Here is a recent paper explaining to obtain optimal portfolios with minimum capital requirements (based on Basel II regulations) and VaR constraints:http://ssrn.com/abstract=1599266

Don't get why the BII 2009 update is just a one page appendix... They should have made that the core not the old version as the revised capital requirements formula has already been implemented by most people and will take effect as the regulatory reporting measure at the end of the year. Also I don't think anyone builds a min-VaR portfolio to be honest it's not an additive method and makes for flaky portfolios, would have wanted to see them do a comparison with a min-CVaR portfolio instead. Not sure why the Risk Metrics CoVar choice blows up the returns by so much though... would have wanted more insight into that (it's just one line) and what they infer from the results based on the different covariance models and how they influence results.

Hansi,It is very easy to apply the reformulation proposed in section 2.3 of the paper to the 'new' capital requirement formula as noted in the appendix. I agree with your point regarding the non additiveness of VaR, but i) this measure is the one used in BII, ii) CVaR leads to higher capital requirements, and iii) if we assume elliptical (symmetric) distributions for the returns, then the optimal solutions for min-VaR and min-CVaR are on the same efficient frontier. Regarding the performance of the Risk Metrics for the Fama-French portfolios, the good results in terms of turnover is probably because this method has much less estimation error than competing models. There is no need to estimate parameters in Risk Metrics, and this leads to a more stable portfolio strategy and less prone to estimation error.Thanks a lot for the very good feedback!