发表机构
University of Toronto（多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对集中股票市场，提出基于随机多样性-离散度模型的主动配置策略，通过随机控制求解最优交易率，在S&P 500样本外回测中超越等权重和市场组合。
AI 中文摘要
等权重投资组合是一种被动的、基于规则的策略，历史上很难被超越，在许多市场和时期都提供了比市值加权“市场”基准更高的回报。随机投资组合理论（SPT）揭示了这种相对表现是依赖于体制的，等权重投资组合在市场集中度上升和高相关性时期（尤其是市场泡沫时期）表现不佳。这些观察促使我们制定并求解一个随机控制问题，在该问题中，投资者在等权重投资组合和市场投资组合之间进行主动配置。投资者的配置决策基于在灵活的随机多样性-离散度（SDD）模型下做出的预测。使用二次替代函数来表示实施摩擦，我们通过线性前向-后向随机微分方程刻画了最优配置，并获得了最优交易率的显式“瞄准移动目标前方”表示，这一思路借鉴了Gârleanu和Pedersen的工作。惩罚参数在样本内进行校准，以匹配比例交易成本的累积财富效应，而样本外表现则通过直接从投资组合财富中扣除这些成本来评估。使用历史标准普尔500指数数据，我们表明均值回归的SDD设定重现了市场多样性和离散度的几个经验特征。在1995年至2024年的样本外回测中，所得策略产生的累计净回报高于等权重投资组合和市场投资组合，并且在15个基点的比例交易成本后，信息比率高于等权重投资组合。
英文摘要
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.
Comments31 pages, 11 figures
