portfolio_entropy#

pymc_marketing.mmm.utility.portfolio_entropy(samples, budgets)[source]#

Calculate the entropy of a portfolio’s asset weights to assess diversification.

Portfolio entropy, derived from Shannon entropy in information theory, quantifies the dispersion of asset weights within a portfolio. A higher entropy value indicates a more diversified portfolio, as investments are more evenly distributed across assets. Conversely, a lower entropy suggests concentration in fewer assets, implying higher risk.

The entropy is calculated using the formula:

\[E = -\sum_{i=1}^{n} w_i \cdot \log(w_i)\]

where \(w_i\) represents the weight of asset ( i ) in the portfolio.

Parameters:

samplespt.TensorVariable: 1D PyTensor tensor variable containing samples.
budgetspt.TensorVariable: 1D PyTensor tensor variable representing the investment amounts in each asset.

Returns:

pt.TensorVariable: Portfolio entropy value.

References

[1]

Bera, A. K., & Park, S. Y. (2008). Optimal Portfolio Diversification using the Maximum Entropy Principle.

[2]

Pola, G. (2013). On entropy and portfolio diversification. Journal of Asset Management, 14(4), 228-238.