The Average Investment Performance Index

In this paper, which is the first step in our efforts to produce an objective standard for use in measuring the investment performance of any portfolio of securities over some period of time, we introduce the average investment performance index (AIPI). The AIPI measures the average return which could have been realized during a particular time period from some specified universe of securities. Our reasons for constructing the AIPI are presented in Section I, where we also formally define the AIPI and discuss the random portfolios which conceptually underlie it. Section II is a mathematical development of the AIPI's properties. We find that the AIPI is equivalent to an unweighted arithmetic average of all actual returns in the given universe of securities, we show how to compute the variance of returns from all possible random portfolios, and we develop a method for linking the values of the AIPI across successive time periods. The use of the AIPI and the variance of random portfolio returns for rating the investment results achieved by portfolio managers is discussed and illustrated in Section III. We feel that the objective evaluations which are the basis of our illustrations should allow the reader to assess the applicability and implications of using the AIPI as a measure of investment performance.