diversification_ratio

pymc_marketing.mmm.utility.diversification_ratio(samples, budgets)

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:

\[\begin{split}DR = \frac{\\sum_{i=1}^{n} w_i \\cdot \\sigma_i}{\\sigma_p}\end{split}\]

where:

• \(w_i\) is the weight of asset \( i \)

• \(\\sigma_i\) is the volatility (standard deviation) of asset \( i \)

• \(\\sigma_p\) is the volatility of the portfolio

Parameters:

samplespt.TensorVariable

2D PyTensor tensor variable where each column represents the returns of an asset.

budgetspt.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.