Portfolio Diversification

Minimizing the Value-at-Risk of Loan Portfolio via Deep Neural Networks ArXiv ID: 2510.07444 “View on arXiv” Authors: Albert Di Wang, Ye Du Abstract Risk management is a prominent issue in peer-to-peer lending. An investor may naturally reduce his risk exposure by diversifying instead of putting all his money on one loan. In that case, an investor may want to minimize the Value-at-Risk (VaR) or Conditional Value-at-Risk (CVaR) of his loan portfolio. We propose a low degree of freedom deep neural network model, DeNN, as well as a high degree of freedom model, DSNN, to tackle the problem. In particular, our models predict not only the default probability of a loan but also the time when it will default. The experiments demonstrate that both models can significantly reduce the portfolio VaRs at different confidence levels, compared to benchmarks. More interestingly, the low degree of freedom model, DeNN, outperforms DSNN in most scenarios. ...

Institutional Adoption and Correlation Dynamics: Bitcoin’s Evolving Role in Financial Markets ArXiv ID: 2501.09911 “View on arXiv” Authors: Unknown Abstract Bitcoin, widely recognized as the first cryptocurrency, has shown increasing integration with traditional financial markets, particularly major U.S. equity indices, amid accelerating institutional adoption. This study examines how Bitcoin exchange-traded funds and corporate Bitcoin holdings affect correlations with the Nasdaq 100 and the S&P 500, using rolling-window correlation, static correlation coefficients, and an event-study framework on daily data from 2018 to 2025.Correlation levels intensified following key institutional milestones, with peaks reaching 0.87 in 2024, and they vary across market regimes. These trends suggest that Bitcoin has transitioned from an alternative asset toward a more integrated financial instrument, carrying implications for portfolio diversification, risk management, and systemic stability. Future research should further investigate regulatory and macroeconomic factors shaping these evolving relationships. ...

The lexical ratio: A new perspective on portfolio diversification ArXiv ID: 2411.06080 “View on arXiv” Authors: Unknown Abstract Portfolio diversification, traditionally measured through asset correlations and volatilitybased metrics, is fundamental to managing financial risk. However, existing diversification metrics often overlook non-numerical relationships between assets that can impact portfolio stability, particularly during market stresses. This paper introduces the lexical ratio (LR), a novel metric that leverages textual data to capture diversification dimensions absent in standard approaches. By treating each asset as a unique document composed of sectorspecific and financial keywords, the LR evaluates portfolio diversification by distributing these terms across assets, incorporating entropy-based insights from information theory. We thoroughly analyze LR’s properties, including scale invariance, concavity, and maximality, demonstrating its theoretical robustness and ability to enhance risk-adjusted portfolio returns. Using empirical tests on S&P 500 portfolios, we compare LR’s performance to established metrics such as Markowitz’s volatility-based measures and diversification ratios. Our tests reveal LR’s superiority in optimizing portfolio returns, especially under varied market conditions. Our findings show that LR aligns with conventional metrics and captures unique diversification aspects, suggesting it is a viable tool for portfolio managers. ...

Modern Portfolio Diversification with Arte-Blue Chip Index ArXiv ID: 2409.18816 “View on arXiv” Authors: Unknown Abstract This paper presents a novel approach to evaluating blue-chip art as a viable asset class for portfolio diversification. We present the Arte-Blue Chip Index, an index that tracks 100 top-performing artists based on 81,891 public transactions from 157 artists across 584 auction houses over the period 1990 to 2024. By comparing blue-chip art price trends with stock market fluctuations, our index provides insights into the risk and return profile of blue-chip art investments. Our analysis demonstrates that a 20% allocation of blue-chip art in a diversified portfolio enhances risk-adjusted returns by around 20%, while maintaining volatility levels similar to the S&P 500. ...

Network-based diversification of stock and cryptocurrency portfolios ArXiv ID: 2408.11739 “View on arXiv” Authors: Unknown Abstract Maintaining a balance between returns and volatility is a common strategy for portfolio diversification, whether investing in traditional equities or digital assets like cryptocurrencies. One approach for diversification is the application of community detection or clustering, using a network representing the relationships between assets. We examine two network representations, one based on a standard distance matrix based on correlation, and another based on mutual information. The Louvain and Affinity propagation algorithms were employed for finding the network communities (clusters) based on annual data. Furthermore, we examine building assets’ co-occurrence networks, where communities are detected for each month throughout a whole year and then the links represent how often assets belong to the same community. Portfolios are then constructed by selecting several assets from each community based on local properties (degree centrality), global properties (closeness centrality), or explained variance (Principal component analysis), with three value ranges (max, med, min), calculated on a maximal spanning tree or a fully connected community sub-graph. We explored these various strategies on data from the S&P 500 and the Top 203 cryptocurrencies with a market cap above 2M USD in the period from Jan 2019 to Sep 2022. Moreover, we study into more details the periods of the beginning of the COVID-19 outbreak and the start of the war in Ukraine. The results confirm some of the previous findings already known for traditional stock markets and provide some further insights, while they reveal an opposing trend in the crypto-assets market. ...

