Active Portfolio Management in Concentrated Equity Markets

2026-09-22

AI Summary

本文通过构建并求解基于随机多样性-分散模型的随机控制问题，提出一种在等权重和市场组合间动态分配的投资策略，以应对集中市场下的表现不佳问题。

Abstract

The equal-weighted portfolio is a passive, rule-based strategy that has historically been difficult to outperform, delivering higher returns than the capitalization-weighted "market" benchmark across many markets and periods. Stochastic portfolio theory (SPT) reveals that this relative performance is regime dependent, with the equal-weighted portfolio underperforming during periods of increasing market concentration and high correlations, particularly market bubbles. These observations have motivated us to formulate and solve a stochastic control problem in which an investor actively allocates between the equal-weighted and market portfolios. The investor bases their allocation decisions on forecasts made under a flexible stochastic diversity--dispersion (SDD) model. Using a quadratic surrogate for implementation frictions, we characterize the optimal allocation through a linear forward--backward SDE and obtain an explicit "aiming in front of a moving target'' representation of the optimal trading rate, in the spirit of Gârleanu and Pedersen. The penalty parameters are calibrated in sample to match the cumulative wealth effect of proportional transaction costs, while out-of-sample performance is evaluated with those costs deducted directly from portfolio wealth. Using historical S&P 500 data, we show that a mean-reverting SDD specification reproduces several empirical features of market diversity and dispersion. In out-of-sample backtests from 1995 to 2024, the resulting strategies deliver higher cumulative net returns than both the equal-weighted and market portfolios, and higher information ratios than the equal-weighted portfolio after 15-basis-point proportional transaction costs.

Problem

• Active Portfolio Management
• Concentrated Equity Markets
• Equal-Weighted Portfolio
• Market Concentration
• Stochastic Portfolio Theory

Innovation

• stochastic portfolio theory
• stochastic diversity--dispersion model
• forward--backward SDE
• active allocation
• mean-reverting SDD