How Any Transaction Vector Can Be Uniquely Partitioned into Soper Transactions with Strictly Decreasing IRRs: And Some Consequences
17 Pages Posted: 4 Oct 2015
Date Written: October 2, 2015
A Soper transaction is defined here as any transaction where the invested capital is non-negative at all times during the life of the transaction. This paper proves that any transaction whose first non-zero term is negative can be uniquely partitioned into Soper transactions with strictly decreasing internal rates of return, (IRR). The IRRs of the partitioning transactions put bounds on the IRRs of the original transaction. The partitioning theorem gives a simple characterisation of the truncation points in Hick’s fundamental theorem. The partitioning theorem also has applications to the problem of the optimal time for an investor to sell the remaining terms in a transaction.
Keywords: investment theory, internal rate of return, net present value
JEL Classification: E22, G31, M40
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