Diversifying Minimum-Variance Portfolios Beyond Bond ETFs
Summary
The document considers why minimum-variance optimization over ETFs may concentrate holdings in bonds and government securities: assets with lower variance can dominate the objective. It presents several ways to pursue broader diversification. Risk parity sets weights so assets have equal marginal contributions to portfolio risk, thereby accounting for volatility and correlation. Maximum diversification is offered as another portfolio objective, while a principal-component approach is mentioned as a way to seek a larger number of independent bets. A separate answer defines maximum decorrelation as minimizing portfolio variance computed from the asset correlation matrix, with weights constrained to be nonnegative and sum to one.
These suggestions address different notions of diversification and are not shown to be equivalent. The document gives no comparative tests, performance results, or implementation details, and one cited approach is described only briefly. The choice of objective and constraints should therefore be evaluated against the investor’s portfolio goals; minimizing correlation alone does not establish that a portfolio will have low volatility or perform well.
Key ideas
- Minimum-variance optimization can concentrate a portfolio in low-volatility asset classes such as bonds.
- Risk parity weights assets so their marginal contributions to portfolio risk are equal.
- Maximum diversification and principal-component analysis offer alternative ways to frame portfolio diversification.
- A maximum-decorrelation objective minimizes weighted portfolio correlation subject to long-only, fully invested weights.
- The document provides no comparative evidence that any one objective produces superior investment results.
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# Reduce correlation in output of Minimum Variance Portfolio Optimization
# 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.
## Answer by Ram Ahluwalia (score 3, accepted)
https://quant.stackexchange.com/a/3113
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).
## Answer by develarist (score 1)
https://quant.stackexchange.com/a/57092
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 returnsShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.