Active Allocation Between Equal-Weighted and Market Portfolios
Summary
This document describes an active strategy that shifts allocation between equal-weighted and capitalization-weighted equity portfolios. Its motivation is that equal weighting has often outperformed over long periods, but can lag when market concentration and correlations rise. Stochastic portfolio theory frames this regime dependence, while a stochastic diversity-dispersion model supplies forecasts for portfolio allocation decisions.
The proposed control method uses a quadratic approximation to trading frictions. It characterizes the optimal trading rate through a linear forward-backward stochastic differential equation, with a rule that anticipates a changing target. The study calibrates penalty parameters in sample and evaluates historical S&P 500 strategies out of sample from 1995 to 2024, deducting proportional costs. It reports higher cumulative net returns than either reference portfolio and higher information ratios than equal weighting after the stated transaction costs. These findings are specific to the model, data, calibration and historical period; they do not establish future performance.
Key ideas
- Equal weighting can lag the capitalization-weighted portfolio when concentration and correlations rise.
- The strategy actively reallocates between equal-weighted and market portfolios using forecasts from a diversity-dispersion model.
- A stochastic control formulation accounts for implementation frictions through a quadratic surrogate.
- The reported out-of-sample S&P 500 results include proportional transaction costs.
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Full text
# Active Portfolio Management in Concentrated Equity Markets # Active Portfolio Management in Concentrated Equity Markets 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.
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