# Reduce correlation in output of Minimum Variance Portfolio Optimization

After running a minimum variance portfolio optimization on a universe of ETF's I see the resulting portfolios tend to be composed of bond ETF or related treasuries/government ETFs.

I suppose that makes sense because bonds have had lower variance in the periods I'm looking at, however I'm wondering what is the best way to ensure my portfolio is not so 'correlated' in one general asset class?

Is it necessary to impose constraints on the 'class' of ETF in the portfolio, or is there something more natural that can be done to ensure the portfolios optimize for both minimum variance as well as low correlation between the names selected?

thanks much, awesome community here.

• You have not accepted any answers to your previous questions, which is why there's a big red zero below your name. That will put people off from answering your newer questions. See How does accepting an answer work? – chrisaycock Mar 22 '12 at 19:52
• Indeed, I was unaware thank you for letting me know. I was visiting Downton so I had Mr. Carson ring the valet and he submitted 'check-marks' on the correct answers. – nxstock-trader Mar 23 '12 at 7:06

min $$\mathbf{w^{T} C w}$$
subject to constraints that weights sum to 1 and are non-negative, where $$\mathbf{C}$$ is the correlation matrix of multivariate asset returns