Portfolio Optimization

Portfolio Management using Deep Reinforcement Learning ArXiv ID: 2405.01604 “View on arXiv” Authors: Unknown Abstract Algorithmic trading or Financial robots have been conquering the stock markets with their ability to fathom complex statistical trading strategies. But with the recent development of deep learning technologies, these strategies are becoming impotent. The DQN and A2C models have previously outperformed eminent humans in game-playing and robotics. In our work, we propose a reinforced portfolio manager offering assistance in the allocation of weights to assets. The environment proffers the manager the freedom to go long and even short on the assets. The weight allocation advisements are restricted to the choice of portfolio assets and tested empirically to knock benchmark indices. The manager performs financial transactions in a postulated liquid market without any transaction charges. This work provides the conclusion that the proposed portfolio manager with actions centered on weight allocations can surpass the risk-adjusted returns of conventional portfolio managers. ...

A novel portfolio construction strategy based on the core-periphery profile of stocks ArXiv ID: 2405.12993 “View on arXiv” Authors: Unknown Abstract This paper highlights the significance of mesoscale structures, particularly the core-periphery structure, in financial networks for portfolio optimization. We build portfolios of stocks belonging to the periphery part of the Planar maximally filtered subgraphs of the underlying network of stocks created from Pearson correlations between pairs of stocks and compare its performance with some well-known strategies of Pozzi et. al. hinging around the local indices of centrality in terms of the Sharpe ratio, returns and standard deviation. Our findings reveal that these portfolios consistently outperform traditional strategies and further the core-periphery profile obtained is statistically significant across time periods. These empirical findings substantiate the efficacy of using the core-periphery profile of the stock market network for both inter-day and intraday trading and provide valuable insights for investors seeking better returns. ...

Subset second-order stochastic dominance for enhanced indexation with diversification enforced by sector constraints ArXiv ID: 2404.16777 “View on arXiv” Authors: Unknown Abstract In this paper we apply second-order stochastic dominance (SSD) to the problem of enhanced indexation with asset subset (sector) constraints. The problem we consider is how to construct a portfolio that is designed to outperform a given market index whilst having regard to the proportion of the portfolio invested in distinct market sectors. In our approach, subset SSD, the portfolio associated with each sector is treated in a SSD manner. In other words in subset SSD we actively try to find sector portfolios that SSD dominate their respective sector indices. However the proportion of the overall portfolio invested in each sector is not pre-specified, rather it is decided via optimisation. Our subset SSD approach involves the numeric solution of a multivariate second-order stochastic dominance problem. Computational results are given for our approach as applied to the S&P500 over the period 3rd October 2018 to 29th December 2023. This period, over 5 years, includes the Covid pandemic, which had a significant effect on stock prices. The S&P500 data that we have used is made publicly available for the benefit of future researchers. Our computational results indicate that the scaled version of our subset SSD approach outperforms the S&P500. Our approach also outperforms the standard SSD based approach to the problem. Our results show, that for the S&P500 data considered, including sector constraints improves out-of-sample performance, irrespective of the SSD approach adopted. Results are also given for Fama-French data involving 49 industry portfolios and these confirm the effectiveness of our subset SSD approach. ...

Quantum computing approach to realistic ESG-friendly stock portfolios ArXiv ID: 2404.02582 “View on arXiv” Authors: Unknown Abstract Finding an optimal balance between risk and returns in investment portfolios is a central challenge in quantitative finance, often addressed through Markowitz portfolio theory (MPT). While traditional portfolio optimization is carried out in a continuous fashion, as if stocks could be bought in fractional increments, practical implementations often resort to approximations, as fractional stocks are typically not tradeable. While these approximations are effective for large investment budgets, they deteriorate as budgets decrease. To alleviate this issue, a discrete Markowitz portfolio theory (DMPT) with finite budgets and integer stock weights can be formulated, but results in a non-polynomial (NP)-hard problem. Recent progress in quantum processing units (QPUs), including quantum annealers, makes solving DMPT problems feasible. Our study explores portfolio optimization on quantum annealers, establishing a mapping between continuous and discrete Markowitz portfolio theories. We find that correctly normalized discrete portfolios converge to continuous solutions as budgets increase. Our DMPT implementation provides efficient frontier solutions, outperforming traditional rounding methods, even for moderate budgets. Responding to the demand for environmentally and socially responsible investments, we enhance our discrete portfolio optimization with ESG (environmental, social, governance) ratings for EURO STOXX 50 index stocks. We introduce a utility function incorporating ESG ratings to balance risk, return, and ESG-friendliness, and discuss implications for ESG-aware investors. ...

Using Machine Learning to Forecast Market Direction with Efficient Frontier Coefficients ArXiv ID: 2404.00825 “View on arXiv” Authors: Unknown Abstract We propose a novel method to improve estimation of asset returns for portfolio optimization. This approach first performs a monthly directional market forecast using an online decision tree. The decision tree is trained on a novel set of features engineered from portfolio theory: the efficient frontier functional coefficients. Efficient frontiers can be decomposed to their functional form, a square-root second-order polynomial, and the coefficients of this function captures the information of all the constituents that compose the market in the current time period. To make these forecasts actionable, these directional forecasts are integrated to a portfolio optimization framework using expected returns conditional on the market forecast as an estimate for the return vector. This conditional expectation is calculated using the inverse Mills ratio, and the Capital Asset Pricing Model is used to translate the market forecast to individual asset forecasts. This novel method outperforms baseline portfolios, as well as other feature sets including technical indicators and the Fama-French factors. To empirically validate the proposed model, we employ a set of market sector ETFs. ...

