Diversifying Investments and Maximizing Sharpe Ratio: a novel QUBO formulation

• URL: http://arxiv.org/abs/2302.12291v2
• Date: Thu, 22 Feb 2024 13:19:08 GMT
• Title: Diversifying Investments and Maximizing Sharpe Ratio: a novel QUBO formulation
• Authors: Mirko Mattesi, Luca Asproni, Christian Mattia, Simone Tufano, Giacomo Ranieri, Davide Caputo and Davide Corbelletto
• Abstract summary: We propose a new QUBO formulation for the task described and provide the mathematical details and required assumptions. We derive results via the available QUBO solvers, as well as discussing the behaviour of Hybrid approaches to tackle large scale problems in the term.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Portfolio Optimization task has long been studied in the Financial Services literature as a procedure to identify the basket of assets that satisfy desired conditions on the expected return and the associated risk. A well-known approach to tackle this task is the maximization of the Sharpe Ratio, achievable with a problem reformulation as Quadratic Programming. While the sole Sharpe Ratio could be efficiently optimized via classical solvers, in business scenarios it is common that multiple additional needs arise, which have to be integrated in the optimization model as either new constraints or objective function terms. Then, in general, the problem may become non-convex and hence could potentially be not efficiently solvable via classical techniques anymore. One example of such additional objective function term consists of maximizing a diversification measure penalizing portfolios holding significant portions of investments on assets belonging to the same sector, while favouring solutions that diversify over multiple sectors. The problem of optimizing both the Sharpe Ratio and a diversification term can be mapped to a QUBO and be solved via quantum annealing devices or Hybrid Computing approaches, which are expected to find high quality solutions. We propose a new QUBO formulation for the task described and provide the mathematical details and required assumptions, showing the ease of modeling the optimization as QUBO against the effort that would be required by classical strategies. We derive results via the available QUBO solvers, as well as discussing the behaviour of Hybrid approaches to tackle large scale problems in the near term. We finally elaborate on the results showing the trade-off between the observed values of the portfolio's Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem.

Related papers

• A Novel Knapsack-based Financial Portfolio Optimization using Quantum Approximate Optimization Algorithm [2.6603181502541986]
  We propose a method that uses the quantum computing capabilities of the quantum walk mixer with the quantum approximate optimization algorithm (QAOA) to address the challenges presented by the NP-hard problem. Our study successfully achieves the approximate ratio of the portfolio optimization technique using a circuit layer of p >= 3, compared to the classical best-known solution of the knapsack problem.
  arXiv  Detail & Related papers  (2024-02-11T08:20:26Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization [59.758009422067]
  We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. We propose a new uncertainty Bellman equation (UBE) whose solution converges to the true posterior variance over values. We introduce a general-purpose policy optimization algorithm, Q-Uncertainty Soft Actor-Critic (QU-SAC) that can be applied for either risk-seeking or risk-averse policy optimization.
  arXiv  Detail & Related papers  (2023-12-07T15:55:58Z)
• Approaching Collateral Optimization for NISQ and Quantum-Inspired Computing [0.0]
  Collateral optimization refers to the systematic allocation of financial assets to satisfy obligations or secure transactions. One of the common objectives is to minimise the cost of collateral required to mitigate the risk associated with a particular transaction or a portfolio of transactions.
  arXiv  Detail & Related papers  (2023-05-25T18:01:04Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• A hybrid level-based learning swarm algorithm with mutation operator for solving large-scale cardinality-constrained portfolio optimization problems [0.0]
  We propose a hybrid variant of the level-based learning swarm (LLSO) for solving large-scale portfolio optimization problems. Our goal is to maximize a modified formulation of the Sharpe ratio subject to cardinality, box and budget constraints. The algorithm involves a projection operator to deal with these three constraints simultaneously and we implicitly control transaction costs thanks to a rebalancing constraint.
  arXiv  Detail & Related papers  (2022-06-29T16:45:37Z)
• Algorithm for Constrained Markov Decision Process with Linear Convergence [55.41644538483948]
  An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs. A new dual approach is proposed with the integration of two ingredients: entropy regularized policy and Vaidya's dual. The proposed approach is shown to converge (with linear rate) to the global optimum.
  arXiv  Detail & Related papers  (2022-06-03T16:26:38Z)
• Comparing Classical-Quantum Portfolio Optimization with Enhanced Constraints [0.0]
  We show how to add fundamental analysis to the portfolio optimization problem, adding in asset-specific and global constraints based on chosen balance sheet metrics. We analyze the current state-of-the-art algorithms for solving such a problem using D-Wave's Quantum Processor and compare the quality of the solutions obtained to commercially-available optimization software.
  arXiv  Detail & Related papers  (2022-03-09T17:46:32Z)
• Learning Proximal Operators to Discover Multiple Optima [66.98045013486794]
  We present an end-to-end method to learn the proximal operator across non-family problems. We show that for weakly-ized objectives and under mild conditions, the method converges globally.
  arXiv  Detail & Related papers  (2022-01-28T05:53:28Z)
• Dynamic Asset Allocation with Expected Shortfall via Quantum Annealing [0.0]
  We propose a hybrid quantum-classical algorithm to solve a dynamic asset allocation problem. We compare the results from D-Wave's 2000Q and Advantage quantum annealers using real-world financial data. Experiments on assets with higher correlations tend to perform better, which may help to design practical quantum applications in the near term.
  arXiv  Detail & Related papers  (2021-12-06T17:39:43Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.