Portfolio Optimization

Evaluation of Deep Reinforcement Learning Algorithms for Portfolio Optimisation ArXiv ID: 2307.07694 “View on arXiv” Authors: Unknown Abstract We evaluate benchmark deep reinforcement learning algorithms on the task of portfolio optimisation using simulated data. The simulator to generate the data is based on correlated geometric Brownian motion with the Bertsimas-Lo market impact model. Using the Kelly criterion (log utility) as the objective, we can analytically derive the optimal policy without market impact as an upper bound to measure performance when including market impact. We find that the off-policy algorithms DDPG, TD3 and SAC are unable to learn the right $Q$-function due to the noisy rewards and therefore perform poorly. The on-policy algorithms PPO and A2C, with the use of generalised advantage estimation, are able to deal with the noise and derive a close to optimal policy. The clipping variant of PPO was found to be important in preventing the policy from deviating from the optimal once converged. In a more challenging environment where we have regime changes in the GBM parameters, we find that PPO, combined with a hidden Markov model to learn and predict the regime context, is able to learn different policies adapted to each regime. Overall, we find that the sample complexity of these algorithms is too high for applications using real data, requiring more than 2m steps to learn a good policy in the simplest setting, which is equivalent to almost 8,000 years of daily prices. ...

Portfolio Optimization: A Comparative Study ArXiv ID: 2307.05048 “View on arXiv” Authors: Unknown Abstract Portfolio optimization has been an area that has attracted considerable attention from the financial research community. Designing a profitable portfolio is a challenging task involving precise forecasting of future stock returns and risks. This chapter presents a comparative study of three portfolio design approaches, the mean-variance portfolio (MVP), hierarchical risk parity (HRP)-based portfolio, and autoencoder-based portfolio. These three approaches to portfolio design are applied to the historical prices of stocks chosen from ten thematic sectors listed on the National Stock Exchange (NSE) of India. The portfolios are designed using the stock price data from January 1, 2018, to December 31, 2021, and their performances are tested on the out-of-sample data from January 1, 2022, to December 31, 2022. Extensive results are analyzed on the performance of the portfolios. It is observed that the performance of the MVP portfolio is the best on the out-of-sample data for the risk-adjusted returns. However, the autoencoder portfolios outperformed their counterparts on annual returns. ...

Sports Betting: an application of neural networks and modern portfolio theory to the English Premier League ArXiv ID: 2307.13807 “View on arXiv” Authors: Unknown Abstract This paper presents a novel approach for optimizing betting strategies in sports gambling by integrating Von Neumann-Morgenstern Expected Utility Theory, deep learning techniques, and advanced formulations of the Kelly Criterion. By combining neural network models with portfolio optimization, our method achieved remarkable profits of 135.8% relative to the initial wealth during the latter half of the 20/21 season of the English Premier League. We explore complete and restricted strategies, evaluating their performance, risk management, and diversification. A deep neural network model is developed to forecast match outcomes, addressing challenges such as limited variables. Our research provides valuable insights and practical applications in the field of sports betting and predictive modeling. ...

Action-State Dependent Dynamic Model Selection ArXiv ID: 2307.04754 “View on arXiv” Authors: Unknown Abstract A model among many may only be best under certain states of the world. Switching from a model to another can also be costly. Finding a procedure to dynamically choose a model in these circumstances requires to solve a complex estimation procedure and a dynamic programming problem. A Reinforcement learning algorithm is used to approximate and estimate from the data the optimal solution to this dynamic programming problem. The algorithm is shown to consistently estimate the optimal policy that may choose different models based on a set of covariates. A typical example is the one of switching between different portfolio models under rebalancing costs, using macroeconomic information. Using a set of macroeconomic variables and price data, an empirical application to the aforementioned portfolio problem shows superior performance to choosing the best portfolio model with hindsight. ...

Liquidity Premium, Liquidity-Adjusted Return and Volatility, and Extreme Liquidity ArXiv ID: 2306.15807 “View on arXiv” Authors: Unknown Abstract We establish innovative liquidity premium measures, and construct liquidity-adjusted return and volatility to model assets with extreme liquidity, represented by a portfolio of selected crypto assets, and upon which we develop a set of liquidity-adjusted ARMA-GARCH/EGARCH models. We demonstrate that these models produce superior predictability at extreme liquidity to their traditional counterparts. We provide empirical support by comparing the performances of a series of Mean Variance portfolios. ...

Mind the Cap! – Constrained Portfolio Optimisation in Heston’s Stochastic Volatility Model ArXiv ID: 2306.11158 “View on arXiv” Authors: Unknown Abstract We consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston’s stochastic volatility model. We apply the duality methods developed in previous work to obtain a closed-form expression for the optimal portfolio allocation. In doing so, we observe that allocation constraints impact the optimal constrained portfolio allocation in a fundamentally different way in Heston’s stochastic volatility model than in the Black Scholes model. In particular, the optimal constrained portfolio may be different from the naive capped portfolio, which caps off the optimal unconstrained portfolio at the boundaries of the constraints. Despite this difference, we illustrate by way of a numerical analysis that in most realistic scenarios the capped portfolio leads to slim annual wealth equivalent losses compared to the optimal constrained portfolio. During a financial crisis, however, a capped solution might lead to compelling annual wealth equivalent losses. ...

