Robustifying the Optimal Portfolio
We saw previous that two optimal portfolio's could be computed:
- the optimum sharpe ratio portfolio
- the minimum variance portfolio
Both these portfolio estimation tend to put the largest weight to some of the smallest eigenvalue eigenvector. For a large enough covariance matrix, this is a recipe for instability.
Marco Lopez de Prado (2019) Results
An excellent article summarizing most recent results by Marco Lopez de Prado has been published since this website was created. The following procedures can be used to robustify the estimation:
- shrinking the covariance matrix
- denoising the eignevalue spectrum by averaging the replacing the lowest eigenvalues by their average value. This ensures that eigenvalues do not tend to 0 because of statistical artifacts.
- nested cluster optimisation by identifying high correlation clusters and performing optimization on each cluster first, and then on the subportfolios
The results are summarized in the paper as the author evaluates out of sample performance using monte-carlo simulation. The author compares results for standard quadratic optimisation with his new NCO algorithm.
- the error on sharpe optimal portfolio are 10x higher than on minimal variance portfolio
- shrinking or denoising have similar performance and halve the error the standard quadratic method
- denoising is performance is slightly better
- shrinking + denoising is slightly better
- NCO is better than denoising or shrinking, S+D+NCO works best.