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Portfolio Performance Measurement: Theory and Applications

By Peter J. Knez and Zhiwu Chen

Abstract

Any admissible portfolio performance measure should satisfy four minimal conditions: it assigns zero performance to each reference portfolio and it is linear, continuous and nontribial. Such an admissible measure exists if and only if the securities market obeys the law of one price. A positive admissible measure exists if and only if there is not arbitrage. This paper characterizes the (infinite) set of admissible performance measures. It is shown that performance evaluation is generally quite arbitrary. A mutual fund data set is also used to demonstrate how the measurement method developed here can be applied.

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