A new decomposition of portfolio return

TL;DR

This paper extends the decomposition of relative log-return in functionally generated portfolios to arbitrary portfolios using Fisk-Stratonovich integration, representing the generating function as a structural process and the drift as a trading process.

Contribution

It introduces a novel extension of portfolio return decomposition applicable to all stock portfolios via Fisk-Stratonovich integration.

Findings

Decomposition applies to arbitrary portfolios.

Generating function represented by a structural process.

Drift process incorporated into a trading profit and loss measure.

Abstract

For a functionally generated portfolio, there is a natural decomposition of the relative log-return into the log-change in the generating function and a drift process. In this note, this decomposition is extended to arbitrary stock portfolios by an application of Fisk-Stratonovich integration. With the extended methodology, the generating function is represented by a structural process, and the drift process is subsumed into a trading process that measures the profit and loss to the portfolio from trading.