A portfolio-analysis tool receives data that describe an actual portfolio.
It computes from those data the returns or other performance measures of
hypothetical portfolios whose holdings are drawn from the assets that the
actual portfolio held during some period. Among the purposes of doing so
is to detect biases made in investment-portfolio actions of the type
taken, for instance, to accommodate cash inflows and withdrawals. For
that purpose, differences between the hypothetical portfolio and the
actual portfolio are so made as to offset portfolio actions identified by
finding differences between the weights that positions actually exhibit
and the weights they would result from return only. Returns for the
hypothetical portfolio are computed by calculating an offset return
incrementally, one such offset at a time, and then computing the
hypothetical portfolio's return as the sum of quantities proportional to
the offset return and that of the actual portfolio.