The classical theory of portfolio selection pioneered by Markowitz (1952) remains to this day an immensely prominent approach to asset allocation and active portfolio management. The key inputs to this approach are the expected returns and the covariance matrix of the assets under consideration in the portfolio selection problem. According to the classical theory, optimal portfolio weights can be found by minimizing the variance of the portfolio’s returns subject to the constraint that the expected portfolio return achieves a specified target value.
In practical applications of mean-variance portfolio theory, the expected returns and the covariance matrix of asset returns obviously need to be estimated from the historical data. As with any model with unknown parameters, this immediately gives rise to the well-known problem of estimation risk; i.e., the estimated optimal portfolio rule is subject to parameter uncertainty and can thus be substantially different from the true optimal rule.
The implementation of mean-variance portfolios with inputs estimated via their sample analogues is notorious for producing extreme portfolio weights that fluctuate substantially over time and perform poorly out of sample; see Hodges and Brealey (1972), Michaud (1989), Best and Grauer (1991), and Litterman (2003). A recent study by DeMiguel, Garlappi, and Uppal (2009) casts further doubt on the usefulness of estimated mean-variance portfolio rules when compared to a naive diversification rule. The naive strategy, or 1/N rule, simply invests equally across the N assets under consideration, relying neither on any model nor on any data.
Those authors consider various static asset-allocation models at the monthly frequency and find that the asset misallocation errors of the suboptimal (from the mean-variance perspective) 1/N rule are smaller than those of the optimizing models in the presence of estimation risk. See also Jobson and Korkie (1980), Michaud and Michaud (2008), and Duchin and Levy (2009) for more on the issue of estimation errors in the implementation of Markowitz portfolios.
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Dynamic Correlations, Estimation Risk, And Porfolio Management During The Financial Crisis