From Portfolio Optimization to Quantum Blockchain and Security: A Systematic Review of Quantum Computing in Finance ArXiv ID: 2307.01155 “View on arXiv” Authors: Unknown Abstract In this paper, we provide an overview of the recent work in the quantum finance realm from various perspectives. The applications in consideration are Portfolio Optimization, Fraud Detection, and Monte Carlo methods for derivative pricing and risk calculation. Furthermore, we give a comprehensive overview of the applications of quantum computing in the field of blockchain technology which is a main concept in fintech. In that sense, we first introduce the general overview of blockchain with its main cryptographic primitives such as digital signature algorithms, hash functions, and random number generators as well as the security vulnerabilities of blockchain technologies after the merge of quantum computers considering Shor’s quantum factoring and Grover’s quantum search algorithms. We then discuss the privacy preserving quantum-resistant blockchain systems via threshold signatures, ring signatures, and zero-knowledge proof systems i.e. ZK-SNARKs in quantum resistant blockchains. After emphasizing the difference between the quantum-resistant blockchain and quantum-safe blockchain we mention the security countermeasures to take against the possible quantumized attacks aiming these systems. We finalize our discussion with quantum blockchain, efficient quantum mining and necessary infrastructures for constructing such systems based on quantum computing. This review has the intention to be a bridge to fill the gap between quantum computing and one of its most prominent application realms: Finance. We provide the state-of-the-art results in the intersection of finance and quantum technology for both industrial practitioners and academicians. ...

Random matrix theory and nested clustered portfolios on Mexican markets ArXiv ID: 2306.05667 “View on arXiv” Authors: Unknown Abstract This work aims to deal with the optimal allocation instability problem of Markowitz’s modern portfolio theory in high dimensionality. We propose a combined strategy that considers covariance matrix estimators from Random Matrix Theory~(RMT) and the machine learning allocation methodology known as Nested Clustered Optimization~(NCO). The latter methodology is modified and reformulated in terms of the spectral clustering algorithm and Minimum Spanning Tree~(MST) to solve internal problems inherent to the original proposal. Markowitz’s classical mean-variance allocation and the modified NCO machine learning approach are tested on financial instruments listed on the Mexican Stock Exchange~(BMV) in a moving window analysis from 2018 to 2022. The modified NCO algorithm achieves stable allocations by incorporating RMT covariance estimators. In particular, the allocation weights are positive, and their absolute value adds up to the total capital without considering explicit restrictions in the formulation. Our results suggest that can be avoided the risky \emph{“short position”} investment strategy by means of RMT inference and statistical learning techniques. ...

Maximally Machine-Learnable Portfolios ArXiv ID: 2306.05568 “View on arXiv” Authors: Unknown Abstract When it comes to stock returns, any form of predictability can bolster risk-adjusted profitability. We develop a collaborative machine learning algorithm that optimizes portfolio weights so that the resulting synthetic security is maximally predictable. Precisely, we introduce MACE, a multivariate extension of Alternating Conditional Expectations that achieves the aforementioned goal by wielding a Random Forest on one side of the equation, and a constrained Ridge Regression on the other. There are two key improvements with respect to Lo and MacKinlay’s original maximally predictable portfolio approach. First, it accommodates for any (nonlinear) forecasting algorithm and predictor set. Second, it handles large portfolios. We conduct exercises at the daily and monthly frequency and report significant increases in predictability and profitability using very little conditioning information. Interestingly, predictability is found in bad as well as good times, and MACE successfully navigates the debacle of 2022. ...

A systematic literature review on solution approaches for the index tracking problem in the last decade ArXiv ID: 2306.01660 “View on arXiv” Authors: Unknown Abstract The passive management approach offers conservative investors a way to reduce risk concerning the market. This investment strategy aims at replicating a specific index, such as the NASDAQ Composite or the FTSE100 index. The problem is that buying all the index’s assets incurs high rebalancing costs, and this harms future returns. The index tracking problem concerns building a portfolio that follows a specific benchmark with fewer transaction costs. Since a subset of assets is required to solve the index problem this class of problems is NP-hard, and in the past years, researchers have been studying solution approaches to obtain tracking portfolios more practically. This work brings an analysis, spanning the last decade, of the advances in mathematical approaches for index tracking. The systematic literature review covered important issues, such as the most relevant research areas, solution methods, and model structures. Special attention was given to the exploration and analysis of metaheuristics applied to the index tracking problem. ...