Abstract The positive relationship between money flows into investment products and their return performance is an important market indicator for market practitioners and academics. This article studies the impact that active versus passive investment styles have on this relationship. We further evaluate the effects of a passive approach in two crucial stages: portfolio selection and asset allocation. We find that a passive investment style in either stage weakens the relationship between flows and returns compared with an active style. However, the investment style in the asset allocation stage has a greater effect than in the portfolio selection stage, on the relationship between flows and returns.

An agent is asked to assess a real-valued variable Yp based on certain characteristics Xp = (Xp1, …, Xpm), and on a database consisting of Xi1, … Xim, Yi) for i = 1, …, n. A possible approach to combine past observations of X and Y with the current values of X to generate an assessment of Y is similarity-weighted averaging. It suggests that the predicted value of Y, Ȳps, be the weighted average of all previously observed values Yi, where the weight of Yi for every i = 1, …, n, is the similarity between the vector Xp1, …, Xpm, associated with Yp, and the previously observed vector, Xi1, …, Xim. We axiomatize this rule. We assume that, given every database, a predictor has a ranking over possible values, and we show that certain reasonable conditions on these rankings imply that they are determined by the proximity to a similarity-weighted average for a certain similarity function. The axiomatization does not suggest a particular similarity function, or even a particular form of this function. We therefore proceed to suggest that the similarity function be estimated from past observations.We develop tools of statistical inference for parametric estimation of the similarity function, for the case of a continuous as well as a discrete variable. Finally, we discuss the relationship of the proposed method to other methods of estimation and prediction.