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In Markowitz's theory the investor optimizes his portfolio according to the
mean-variance approach. The weight of assets in a portfolio is based on their expected return,
standard deviation and coefficient of correlation with the other assets included in the
portfolio. Investors act following a procedure characterized by different steps. First, they
determine their preferred strategic asset allocation and then they select the individual assets to
place in typical asset classes. If the investor believes that the market selected is efficient, he
can add index funds or other cheap products to the portfolio in response to the
perceived efficiency of the market, otherwise he can adopt active strategies. Thus, investors need
to be skilled at assessing the best sectors of activity to include in a portfolio.
In this context, the managers know that the use of the mean-variance
approach in building portfolios on the efficient frontier is an exercise in error
maximization, since the assumptions used (i.e., expected returns, risk measures, and correlations)
are many and the results obtained in terms of decision variables (the weights
of portfolios) are not robust as they are highly dependent on minor variations in
inputs. Various mitigation techniques are suggested to solve these problems. The full
list, which is beyond the aim of this work, includes: techniques of estimations of
the variance-covariance matrix in different market
scenarios, skewness, kurtosis and non-normality
(Scherer, 2004), the Bayesian approach, resampling
techniques (Michaud, 1998) and robust
optimization.
Apart from the solutions cited, there are other alternative approaches to beta
portfolio construction, which are simpler in terms of the number of inputs compared to the
mean-variance approach and thus have less estimation errors. Attention has recently
been focused on the 1/n approach, assigning equal weights to all the assets in a
portfolio by naïve diversification. |
