Often readers ask about methods for approximating minimum variance portfolios. In practice the minimum variance portfolio can be calculated in closed form only for long-short portfolios, and requires a quadratic optimizer to solve for long-only portfolios. Source code and examples for  long-only minimum variance can be found at Systematic Investor – a very good blog that also has a toolkit for a lot of standard optimization methods. Michael Kapler (the man behind Systematic Investor) and I wrote a whitepaper about an algorithm for finding minimum correlation called the Minimum Correlation Algorithm (MCA), which was meant to approximate maximum diversification portfolios. The primary benefits of the algorithm versus the conventional optimization were: 1) speed of computation and ease of calculation 2) greater robustness to estimation error and 3) superior risk dispersion.  Testing results across a wide array of universes also demonstrated the superiority of MCA in terms of risk-adjusted returns versus its maximum diversification counterpart. The Minimum Variance Algorithm (MVA) is a close relative to MCA and shares the same benefits versus conventional minimum variance optimization. In testing, MVA showed superior risk-adjusted returns to MCA across most universes. While I have not yet conducted comparisons versus conventional minimum variance, preliminary results are very competitive. This is encouraging considering that MVA is very simple to calculate. Later this week I will present the logic and also post a spreadsheet for calculation along with some test results.

April 1, 2013 2:10 am

Hi David,
Thank you for the excellent sharing. To my understanding “minimum variance portfolio” tends to bias on low volatility assets. For example, if we add a “bond” into the pool of equities, then the weight will concentrate on the “bond”, making the portfolio not “well-diversified”.
Except for putting the lower bond on the individual weight, does anyone have any idea to fix this (Or Does this bias need to be fixed?)