We investigate portfolio optimization in financial markets from a trading and risk management perspective. We term this task Risk-Aware Trading Portfolio Optimization (RATPO), formulate the corresponding optimization problem, and propose an efficient Risk-Aware Trading Swarm (RATS) algorithm to solve it. The key elements of RATPO are a generic initial portfolio P, a specific set of Unique Eligible Instruments (UEIs), their combination into an Eligible Optimization Strategy (EOS), an objective function, and a set of constraints. RATS searches for an optimal EOS that, added to P, improves the objective function repecting the constraints.
RATS is a specialized Particle Swarm Optimization method that leverages the parameterization of P in terms of UEIs, enables parallel computation with a large number of particles, and is fully general with respect to specific choices of the key elements, which can be customized to encode financial knowledge and needs of traders and risk managers.
We showcase two RATPO applications involving a real trading portfolio made of hundreds of different financial instruments, an objective function combining both market risk (VaR) and profit&loss measures, constrains on market sensitivities and UEIs trading costs. In the case of small-sized EOS, RATS successfully identifies the optimal solution and demonstrates robustness with respect to hyper-parameters tuning. In the case of large-sized EOS, RATS markedly improves the portfolio objective value, optimizing risk and capital charge while respecting risk limits and preserving expected profits.
Our work bridges the gap between the implementation of effective trading strategies and compliance with stringent regulatory and economic capital requirements, allowing a better alignment of business and risk management objectives.
We use an optimization procedure based on simulated bifurcation (SB) to solve the integer portfolio and trading trajectory problem with an unprecedented computational speed. The underlying algorithm is based on a classical description of quantum adiabatic evolutions of a network of non-linearly interacting oscillators. This formulation has already proven to beat state of the art computation times for other NP-hard problems and is expected to show similar performance for certain portfolio optimization problems. Inspired by such we apply the SB approach to the portfolio integer optimization prob…
Neural Networks for Portfolio-Level Risk Management: Portfolio Compression, Static Hedging, Counterparty Credit Risk Exposures and Impact on Capital Requirement
Shandong University of Finance and Economic（山东财经大学）
This scientific paper propose a novel portfolio optimization model using an improved deep reinforcement learning algorithm. The objective function of the optimization model is the weighted sum of the expectation and value at risk(VaR) of portfolio cumulative return. The proposed algorithm is based on actor-critic architecture, in which the main task of critical network is to learn the distribution of portfolio cumulative return using quantile regression, and actor network outputs the optimal portfolio weight by maximizing the objective function mentioned above. Meanwhile, we exploit a linear t…
Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework that uses only simulations of returns for estimating risk budgeting portfolios. Besides a general cutting planes algorithm for determining the weights of risk budgeting portfolios for arbitrary coherent distortion risk measures, we provide a specialised version for the Expected Shortfall, and a tailored Stochastic Gradient Descent (SGD) algorithm, also for the Expected Shortfall. We compare our algorithm to s…
This paper proposes analytic forms of portfolio CoVaR and CoCVaR on the normal tempered stable market model. Since CoCVaR captures the relative risk of the portfolio with respect to a benchmark return, we apply it to the relative portfolio optimization. Moreover, we derive analytic forms for the marginal contribution to CoVaR and the marginal contribution to CoCVaR. We discuss the Monte-Carlo simulation method to calculate CoCVaR and the marginal contributions of CoVaR and CoCVaR. As the empirical illustration, we show relative portfolio optimization with thirty stocks under the distress condi…
This paper studies a mean-risk portfolio choice problem for log-returns in a continuous-time, complete market. This is a growth-optimal problem with risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which is a generalization of Value-at-Risk (VaR) and Expected Shortfall (ES). We characterize the optimal terminal wealth up to the concave envelope of a certain function, and obtain analytical expressions for the optimal wealth and portfolio policy when the risk is measured by VaR or ES. In addition, we find that the efficient frontier is a concave curve that conn…
This paper proposes a dynamic process of portfolio risk measurement to address potential information loss. The proposed model takes advantage of financial big data to incorporate out-of-target-portfolio information that may be missed when one considers the Value at Risk (VaR) measures only from certain assets of the portfolio. We investigate how the curse of dimensionality can be overcome in the use of financial big data and discuss where and when benefits occur from a large number of assets. In this regard, the proposed approach is the first to suggest the use of financial big data to improve…
We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio manager is of primary concern, hence, it appears in the objective function, and the risk perception of an external authority needs to be taken into account as well, which appears in the form of a risk constraint. The problem covers the risk minimization problem with an expected return constraint and the expected return maximization problem with a risk const…
We present a method for finding optimal hedging policies for arbitrary initial portfolios and market states. We develop a novel actor-critic algorithm for solving general risk-averse stochastic control problems and use it to learn hedging strategies across multiple risk aversion levels simultaneously. We demonstrate the effectiveness of the approach with a numerical example in a stochastic volatility environment.
Risk statistic is a critical factor not only for risk analysis but also for financial application. However, the traditional risk statistics may fail to describe the characteristics of regulator-based risk. In this paper, we consider the regulator-based risk statistics for portfolios. By further developing the properties related to regulator-based risk statistics, we are able to derive dual representation for such risk.
Risk contributions of portfolios form an indispensable part of risk adjusted performance measurement. The risk contribution of a portfolio, e.g., in the Euler or Aumann-Shapley framework, is given by the partial derivatives of a risk measure applied to the portfolio profit and loss in direction of the asset units. For risk measures that are not positively homogeneous of degree 1, however, known capital allocation principles do not apply. We study the class of lambda quantile risk measures that includes the well-known Value-at-Risk as a special case but for which no known allocation rule is app…
