As already mentioned above, those compositions close to the minimum-variance portfolio comprise rather small fractions of government and corporate bonds.
With regard to the efficient frontier for the restricted assets, we find that the insurer may not chose points in the wider proximity of the minimum-variance portfolio, whereas a large range of points from the first third toward the right end of the curve are admissible.
For extremely high values of [kappa], in contrast, the tangency points are located near the minimum-variance portfolio.
Moreover, note that the minimum-variance portfolio on all three frontiers actually lies slightly to the upper left of a pure investment in money market instruments.
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.
The minimum-variance portfolio also performed similarly in relation to robust alternatives, indicating that this approach is a simple alternative able to alleviate the effects of estimation errors in means.