas the optimizer was always giving 1D samples before #1357

pymc-marketing/pymc_marketing/mmm/utility.py

Lines 504 to 551 in 32f44c7

	def diversification_ratio(
	samples: pt.TensorVariable, budgets: pt.TensorVariable
	) -> pt.TensorVariable:
	R"""
	Calculate the Diversification Ratio of a portfolio to evaluate risk distribution.
	The Diversification Ratio measures the effectiveness of diversification by comparing
	the weighted average volatility of individual assets to the overall portfolio volatility.
	A higher ratio indicates better diversification, as it reflects lower correlations among
	assets, leading to reduced portfolio risk.
	The Diversification Ratio is calculated as:
	.. math::
	DR = \frac{\\sum_{i=1}^{n} w_i \\cdot \\sigma_i}{\\sigma_p}
	where:
	- :math:`w_i` is the weight of asset \\( i \\)
	- :math:`\\sigma_i` is the volatility (standard deviation) of asset \\( i \\)
	- :math:`\\sigma_p` is the volatility of the portfolio
	Parameters
	----------
	samples : pt.TensorVariable
	2D PyTensor tensor variable where each column represents the returns of an asset.
	budgets : pt.TensorVariable
	1D PyTensor tensor variable representing the investment amounts in each asset.
	Returns
	-------
	pt.TensorVariable
	Diversification Ratio.
	This ratio provides insight into how individual asset volatilities and their correlations
	contribute to the overall portfolio risk.
	References
	----------
	- Choueifaty, Y., & Coignard, Y. (2008). Toward Maximum Diversification. *Journal of Portfolio Management*.
	- Meucci, A. (2009). Managing Diversification. *Risk*, 22(5), 74-79.
	"""
	weights = budgets / pt.sum(budgets)
	individual_volatilities = pt.std(samples, axis=0, ddof=1)
	cov_matrix = _covariance_matrix(samples)
	portfolio_volatility = pt.sqrt(pt.dot(weights, pt.dot(cov_matrix, weights.T)))
	weighted_avg_volatility = pt.sum(weights * individual_volatilities)
	diversification_ratio = weighted_avg_volatility / portfolio_volatility
	return diversification_ratio

CC @cetagostini