Maximize Adjusted R2
In this model, the utility function is the adjusted R2, i.e., StyleADVISOR chooses the subset of indices that gives the highest adjusted R2. Recall that the adjusted R2 is defined as follows:
Adjusted R2 = 1 - ((m - 1) / (m - n)) * (Var(e) / Var(M))
Var(M) = variance of manager returns
Var(e) = variance of excess return of manager over benchmark, using current subset
n = number of indices in current subset
m = number of returns
Again, the workbook Models.zsa provides an example. On the page named "Standard Model," the adjusted R2 as seen in the right hand style table is 88.68. On the page named "Adjusted R2 Model," the adjusted R2 has increased to 88.74. That is why StyleADVISOR chose to drop the Russell 1000 Value index in this model.