Some researchers have even expressed interest in minimum-variance portfolios, which depend entirely on the covariance matrix or excluding returns.
For example, as we travel down the efficient frontier from the tangent portfolio toward the minimum-variance portfolio, the quality of each security (as measured in terms of its return-to-risk ratio) declines.
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. We will evaluate the out-of-sample performance of those portfolio allocation approaches according to the methodology of rolling horizon proposed in DeMiguel and Nogales (2009).
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.
