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There are various models for portfolio selection in literature, like,

  1. Harry Markowitz (HM) model ( Mean-Variance Model) [well known model]
  2. Konno and Yamazaki (1991) model: minimizes the sum of absolute deviations
  3. Markowitz- semi-variance model (1959)
  4. Speranza- mean-absolute semi-deviation (1993)

There are many more such variants. I just want to know what kind of models are used by practitioners in reality to construct portfolio? How they takes into account the assumption of various model when constructing portfolio (You may assume assumption of HM model)?

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    $\begingroup$ Portfolio optimalisation depends heavily on the estimation of the moments. Even though it's useful for comparing and analysing different strategies, I think practitioners are moving more towards the usage of factor portfolios for the strategies themselves (e.g. Fama-French). This because the exploitation of such anomalies have been proven to be quite persistent and relatively profitable. $\endgroup$ – Jean-Paul Feb 20 '16 at 18:36
  • $\begingroup$ In addition to what @Jean-Paul said when constructing a portfolio you want to go off methodology that is robust, persistent across markets, lower costs (lower turnover), etc. For example Mean variance model gives you formulation on how to weight portfolio (not which stocks to pick), but most people just weight by market cap because for one low turnover (it reweights itself) $\endgroup$ – Kamster Feb 20 '16 at 23:27
  • $\begingroup$ Could you specify which type of portfolio construction you are asking about ? Multi-Assets ? Equities ? Derivatives ? Fixed Income ? I think the practitioner take will change a lot depending on which asset class you are talking about. $\endgroup$ – NegativeJo Feb 27 '16 at 9:56
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Portfolio optimalisation depends heavily on the estimation of the moments (and therefore has HUGE estimation uncertainty).

Even though it's useful for comparing and analysing different existing strategies, I think practitioners are moving more towards the usage of factor portfolios for the strategies themselves (e.g. Fama-French). Also because the exploitation of such anomalies have been proven to be quite persistent and relatively profitable.

To give you an example of the estimation uncertainty that goes together with portfolio optimalisation, a simple plug-in Markowitz regression on the S&P 500 (1997-2006) using the delta method yields a weight of w=0.5 and a standard error of 0.4! So the estimation says that we should invest half our portfolio in the risky asset (S&P 500), with a standard deviation of 0.4. You can imagine that a 95% confidence interval would range all the way from investing nothing in the market to investing everything. So what is really optimal? The estimation uncertainty can be improved using shrinkage methods but you get the picture.

Another disadvantage of such portfolio optimalisation is that it doesn't really capture anomalies like factor models can. It's of course possible to combine the optimalisation of weights with the results from factor models to sort of 'get the best of both worlds'.

Besides, most portfolio optimalisation models can't beat the 1/N portfolio out of sample. Even if they do beat the benchmark, they often still have transaction costs which need to be corrected for. After correction, you will find again that the models are quite useless and you're better off investing in the 1/N portfolio instead. Like I said before, this is not true for cross-sectional anomalies. It has been shown numerous times that various factor models and predictive variables perform quite well. See for example Fama and French (2008), Campbell and Thompson (2008) and Goyal and Welch (2008).

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Many pension funds and mutual funds acquire small positions in many stocks, therefore just banking on the main results of the Markowitz framework: diversification. This could also just be seen as a plain 1/N rule: naive diversification. In the limit, this just equals the market portfolio.

Alternatively, to overcome the sensitivity in changes in the return/ variance-covariance matrix, you could apply Michaud's method (resampled efficient frontier) method to portoflio construction.

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I doubt anyone in practice uses Markowitz or similar things. My guess is that industry are moving towards stuff in the line of Parametric Portfolio Policies (e.g. Brandt, Santa-Clara and Valkanov 2009).

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    $\begingroup$ can you please provide your answer in much more details? $\endgroup$ – Neeraj Feb 20 '16 at 6:34

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