Portfolio Rebalancing

Non-conservative optimal transport ArXiv ID: 2510.03332 “View on arXiv” Authors: Gabriela Kováčová, Georg Menz, Niket Patel Abstract Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation or destruction of mass. We discuss applications and position the framework alongside unbalanced, entropic, and unnormalized optimal transport. The existence of optimal transport plans and strong duality are established. The existence of optimal maps are deduced in two central regimes, i.e., perturbative mass-change and quadratic mass-loss. For $\ell_p$ costs we derive the analogue of the Benamou-Brenier dynamic formulation. ...

Cost-aware Portfolios in a Large Universe of Assets ArXiv ID: 2412.11575 “View on arXiv” Authors: Unknown Abstract This paper considers the finite horizon portfolio rebalancing problem in terms of mean-variance optimization, where decisions are made based on current information on asset returns and transaction costs. The study’s novelty is that the transaction costs are integrated within the optimization problem in a high-dimensional portfolio setting where the number of assets is larger than the sample size. We propose portfolio construction and rebalancing models with nonconvex penalty considering two types of transaction cost, the proportional transaction cost and the quadratic transaction cost. We establish the desired theoretical properties under mild regularity conditions. Monte Carlo simulations and empirical studies using S&P 500 and Russell 2000 stocks show the satisfactory performance of the proposed portfolio and highlight the importance of involving the transaction costs when rebalancing a portfolio. ...

Dynamic Portfolio Rebalancing: A Hybrid new Model Using GNNs and Pathfinding for Cost Efficiency ArXiv ID: 2410.01864 “View on arXiv” Authors: Unknown Abstract This paper introduces a novel approach to optimizing portfolio rebalancing by integrating Graph Neural Networks (GNNs) for predicting transaction costs and Dijkstra’s algorithm for identifying cost-efficient rebalancing paths. Using historical stock data from prominent technology firms, the GNN is trained to forecast future transaction costs, which are then applied as edge weights in a financial asset graph. Dijkstra’s algorithm is used to find the least costly path for reallocating capital between assets. Empirical results show that this hybrid approach significantly reduces transaction costs, offering a powerful tool for portfolio managers, especially in high-frequency trading environments. This methodology demonstrates the potential of combining advanced machine learning techniques with classical optimization algorithms to improve financial decision-making processes. Future research will explore expanding the asset universe and incorporating reinforcement learning for continuous portfolio optimization. ...

Decomposition Pipeline for Large-Scale Portfolio Optimization with Applications to Near-Term Quantum Computing ArXiv ID: 2409.10301 “View on arXiv” Authors: Unknown Abstract Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline targeting portfolio optimization and rebalancing problems with constraints. The pipeline decomposes the optimization problem into constrained subproblems, which are then solved separately and aggregated to give a final result. Our pipeline includes three main components: preprocessing of correlation matrices based on random matrix theory, modified spectral clustering based on Newman’s algorithm, and risk rebalancing. Our empirical results show that our pipeline consistently decomposes real-world portfolio optimization problems into subproblems with a size reduction of approximately 80%. Since subproblems are then solved independently, our pipeline drastically reduces the total computation time for state-of-the-art solvers. Moreover, by decomposing large problems into several smaller subproblems, the pipeline enables the use of near-term quantum devices as solvers, providing a path toward practical utility of quantum computers in portfolio optimization. ...

To Trade Or Not To Trade: Cascading Waterfall Round Robin Rebalancing Mechanism for Cryptocurrencies ArXiv ID: 2407.12150 “View on arXiv” Authors: Unknown Abstract We have designed an innovative portfolio rebalancing mechanism termed the Cascading Waterfall Round Robin Mechanism. This algorithmic approach recommends an ideal size and number of trades for each asset during the periodic rebalancing process, factoring in the gas fee and slippage. The essence of the model we have created gives indications regarding whether trades should be made on individual assets depending on the uncertainty in the micro - asset level characteristics - and macro - aggregate market factors - environments. In the hyper-volatile crypto market, our approach to daily rebalancing will benefit from volatility. Price movements will cause our algorithm to buy assets that drop in prices and sell as they soar. In fact, the buying and selling happen only when certain boundaries are crossed in order to weed out any market noise and ensure sound trade execution. We have provided several numerical examples to illustrate the steps - including the calculation of several intermediate variables - of our rebalancing mechanism. The Algorithm we have developed can be easily applied outside blockchain to investment funds across all asset classes at any trading frequency and rebalancing duration. Shakespeare As A Crypto Trader: To Trade Or Not To Trade, that is the Question, Whether an Optimizer can Yield the Answer, Against the Spikes and Crashes of Markets Gone Wild, To Quench One’s Thirst before Liquidity Runs Dry, Or Wait till the Tide of Momentum turns Mild. ...

Optimal Rebalancing in Dynamic AMMs ArXiv ID: 2403.18737 “View on arXiv” Authors: Unknown Abstract Dynamic AMM pools, as found in Temporal Function Market Making, rebalance their holdings to a new desired ratio (e.g. moving from being 50-50 between two assets to being 90-10 in favour of one of them) by introducing an arbitrage opportunity that disappears when their holdings are in line with their target. Structuring this arbitrage opportunity reduces to the problem of choosing the sequence of portfolio weights the pool exposes to the market via its trading function. Linear interpolation from start weights to end weights has been used to reduce the cost paid by pools to arbitrageurs to rebalance. Here we obtain the $\textit{“optimal”}$ interpolation in the limit of small weight changes (which has the downside of requiring a call to a transcendental function) and then obtain a cheap-to-compute approximation to that optimal approach that gives almost the same performance improvement. We then demonstrate this method on a range of market backtests, including simulating pool performance when trading fees are present, finding that the new approximately-optimal method of changing weights gives robust increases in pool performance. For a BTC-ETH-DAI pool from July 2022 to June 2023, the increases of pool P&L from approximately-optimal weight changes is $\sim25%$ for a range of different strategies and trading fees. ...

Planning for the Efficient Updating of Mutual Fund Portfolios ArXiv ID: 2311.16204 “View on arXiv” Authors: Unknown Abstract Once there is a decision of rebalancing or updating a portfolio of funds, the process of changing the current portfolio to the target one, involves a set of transactions that are susceptible of being optimized. This is particularly relevant when managers have to handle the implications of different types of instruments. In this work we present linear programming and heuristic search approaches that produce plans for executing the update. The evaluation of our proposals shows cost improvements over the compared based strategy. The models can be easily extended to other realistic scenarios in which a holistic portfolio management is required ...

A Portfolio Rebalancing Approach for the Indian Stock Market ArXiv ID: 2310.09770 “View on arXiv” Authors: Unknown Abstract This chapter presents a calendar rebalancing approach to portfolios of stocks in the Indian stock market. Ten important sectors of the Indian economy are first selected. For each of these sectors, the top ten stocks are identified based on their free-float market capitalization values. Using the ten stocks in each sector, a sector-specific portfolio is designed. In this study, the historical stock prices are used from January 4, 2021, to September 20, 2023 (NSE Website). The portfolios are designed based on the training data from January 4, 2021 to June 30, 2022. The performances of the portfolios are tested over the period from July 1, 2022, to September 20, 2023. The calendar rebalancing approach presented in the chapter is based on a yearly rebalancing method. However, the method presented is perfectly flexible and can be adapted for weekly or monthly rebalancing. The rebalanced portfolios for the ten sectors are analyzed in detail for their performances. The performance results are not only indicative of the relative performances of the sectors over the training (i.e., in-sample) data and test (out-of-sample) data, but they also reflect the overall effectiveness of the proposed portfolio rebalancing approach. ...