Multi-Period Optimization of Portfolio Transitions: Incorporating Short-Term Alpha Signals and Practical Constraints

Abstract

This thesis develops a multi–period portfolio optimization framework that integrates short–term alpha signals with practical trading constraints, including market impact and deviation risk. By transforming the problem from portfolio–space variables to impact–space variables, our model captures the primary trade–off between harnessing alpha and mitigating market impact, while a risk penalty is imposed to ensure adherence to a target portfolio. After deriving the foundational objective function, the framework is enhanced through the incorporation of multiple alpha signals with distinct decay profiles and Monte Carlo simulations to account for forecast uncertainty. Comprehensive performance evaluations are conducted using an array of benchmarks—including linear trading, all–at–once execution, and half–at–midpoint trading—across metrics such as final wealth, cumulative return, volatility, maximum drawdown, turnover, tracking error, and implementation shortfall. The approach is further extended to multi–asset portfolios, where outcomes are compared across varying levels of stock correlation. Our results demonstrate that, despite the optimized trade schedule often resembling a nearly linear strategy, subtle deviations to exploit alpha allow for meaningful improvements in risk–adjusted performance. This work contributes both theoretical insights and practical tools for managing portfolio transitions in the presence of realistic market frictions and dynamic return forecasts, offering a pathway for future research into more complex cross–asset dynamics and nonlinear impact functions.