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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.

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    $\begingroup$ 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? $\endgroup$ – chrisaycock Mar 22 '12 at 19:52
  • $\begingroup$ 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. $\endgroup$ – nxstock-trader Mar 23 '12 at 7:06
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You are looking for a Risk Parity based utility function. Risk Parity assigns weights to assets in the portfolio such that the marginal contribution to risk of all assets is equal. As a result, Risk Parity penalizes assets with high volatility and high correlation. AQR has a multi-decade research on the performance of Risk Parity portfolios and it is quite favorable.

Some other utility functions you should consider are Maximum Diversification Portfolio described by Choueifaty and Coignard in “Toward Maximum Diversification".

Also, Atillio Meucci has a paper on constructing portfolios by maximizing the number of independent bets by applying a PCA treatment. (I'll post the link if I can find that one).

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The maximum decorrelation portfolio can ensure your portfolio is not so correlated in one general asset class:

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

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