Markowitz portfolio selection

In this tutorial we show how to solve the Markowitz portfolio selection problem in Excel by help of Solver. The expected returns for each asset and covariance matrix are given. The optimal portfolio with the highest expected return is calculated. It contains always one single asset. In a second step we determine the minimum variance portfolio by minimizing the risk in terms of variance or standard deviation (classical portfolio theory). In the end we calculate the market portfolio by maximization of the Sharpe-Ratio (CAPM). The constraints are: no transaction costs, no consumption and no-shortselling. This approach is also called mean-variance optimization and is a specific type of portfolio management.



  • 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.


For solving a portfolio selection problem a solver is required. The installation of a simple, but sufficient solver in Excel, is shown in MS Solver for Excel.

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