Estimation risk in portfolio selection: the mean variance model versus the mean absolute deviation model
Article Abstract:
The mean absolute deviation (MAD) model introduced by Konno and Yamazaki (1992) as an alternative to the Markowitz mean-variance (MV) portfolio selection model is examined. The new model turns the portfolio selection problem from a quadratic problem to a linear problem by substituting the variance in the MV objective function with the mean absolute deviation. Konno and Yamazaki claim that their model possesses all the favorable attributes of the MV model and offers additional advantages. They contend that the model does not require the covariance matrix of asset returns; that MAD portfolios have less assets and, therefore, lesser transaction costs in portfolio revisions; and that linear problems are easier to solve than quadratic problems. It is shown that the MAD model entails higher estimation risk than the MV model because it ignores the covariance matrix.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1997
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What is the opportunity cost of mean-variance investment strategies?
Article Abstract:
Mean-variance portfolio selection strategies are evaluated as to foregone opportunity cost. Given a riskless investment opportunity, mean-variance investment strategies results in an approximation of 0.05% asset value opportunity cost, regardless of the degree of risk aversion. However, denial of the riskless asset only results in fair estimates up to a given risk aversion level, beyond which approximation of the opportunity cost is poor. Inaccurate approximation at suchhigh risk aversion levels occurs because the highly risk-averse investor will persist in the safest possible strategy even in the presence of rewarding but slightly more risky options. This obsessive behavior accounts for the poor performance of mean-variance investment strategies in certain cases.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1993
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Portfolio selection and asset pricing - three-parameter framework
Article Abstract:
A three-moment model of portfolio selection that describes idiosyncratic security risks is developed. These risksare jointly and spherically distributed, with a generalized covariance matrix and a mean vector. Different securities have different loadings upon a single factor which generates skewness, resulting in three funds: two to span the spherical risk and another to span the skewed risk. The model involves short sales restrictions and describes an investor's risk attitude as a function of the variance and a shape factor of the portfolio distribution, upon which the portfolio skewness depends. This framework, which is similar to the mean-variance model, results in a set of zero-beta portfolios in two dimensions.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1993
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