The EF coincides with the top portion of the minimum-variance portfolio
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.
Some researchers have even expressed interest in minimum-variance portfolios, which depend entirely on the covariance matrix or excluding returns.
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.
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:
The first part in (13), as in (11), shows the weights on minimum-variance portfolio
, which can be construed as the hedging demand for the set of risky assets since it is independent of A which measures the degree of risk aversion.
Furthermore, after-tax efficient rays for investors of different tax rates radiate from a common starting point, i.e., the after-tax minimum-variance portfolio
. For example, in Figure 1, investors C, D, and E face the same tax rate on capital gains as do investors A and B.
Of course, outperformance isn't necessarily a sign that something is amiss, and there's solid research that shows a low-volatility anomaly does exist (see "Minimum-Variance Portfolios
in the U.S.