# Markowitz portfolio optimization

Say that there are 5 assets with given mean values, standard deviations and correlations. Is it possible to find the expected return of a risk-seeking portfolio (maximum expected return) by using markowitz model ? I am guessing that since I have the means if I can somehow find the weights it should be fine but not sure..

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Yes. If your returns vector is $\mu$ and your covariance matrix is $\Sigma$ then the optimal allocation is
$$w = \frac{1}{\lambda}\Sigma^{-1}\mu$$
where $\lambda$ is your risk aversion. There are many variations on this, taking into account target return, position limits, fully invested constraints, trading costs, parameter uncertainty, model risk etc.
One approach is to think of the 'risk aversion' as a parameter that you tune, giving you a family of portfolios. Another (more sensible) approach is to notice that your variance with this portfolio is $(1/\lambda^2)\mu' \Sigma^{-1}\mu$. If your target variance is $\sigma^2$ you should therefore choose $\lambda = (1/\sigma) \sqrt{\mu'\Sigma^{-1}\mu}$ –  Chris Taylor Feb 17 '12 at 18:21