Instructions for Reverse Optimization Worksheet

Inputs

The Inputs box should contain all the needed input information other than the expected returns for two asset classes. Each row provides the inputs for a single decision variable (for example, an asset class). The columns must be in the order indicated below. Each must be given a short heading, although these are not actually checked for content.

The first column indicates the proportions invested in the assets for a portfolio that is assumed to be efficient -- that is, to maximize utility for some risk tolerance. These proportions will usually sum to 1.0 although this is not necessary.

The next column provides the Standard Deviations (StdDev) for the decision variables. These are usually stated in terms of return per year (for example, 10.5 for 10.5% per year). The remaining columns provide the Correlation Coefficients for the variables. The order must be the same as that used for the rows in the table.

The other input boxes provides the Expected Returns for two selected asset classes (decision variables). Any two may be chosen and the expected returns must differ.

You may choose either of two output formats. The first provides only the computed expected returns. The second provides all the information in the format used for inputs in the optimization worksheet.

Algorithm

The worksheet uses the method described in Sharpe [ "Imputing Expected Returns From Portfolio Composition", Journal of Financial and Quantitative Analysis, June 1974, pp. 463-472 ] to find a full set of expected returns compatible with the inputs. If a unique solution cannot be obtained, an error message is shown.

Output

The major outputs are provided in a single box. A separate box shows the risk tolerance for which the given portfolio is optimal.

Notes

You may enter any desired text in this box to describe the source of the input data, etc...