Continuous Portfolio Model and Performance Decomposition

Despite a rich academic literature dedicated to mutual fund performance, the question of the portfolio manager added value remains subject to discussion. The debate between active and passive investing is expected to last while there is no consensus on the appropriate measure for evaluating a portfolio manager. Proposed performance measures are based on partial representation of a portfolio, they neglect part of the available information such as some improvements are likely to be achieved.A complete representation of a mutual fund is complex. For the sake of simplicity, a fund is often described by the consideration of its attributes: the asset allocation, the fund total asset under management, the share net asset value. This decomposition is convenient because each of the fund elements can be managed independently from the others. But it neglects an important part of the fund information: the dynamic coming from trade executions and investor flows. The goal of this paper is to propose a framework ensuring a complete and exact representation of portfolio such that accurate performance measures can be proposed.We depart from the fund accounting representation to further develop a model including internal valuation and centralization processes. The explicit simulation of an only share allows us to measure the contribution of any strategy to the fund net asset value. We then seek to characterize the performance and propose a decomposition of performance in static and dynamic effects; the latter provides a measure of market timing ability. Finally, we provide an empirical application with the simulation of a real fund and the decomposition of its performances