Does "standard Markowitz approach" include only mean-variance approach or does it also include other approach such as minimum-variance approach?

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    $\begingroup$ The standard Markowitz approach (known as modern portfolio theory (MPT)) indeed deals with the mean-variance optimisation as estabilished by Markowitz (1952). What else should it include? $\endgroup$ – KeSchn Nov 22 '19 at 20:18

The Markowitz mean-variance model is the basis for many extensions and portfolio solutions that have been discovered over the years:

The standard model (Markowitz, 1952, 1959) originally only considered:

  • Constrained model where short sales are forbidden
  • Only risky assets considered for investment (no risk-free asset)

Scenarios that the mean-variance model can be extended to include one, or a combination of, the following:

  • Unconstrained model where short sales are allowed (Black, 1972)
  • Inclusion of a risk-free asset (Tobin, 1958, 1965)
  • Dynamic model that looks at multi-period rebalancing of portfolios
  • Inclusion of transaction costs

To deal with estimation error in the mean-variance model, the following techniques are popular:

  • Resampled efficient frontier (Michaud and Michaud, 1998)
  • Covariance shrinkage (Ledoit-Wolf, 2003, 2004 and Jagannathan-Ma, 2003)
  • Robust portfolio optimization that uses uncertainty of inputs (Goldfarb and Iyengar, 2003)
  • Portfolio regularization (de Miguel et al, 2009 and Brodie et al, 2009)
  • replacing variance with Value-at-risk: these are mean-VaR and mean-CVaR models

Classical portfolios that can be solved using different objective functions (equations) for many combinations of the scenarios above, including obviously the standard model, are:

  • the Global Minimum Variance portfolio (GMV)
  • the Tangency portfolio that has the highest reward-to-risk Sharpe ratio
  • all other frontier portfolios that lie on the efficient frontier

Portfolio risk optimization, a subfield of modern portfolio theory, further revealed equations for the mean-variance model that use different objective functions to provide:

  • the Maximum Diversification portfolio
  • the Risk Parity portfolio
  • the Volatility Targeting portfolio

while common benchmarks (for comparing new strategies with) that don't require optimization but have profound performance in mean-variance space are:

  • the equally-weighted portfolio that weights each risky asset $1/N$
  • the inverse-volatility weighted portfolio

Common active strategies that modify the optimization problem are:

  • the Treynor-Black model (1973)
  • the Black-Litterman model (1992)

Although all of the above tend to focus on the optimization approach, there are alternative approaches to obtain equivalent solutions to the optimization approach:

  • the optimization approach
  • analytical closed-form solutions (Merton, 1972)
  • the regression approach (Britten-Jones, 1999 and Kempf and Memmel, 2006)
  • system of linear equations
  • $\begingroup$ Thank you for your answer. In a academic paper, would it be appropriate to refer to "minimum variance approach" as being included in "mean-variance approach"? $\endgroup$ – Aqqqq Nov 24 '19 at 15:07
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    $\begingroup$ An efficient portfolio is one that has the lowest portfolio risk for a given level of expected return. In the mean-variance model, all portfolios, including the GMV, tangency and other portfolios along the efficient frontier have the lowest variance for their respective levels of expected return. Therefore, mean-variance speaks to the overall trade-off the model tries to affect, by defining portfolios by their mean and variance, while minimum variance is an optimal criterion of this trade-off. no reason to separate these concepts into approaches because they are both inherent $\endgroup$ – develarist Nov 24 '19 at 15:27

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