Optimization Solutions - Investment Examples

Investment Examples

This free Investment Examples workbook contains eight example models from the area of investment and portfolio management.  In nearly any browser, you can click the links below to display each worksheet model in the browser area.  Click the Back button to return to this page, or visit the Solver.com Home Page.

You can use the worksheet that most closely models your situation as a starting point.  Solving your real problem may require "scaling up" the model to include more variables and constraints -- but rest assured that you can solve your full-size problem with the power of our Excel Solver upgrades, even if it requires hundreds of thousands of variables!

To download and save the workbook, right-click Investment Examples and select Save Target As... from the context menu.  You can then actually solve these small example models in Microsoft Excel, using either the standard Excel Solver or the Premium Solver or Premium Solver Platform.

• Theory - Display this worksheet for a brief discussion of the theory of efficient portfolios and the principles of duration matching in bond portfolios
• Markowitz - Portfolio Optimization - Markowitz Model:  Allocate funds to stocks to minimize risk for a target rate of return - assumes that variances and covariances are known
• Full Markowitz - Portfolio Optimization - Markowitz Model:  Allocate funds to stocks to minimize risk for a target rate of return - calculates variances and covariances from historical stock prices
• Efficient Frontier - Stock Portfolio Management:  Uses a VBA program to optimize several scenarios for minimum risk at different target rates of return, then draws a graph of the efficient frontier
• Sharpe - Portfolio Optimization - Sharpe Model (CAPM):  Uses Excel's regression functions to calculate alphas and betas for stocks relative to a market index, then uses these to find an efficient portfolio.
• Bond1 and Bond2 - Bond Portfolio Management:  Allocate funds to bonds to maximize return while ensuring that the portfolio duration equals the investment horizon for maturity - Bond1 assumes that bond durations are known, Bond2 calculates bond durations from yields, coupons and face values
• Bond3 and Bond4 - Bond Portfolio Exact Matching:  Allocate funds to bonds to maximize portfolio return while ensuring that periodic liabilities (cash outflows) are met - Bond3 uses bond coupons alone, Bond4 allows for reinvestment of interest in excess of periodic liabilities

On each example worksheet, read the description at the bottom, then select Tools Solver... to examine the decision variables, constraints, and objective in the Solver Parameters dialog.  To find the optimal solution, click the Solve button.

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