Dynamics and Performance of Decentralized Portfolios with Size-Induced Fund Flows

We examine the implications of fund sizes for portfolio dynamics and performance

within a decentralized structure, where the chief investment officer

optimally allocates capital to two fund managers who invest in multiple

assets within their own asset classes. The managers experience fund

inflows/outflows depending on not only their investment performances but

also their fund sizes that are mainly driven by their optimal portfolios. We

characterize these practical features through a two-layer dynamic optimization

model where the managers maximize their size-dependent compensations.

We solve the highly path-dependent optimization problem using a

simulation-projection method with a multidimensional grid search and policy

iteration. Our analysis provides new interpretations on the controversial scale effects on fund performance, along with insights into portfolio dynamics

and management fees for bond funds and stock funds under different fund

ages.