Corresponding to my "Dollar Cost Averaging Risk" article, in a 2014 Society of Actuaries publication. Please download the spreadsheet.
Background
There are two spreadsheets (Theoretical, and Simulations).
Per paper, enter 3 assumptions in green, on the 2nd row of Theoretical spreadhseet.
The red data on the left is the traditional declining-balance method.
The blue data on the left is the proposed incremental-time method.
The two yellow left-side risk (from the fixed σ approach), on both the Theoretical, and Simulations tabs, all agree.
The right-side of both spreadsheets shows the mathematics of the varying σ approach.