Portfolio optimization is a process of selecting the most optimal combination of assets that maximize returns while minimizing risk. In Excel, you can use Solver to perform portfolio optimization using mean-variance analysis. Here are the steps to perform portfolio optimization in Excel:
Data Preparation: The first step is to prepare the data for analysis. You need to gather historical data on the returns of each asset in the portfolio. You will also need to calculate the expected returns and the covariance matrix of the asset returns.
Portfolio Optimization Model: The next step is to create a portfolio optimization model in Excel. The model will have two objective functions: maximize portfolio return and minimize portfolio risk. The portfolio return is calculated as the weighted average of the asset returns, while portfolio risk is measured as the standard deviation of the portfolio returns. You can use Excel's built-in functions such as SUMPRODUCT, SUMSQ, and SQRT to calculate these values.
Set up Solver: Set up Solver by adding it to the Excel add-ins. You can do this by going to the "File" menu, selecting "Options", and then selecting "Add-ins". In the "Manage" dropdown, select "Excel Add-ins" and click "Go". In the "Add-Ins" box, check "Solver Add-in" and click "OK".
Solver Parameters: Next, you will need to set up the Solver parameters. You need to specify the objective cell, the variables (weights of each asset), and the constraints. The constraints should ensure that the weights of the assets add up to 1 and that each weight is between 0 and 1. You can also set a target return or a target risk level as a constraint.
Run Solver: After setting up the Solver parameters, you can run Solver by clicking on the "Solver" button on the "Data" tab. You should select "GRG Nonlinear" as the solving method and set the convergence criteria. Solver will find the optimal weights for each asset that maximize the portfolio return while minimizing the portfolio risk.
Analysis: Finally, you can analyze the results of the portfolio optimization. You can create a chart to visualize the efficient frontier, which shows the trade-off between portfolio return and risk. You can also calculate the Sharpe ratio, which measures the excess return of the portfolio per unit of risk. This will help you determine if the optimized portfolio is worth the risk.
Excel provides built-in functions such as COVAR, AVERAGE, and STDEV to calculate expected returns and covariance matrices of asset returns, as well as Solver to perform portfolio optimization. Additionally, you can use Excel's charting tools to create visual representations of the efficient frontier and other portfolio metrics.