In portfolio optimization, the goal is to calibrate the weights of assets in a portfolio according to a stated objective (mean-variance, minimum-variance, risk parity etc.). Often, mean-variance or minimum-variance objectives produce zero weights for many assets in a portfolio with a large number of assets due to the calibration - this is not ideal due to lack of diversification.
One solution is L2 regularization. The minimum-variance objective function is stated as below:
$$\underset{w}{min} \; w' \Sigma w \rightarrow \underset{w}{min} \; w' \Sigma w + \gamma w' w$$
where $\gamma w' w$ is minimized (maximized) when weights are equally distributed among all assets (weights are fully allocated to a single asset). Therefore, the calibration is forced to find an optimum between hitting the minimum-variance objective and the penalty function.
Question: How often is this used in the industry or do practitioners rely on rough estimates like minimum 1% weight per asset to ensure diversification in their portfolio? Are there more modern techniques?
Source: https://pyportfolioopt.readthedocs.io/en/latest/MeanVariance.html#l2-regularisation
