# Minimum Variance Algorithm (MVA)

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.

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?)

Hi Ray, the minimum variance portfolio (regardless of method used) will tend to favor low volatility assets like bonds simply because of their assumption that the returns of all assets are equal to zero. Thus lower risk is better than higher risk. The minimum correlation algorithm will tend to be less biased towards low vol assets, since it seeks diversification as its primary goal. However it is important to note that while minimum variance tends to favor low vol assets like bonds, it will only do so when bonds have low volatility. In recent times the long bond has been higher risk than the S&P500 (equities) and minimum variance has instead favored equities over bonds. Not surprisingly this has coincided with poor performance for bonds. Thus minimum variance does not neccessarily imply that investors will be “left holding the bag” when interest rates finally go up since that is likely to also coincide with higher volatility. An important point to remember.

best

david

Got it. Thanks a lot.