## Markowitz Portfolio Selection Description

In portfolio selection the objective is, to allocate an initial wealth among a set of different assets. In Markowitz Portfolio Selection Problem the investor try to minimize the portfolio risk for a given level of expected portfolio return. For this, the assets are represented by the expected returns and the covariance matrix of the assets returns. To find the portfolio with the lowest possible risk, the investor minimize the portfolio variance (minimum variance portfolio). To find the portfolio with the best allocation of wealth related to risk and return, the investor maximize the Sharpe-ratio (market portfolio). The constraints are: no transaction costs, no consumption and no-shortselling.

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## References

- Markowitz, Harry. "Portfolio selection" The journal of finance 7.1 (1952): 77-91.
- Sharpe, William F. "CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK" The journal of finance 19.3 (1964): 425-442.