# Minimum-variance portfolio

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## Minimum-variance portfolio

The portfolio of risky assets with lowest variance.

## Minimum-Variance Portfolio

A portfolio of individually risky assets that, when taken together, result in the lowest possible risk level for the rate of expected return. Such a portfolio hedges each investment with an offsetting investment; the individual investor's choice on how much to offset investments depends on the level of risk and expected return he/she is willing to accept. The investments in a minimum variance portfolio are individually riskier than the portfolio as a whole. The name of the term comes from how it is mathematically expressed in Markowitz Portfolio Theory, in which volatility is used as a replacement for risk, and in which less variance in volatility correlates to less risk in an investment.
References in periodicals archive ?
In order to compare the performance of robust optimization approaches detailed in the previous section with traditional mean-variance and minimum-variance portfolios, we use a rolling horizon procedure similar as in DeMiguel and Nogales (2009).
We can check that both robust and minimum-variance portfolios provided an improved stability in the portfolio composition over mean-variance portfolios.
Jagannathan and Ma (2003) propose a minimum-variance portfolio with a short selling restriction.
We will empirically compare two versions of robust portfolio optimization, the standard approach and the zero net alpha-adjusted robust optimization proposed by Ceria and Stubbs (2006) (hereafter adjusted robust optimization), with two well-established traditional techniques: Markowitz's mean-variance portfolio and minimum-variance portfolio.
The minimum-variance portfolio is the solution to the following optimization problem:
It is also worth noting that the minimum-variance portfolio is the mean-variance portfolio corresponding to an infinite risk aversion parameter.
We can check that all robust specifications delivered Sharpe ratios statistically higher than than the one obtained with the mean-variance portfolio policy, and similar to the one obtained minimum-variance portfolio policy regardless the size of the data sets.
We also note that the minimum-variance portfolio also performed better than the mean-variance portfolio.
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