Portfolio management using graph centralities: Review and comparison ArXiv ID: 2404.00187 “View on arXiv” Authors: Unknown Abstract We investigate an application of network centrality measures to portfolio optimization, by generalizing the method in [“Pozzi, Di Matteo and Aste, \emph{“Spread of risks across financial markets: better to invest in the peripheries”}, Scientific Reports 3:1665, 2013”], that however had significant limitations with respect to the state of the art in network theory. In this paper, we systematically compare many possible variants of the originally proposed method on S&P 500 stocks. We use daily data from twenty-seven years as training set and their following year as test set. We thus select the best network-based methods according to different viewpoints including for instance the highest Sharpe Ratio and the highest expected return. We give emphasis in new centrality measures and we also conduct a thorough analysis, which reveals significantly stronger results compared to those with more traditional methods. According to our analysis, this graph-theoretical approach to investment can be used successfully by investors with different investment profiles leading to high risk-adjusted returns. ...

High-Dimensional Mean-Variance Spanning Tests ArXiv ID: 2403.17127 “View on arXiv” Authors: Unknown Abstract We introduce a new framework for the mean-variance spanning (MVS) hypothesis testing. The procedure can be applied to any test-asset dimension and only requires stationary asset returns and the number of benchmark assets to be smaller than the number of time periods. It involves individually testing moment conditions using a robust Student-t statistic based on the batch-mean method and combining the p-values using the Cauchy combination test. Simulations demonstrate the superior performance of the test compared to state-of-the-art approaches. For the empirical application, we look at the problem of domestic versus international diversification in equities. We find that the advantages of diversification are influenced by economic conditions and exhibit cross-country variation. We also highlight that the rejection of the MVS hypothesis originates from the potential to reduce variance within the domestic global minimum-variance portfolio. ...

Nonlinear shifts and dislocations in financial market structure and composition ArXiv ID: 2403.15163 “View on arXiv” Authors: Unknown Abstract This paper develops new mathematical techniques to identify temporal shifts among a collection of US equities partitioned into a new and more detailed set of market sectors. Although conceptually related, our three analyses reveal distinct insights about financial markets, with meaningful implications for investment managers. First, we explore a variety of methods to identify nonlinear shifts in market sector structure and describe the mathematical connection between the measure used and the captured phenomena. Second, we study network structure with respect to our new market sectors and identify meaningfully connected sector-to-sector mappings. Finally, we conduct a series of sampling experiments over different sample spaces and contrast the distribution of Sharpe ratios produced by long-only, long-short and short-only investment portfolios. In addition, we examine the sector composition of the top-performing portfolios for each of these portfolio styles. In practice, the methods proposed in this paper could be used to identify regime shifts, optimally structured portfolios, and better communities of equities. ...

Asset management with an ESG mandate ArXiv ID: 2403.11622 “View on arXiv” Authors: Unknown Abstract We investigate the portfolio frontier and risk premia in equilibrium when institutional investors aim to minimize the tracking error variance under an ESG score mandate. If a negative ESG premium is priced in the market, this mandate can reduce portfolio inefficiency when the return over-performance target is limited. In equilibrium, with asset managers endowed with an ESG mandate and mean-variance investors, a negative ESG premium arises. A result that is supported by empirical data. The negative ESG premium is due to the ESG constraint imposed on institutional investors and is not associated with a risk factor. ...

Pairs Trading Using a Novel Graphical Matching Approach ArXiv ID: 2403.07998 “View on arXiv” Authors: Unknown Abstract Pairs trading, a strategy that capitalizes on price movements of asset pairs driven by similar factors, has gained significant popularity among traders. Common practice involves selecting highly cointegrated pairs to form a portfolio, which often leads to the inclusion of multiple pairs sharing common assets. This approach, while intuitive, inadvertently elevates portfolio variance and diminishes risk-adjusted returns by concentrating on a small number of highly cointegrated assets. Our study introduces an innovative pair selection method employing graphical matchings designed to tackle this challenge. We model all assets and their cointegration levels with a weighted graph, where edges signify pairs and their weights indicate the extent of cointegration. A portfolio of pairs is a subgraph of this graph. We construct a portfolio which is a maximum weighted matching of this graph to select pairs which have strong cointegration while simultaneously ensuring that there are no shared assets within any pair of pairs. This approach ensures each asset is included in just one pair, leading to a significantly lower variance in the matching-based portfolio compared to a baseline approach that selects pairs purely based on cointegration. Theoretical analysis and empirical testing using data from the S&P 500 between 2017 and 2023, affirm the efficacy of our method. Notably, our matching-based strategy showcases a marked improvement in risk-adjusted performance, evidenced by a gross Sharpe ratio of 1.23, a significant enhancement over the baseline value of 0.48 and market value of 0.59. Additionally, our approach demonstrates reduced trading costs attributable to lower turnover, alongside minimized single asset risk due to a more diversified asset base. ...