Transaction Costs

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. ...

Optimal two-parameter portfolio management strategy with transaction costs ArXiv ID: 2411.07949 “View on arXiv” Authors: Unknown Abstract We consider a simplified model for optimizing a single-asset portfolio in the presence of transaction costs given a signal with a certain autocorrelation and cross-correlation structure. In our setup, the portfolio manager is given two one-parameter controls to influence the construction of the portfolio. The first is a linear filtering parameter that may increase or decrease the level of autocorrelation in the signal. The second is a numerical threshold that determines a symmetric “no-trade” zone. Portfolio positions are constrained to a single unit long or a single unit short. These constraints allow us to focus on the interplay between the signal filtering mechanism and the hysteresis introduced by the “no-trade” zone. We then formulate an optimization problem where we aim to minimize the frequency of trades subject to a fixed return level of the portfolio. We show that maintaining a no-trade zone while removing autocorrelation entirely from the signal yields a locally optimal solution. For any given “no-trade” zone threshold, this locally optimal solution also achieves the maximum attainable return level, and we derive a quantitative lower bound for the amount of improvement in terms of the given threshold and the amount of autocorrelation removed. ...

On Cost-Sensitive Distributionally Robust Log-Optimal Portfolio ArXiv ID: 2410.23536 “View on arXiv” Authors: Unknown Abstract This paper addresses a novel \emph{“cost-sensitive”} distributionally robust log-optimal portfolio problem, where the investor faces \emph{“ambiguous”} return distributions, and a general convex transaction cost model is incorporated. The uncertainty in the return distribution is quantified using the \emph{“Wasserstein”} metric, which captures distributional ambiguity. We establish conditions that ensure robustly survivable trades for all distributions in the Wasserstein ball under convex transaction costs. By leveraging duality theory, we approximate the infinite-dimensional distributionally robust optimization problem with a finite convex program, enabling computational tractability for mid-sized portfolios. Empirical studies using S&P 500 data validate our theoretical framework: without transaction costs, the optimal portfolio converges to an equal-weighted allocation, while with transaction costs, the portfolio shifts slightly towards the risk-free asset, reflecting the trade-off between cost considerations and optimal allocation. ...

Optimal execution with deterministically time varying liquidity: well posedness and price manipulation ArXiv ID: 2410.04867 “View on arXiv” Authors: Unknown Abstract We investigate the well-posedness in the Hadamard sense and the absence of price manipulation in the optimal execution problem within the Almgren-Chriss framework, where the temporary and permanent impact parameters vary deterministically over time. We present sufficient conditions for the existence of a unique solution and provide second-order conditions for the problem, with a particular focus on scenarios where impact parameters change monotonically over time. Additionally, we establish conditions to prevent transaction-triggered price manipulation in the optimal solution, i.e. the occurence of buying and selling in the same trading program. Our findings are supported by numerical analyses that explore various regimes in simple parametric settings for the dynamics of impact parameters. ...

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. ...

Hedging in Jump Diffusion Model with Transaction Costs ArXiv ID: 2408.10785 “View on arXiv” Authors: Unknown Abstract We consider the jump-diffusion risky asset model and study its conditional prediction laws. Next, we explain the conditional least square hedging strategy and calculate its closed form for the jump-diffusion model, considering the Black-Scholes framework with interpretations related to investor priorities and transaction costs. We investigate the explicit form of this result for the particular case of the European call option under transaction costs and formulate recursive hedging strategies. Finally, we present a decision tree, table of values, and figures to support our results. ...

Portfolio optimisation: bridging the gap between theory and practice ArXiv ID: 2407.00887 “View on arXiv” Authors: Unknown Abstract Portfolio optimisation is essential in quantitative investing, but its implementation faces several practical difficulties. One particular challenge is converting optimal portfolio weights into real-life trades in the presence of realistic features, such as transaction costs and integral lots. This is especially important in automated trading, where the entire process happens without human intervention. Several works in literature have extended portfolio optimisation models to account for these features. In this paper, we highlight and illustrate difficulties faced when employing the existing literature in a practical setting, such as computational intractability, numerical imprecision and modelling trade-offs. We then propose a two-stage framework as an alternative approach to address this issue. Its goal is to optimise portfolio weights in the first stage and to generate realistic trades in the second. Through extensive computational experiments, we show that our approach not only mitigates the difficulties discussed above but also can be successfully employed in a realistic scenario. By splitting the problem in two, we are able to incorporate new features without adding too much complexity to any single model. With this in mind we model two novel features that are critical to many investment strategies: first, we integrate two classes of assets, futures contracts and equities, into a single framework, with an example illustrating how this can help portfolio managers in enhancing investment strategies. Second, we account for borrowing costs in short positions, which have so far been neglected in literature but which significantly impact profits in long/short strategies. Even with these new features, our two-stage approach still effectively converts optimal portfolios into actionable trades. ...

Asymptotic methods for transaction costs ArXiv ID: 2407.07100 “View on arXiv” Authors: Unknown Abstract We propose a general approximation method for determining optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems from optimally tracking benchmarks, hedging the Log contract, to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between trading frequency and trade sizes to have satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity. ...

Application of Deep Learning for Factor Timing in Asset Management ArXiv ID: 2404.18017 “View on arXiv” Authors: Unknown Abstract The paper examines the performance of regression models (OLS linear regression, Ridge regression, Random Forest, and Fully-connected Neural Network) on the prediction of CMA (Conservative Minus Aggressive) factor premium and the performance of factor timing investment with them. Out-of-sample R-squared shows that more flexible models have better performance in explaining the variance in factor premium of the unseen period, and the back testing affirms that the factor timing based on more flexible models tends to over perform the ones with linear models. However, for flexible models like neural networks, the optimal weights based on their prediction tend to be unstable, which can lead to high transaction costs and market impacts. We verify that tilting down the rebalance frequency according to the historical optimal rebalancing scheme can help reduce the transaction costs. ...

A Note on Optimal Liquidation with Linear Price Impact ArXiv ID: 2402.14100 “View on arXiv” Authors: Unknown Abstract In this note we consider the maximization of the expected terminal wealth for the setup of quadratic transaction costs. First, we provide a very simple probabilistic solution to the problem. Although the problem was largely studied, as far as we know up to date this simple and probabilistic form of the solution has not appeared in the literature. Next, we apply the general result for the numerical study of the case where the risky asset is given by a fractional Brownian Motion and the information flow of the investor can be diversified. ...