Financial Assets Dependency Prediction Utilizing Spatiotemporal Patterns ArXiv ID: 2406.11886 “View on arXiv” Authors: Unknown Abstract Financial assets exhibit complex dependency structures, which are crucial for investors to create diversified portfolios to mitigate risk in volatile financial markets. To explore the financial asset dependencies dynamics, we propose a novel approach that models the dependencies of assets as an Asset Dependency Matrix (ADM) and treats the ADM sequences as image sequences. This allows us to leverage deep learning-based video prediction methods to capture the spatiotemporal dependencies among assets. However, unlike images where neighboring pixels exhibit explicit spatiotemporal dependencies due to the natural continuity of object movements, assets in ADM do not have a natural order. This poses challenges to organizing the relational assets to reveal better the spatiotemporal dependencies among neighboring assets for ADM forecasting. To tackle the challenges, we propose the Asset Dependency Neural Network (ADNN), which employs the Convolutional Long Short-Term Memory (ConvLSTM) network, a highly successful method for video prediction. ADNN can employ static and dynamic transformation functions to optimize the representations of the ADM. Through extensive experiments, we demonstrate that our proposed framework consistently outperforms the baselines in the ADM prediction and downstream application tasks. This research contributes to understanding and predicting asset dependencies, offering valuable insights for financial market participants. ...

Diversification for infinite-mean Pareto models without risk aversion ArXiv ID: 2404.18467 “View on arXiv” Authors: Unknown Abstract We study stochastic dominance between portfolios of independent and identically distributed (iid) extremely heavy-tailed (i.e., infinite-mean) Pareto random variables. With the notion of majorization order, we show that a more diversified portfolio of iid extremely heavy-tailed Pareto random variables is larger in the sense of first-order stochastic dominance. This result is further generalized for Pareto random variables caused by triggering events, random variables with tails being Pareto, bounded Pareto random variables, and positively dependent Pareto random variables. These results provide an important implication in investment: Diversification of extremely heavy-tailed Pareto profits uniformly increases investors’ profitability, leading to a diversification benefit. Remarkably, different from the finite-mean setting, such a diversification benefit does not depend on the decision maker’s risk aversion. ...

Stock Recommendations for Individual Investors: A Temporal Graph Network Approach with Mean-Variance Efficient Sampling ArXiv ID: 2404.07223 “View on arXiv” Authors: Unknown Abstract Recommender systems can be helpful for individuals to make well-informed decisions in complex financial markets. While many studies have focused on predicting stock prices, even advanced models fall short of accurately forecasting them. Additionally, previous studies indicate that individual investors often disregard established investment theories, favoring their personal preferences instead. This presents a challenge for stock recommendation systems, which must not only provide strong investment performance but also respect these individual preferences. To create effective stock recommender systems, three critical elements must be incorporated: 1) individual preferences, 2) portfolio diversification, and 3) the temporal dynamics of the first two. In response, we propose a new model, Portfolio Temporal Graph Network Recommender PfoTGNRec, which can handle time-varying collaborative signals and incorporates diversification-enhancing sampling. On real-world individual trading data, our approach demonstrates superior performance compared to state-of-the-art baselines, including cutting-edge dynamic embedding models and existing stock recommendation models. Indeed, we show that PfoTGNRec is an effective solution that can balance customer preferences with the need to suggest portfolios with high Return-on-Investment. The source code and data are available at https://github.com/youngandbin/PfoTGNRec. ...

A Portfolio’s Common Causal Conditional Risk-neutral PDE ArXiv ID: 2401.00949 “View on arXiv” Authors: Unknown Abstract Portfolio’s optimal drivers for diversification are common causes of the constituents’ correlations. A closed-form formula for the conditional probability of the portfolio given its optimal common drivers is presented, with each pair constituent-common driver joint distribution modelled by Gaussian copulas. A conditional risk-neutral PDE is obtained for this conditional probability as a system of copulas’ PDEs, allowing for dynamical risk management of a portfolio as shown in the experiments. Implied conditional portfolio volatilities and implied weights are new risk metrics that can be dynamically monitored from the PDEs or obtained from their solution. ...

Portfolio diversification with varying investor abilities ArXiv ID: 2311.06519 “View on arXiv” Authors: Unknown Abstract We introduce new mathematical methods to study the optimal portfolio size of investment portfolios over time, considering investors with varying skill levels. First, we explore the benefit of portfolio diversification on an annual basis for poor, average and strong investors defined by the 10th, 50th and 90th percentiles of risk-adjusted returns, respectively. Second, we conduct a thorough regression experiment examining quantiles of risk-adjusted returns as a function of portfolio size across investor ability, testing for trends and curvature within these functions. Finally, we study the optimal portfolio size for poor, average and strong investors in a continuously temporal manner using more than 20 years of data. We show that strong investors should hold concentrated portfolios, poor investors should hold diversified portfolios; average investors have a less obvious distribution with the optimal number varying materially over time. ...