ggiecold-zz / pyrmt Goto Github PK

After applying the algorithm to very small portfolio of ~15 assets, I noticed that the covariance is very underestimated. For instance, correlation between MSCI WLD and S&P 500 was negative (!!)

Mean absolute error on cross validation on my data was 0.41.

After reviewing the literature, most notably https://arxiv.org/pdf/1610.08104.pdf : see 8.1.2. Regularizing the empirical RIE,There exists a regularization technique called Invesrse Wishart, that would correct estimation error on the smallest eigenvalues:
kappa=2*lambda_N/((1-q-lambda_N)**2-4*q*lambda_N) alpha_s=1/(1+2*q*kappa) denom=x/(1+alpha_s*(x-1.)) Gamma /= denom

After applying this technique, MAE on my sample fell to 0.381, and correlation between WLD and S&P went back to 0.73. Markowitz optimization was also improved.

Errors are still much worse than a regular empirical or scikit MinCovDet estimator.

Please advise.

I might be mistaken, but I think the code on https://github.com/GGiecold/pyRMT/blob/master/pyRMT.py#L452-L455 does not reflect what is written in the green Box 1. on the last page of one of the referenced papers: https://www.cfm.fr/assets/ResearchPapers/2016-Cleaning-Correlation-Matrices.pdf

I think that
gmp = z + sigma_2 * (q - 1) - np.sqrt((z - lambda_N) * (z - lambda_plus))
should be
gmp = z + sigma_2 * (q - 1) - np.sqrt(z - lambda_N) * np.sqrt(z - lambda_plus)