This thesis by Alexander Fadeev explores the optimization of trading strategies for complex portfolio transitions, particularly in the context of institutional investors rebalancing their portfolios or transitioning between asset managers. The costs associated with these transitions include trading costs (transaction and market impact), opportunity costs, and the risk of divergence between the current and target portfolios. The thesis proposes a methodology to measure and minimize the opportunity cost through optimal portfolio transition execution (OPT). The research is grounded in existing portfolio trading literature and draws inspiration from Mark Kritzman, Simon Myrgren, and Sébastien Page's work on "Optimal Execution for Portfolio Transitions." The proposed OPT method aims to minimize tracking error by optimizing the sequence and size of trades, focusing on reducing the value deviation between the legacy and target portfolios rather than absolute performance. The thesis includes a detailed review of portfolio trading research, a description of the OPT methodology, and a numerical analysis of its implementation. The OPT method is benchmarked against industry-standard practices, and its performance is evaluated through simulations and real-world data from a $1 billion portfolio. The results show that the OPT method consistently outperforms the baseline method in reducing tracking error, with an average improvement of 59.26%. The thesis concludes by discussing the practical implications of the OPT method, its computational efficiency, and potential future research directions, including calibrating and optimizing the current model and extending it to incorporate market impact estimation. The OPT method is found to be effective for portfolios up to 1,000 assets but may face computational challenges for larger portfolios.This thesis by Alexander Fadeev explores the optimization of trading strategies for complex portfolio transitions, particularly in the context of institutional investors rebalancing their portfolios or transitioning between asset managers. The costs associated with these transitions include trading costs (transaction and market impact), opportunity costs, and the risk of divergence between the current and target portfolios. The thesis proposes a methodology to measure and minimize the opportunity cost through optimal portfolio transition execution (OPT). The research is grounded in existing portfolio trading literature and draws inspiration from Mark Kritzman, Simon Myrgren, and Sébastien Page's work on "Optimal Execution for Portfolio Transitions." The proposed OPT method aims to minimize tracking error by optimizing the sequence and size of trades, focusing on reducing the value deviation between the legacy and target portfolios rather than absolute performance. The thesis includes a detailed review of portfolio trading research, a description of the OPT methodology, and a numerical analysis of its implementation. The OPT method is benchmarked against industry-standard practices, and its performance is evaluated through simulations and real-world data from a $1 billion portfolio. The results show that the OPT method consistently outperforms the baseline method in reducing tracking error, with an average improvement of 59.26%. The thesis concludes by discussing the practical implications of the OPT method, its computational efficiency, and potential future research directions, including calibrating and optimizing the current model and extending it to incorporate market impact estimation. The OPT method is found to be effective for portfolios up to 1,000 assets but may face computational challenges for larger portfolios.