Partitioning transaction vectors into pure investments

摘要

A pure investment is defined here as any transaction where the invested capital is nonnegative at all times during the life of the transaction. This article proves that any transaction whose first non-zero term is negative can be uniquely partitioned into pure investments with strictly decreasing internal rates of return (IRRs). The IRRs of the partitioning transactions put bounds on the IRRs of the original transaction. The partitioning theorem gives a simple characterisation of Arrow/Levhari's results on the optimal truncation of a transaction. The partitioning theorem also has applications to the problem of the optimal time for an investor to sell the remaining terms in a transaction.