### Victor DeMiguel (London Business School)

#### Portfolio selection with robust estimates of risk

*Wednesday 18 October 2006 at 15.30, JCMB 5327*

##### Abstract

Mean-variance portfolios constructed using the sample mean and
covariance matrix of asset returns perform poorly due to estimation
error. Moreover, it is commonly accepted that estimation error in the
sample mean is much larger than in the sample covariance matrix. For
this reason, recent research has focused on the minimum-variance
portfolio, which relies only on estimates of the covariance matrix and
thus usually performs better out-of-sample. But even minimum-variance
portfolios are quite sensitive to estimation error and have unstable
weights that fluctuate substantially over time. In this paper, we
propose a class of portfolio policies that have better stability
properties than the traditional minimum-variance portfolio. The
proposed policies are based on certain robust estimators of risk and
can be computed by solving a single nonlinear program, where estimation
and portfolio optimization are performed in one step. We show
analytically that the portfolio weights of the resulting policies are
less sensitive to changes in the distributional assumptions than those
of the traditional minimum-variance policy. Moreover, our numerical
results on simulated and empirical data confirm that the proposed
policies are more stable and that they preserve (or slightly improve)
the already relatively high out-of-sample Sharpe ratio of the
minimum-variance policy.

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