Portfolio Risk Management

Beyond Correlation: Positive Definite Dependence Measures for Robust Inference, Flexible Scenarios, and Causal Modeling for Financial Portfolios ArXiv ID: 2504.15268 “View on arXiv” Authors: Unknown Abstract We live in a multivariate world, and effective modeling of financial portfolios, including their construction, allocation, forecasting, and risk analysis, simply is not possible without explicitly modeling the dependence structure of their assets. Dependence structure can drive portfolio results more than the combined effects of other parameters in investment and risk models, but the literature provides relatively little to define the finite-sample distributions of dependence measures under challenging, real-world financial data conditions. Yet this is exactly what is needed to make valid inferences about their estimates, and to use these inferences for essential purposes such as hypothesis testing, dynamic monitoring, realistic and granular scenario and reverse scenario analyses, and mitigating the effects of correlation breakdowns during market upheavals. This work develops a new and straightforward method, Nonparametric Angles-based Correlation (NAbC), for defining the finite-sample distributions of any dependence measure whose matrix of pairwise associations is positive definite (e.g. Pearsons, Kendalls, Spearmans, the Tail Dependence Matrix, and others). The solution remains valid under marginal asset distributions characterized by notably different and varying degrees of serial correlation, non-stationarity, heavy-tailedness, and asymmetry. Importantly, it provides p-values and confidence intervals at the matrix level, even when selected cells in the matrix are frozen, thus enabling flexible, granular, and realistic scenarios, reverse scenarios, and stress tests. Finally, when applied to directional dependence measures, NAbC enables accurate DAG recovery in causal modeling. NAbC stands alone in providing all of these capabilities simultaneously, and should prove to be a very useful means by which we can better understand and manage financial portfolios in our multivariate world. ...

Portfolio Stress Testing and Value at Risk (VaR) Incorporating Current Market Conditions ArXiv ID: 2409.18970 “View on arXiv” Authors: Unknown Abstract Value at Risk (VaR) and stress testing are two of the most widely used approaches in portfolio risk management to estimate potential market value losses under adverse market moves. VaR quantifies potential loss in value over a specified horizon (such as one day or ten days) at a desired confidence level (such as 95’th percentile). In scenario design and stress testing, the goal is to construct extreme market scenarios such as those involving severe recession or a specific event of concern (such as a rapid increase in rates or a geopolitical event), and quantify potential impact of such scenarios on the portfolio. The goal of this paper is to propose an approach for incorporating prevailing market conditions in stress scenario design and estimation of VaR so that they provide more accurate and realistic insights about portfolio risk over the near term. The proposed approach is based on historical data where historical observations of market changes are given more weight if a certain period in history is “more similar” to the prevailing market conditions. Clusters of market conditions are identified using a Machine Learning approach called Variational Inference (VI) where for each cluster future changes in portfolio value are similar. VI based algorithm uses optimization techniques to obtain analytical approximations of the posterior probability density of cluster assignments (market regimes) and probabilities of different outcomes for changes in portfolio value. Covid related volatile period around the year 2020 is used to illustrate the performance of the proposed approach and in particular show how VaR and stress scenarios adapt quickly to changing market conditions. Another advantage of the proposed approach is that classification of market conditions into clusters can provide useful insights about portfolio performance under different market conditions. ...

Temporal distribution of clusters of investors and their application in prediction with expert advice ArXiv ID: 2406.19403 “View on arXiv” Authors: Unknown Abstract Financial organisations such as brokers face a significant challenge in servicing the investment needs of thousands of their traders worldwide. This task is further compounded since individual traders will have their own risk appetite and investment goals. Traders may look to capture short-term trends in the market which last only seconds to minutes, or they may have longer-term views which last several days to months. To reduce the complexity of this task, client trades can be clustered. By examining such clusters, we would likely observe many traders following common patterns of investment, but how do these patterns vary through time? Knowledge regarding the temporal distributions of such clusters may help financial institutions manage the overall portfolio of risk that accumulates from underlying trader positions. This study contributes to the field by demonstrating that the distribution of clusters derived from the real-world trades of 20k Foreign Exchange (FX) traders (from 2015 to 2017) is described in accordance with Ewens’ Sampling Distribution. Further, we show that the Aggregating Algorithm (AA), an on-line prediction with expert advice algorithm, can be applied to the aforementioned real-world data in order to improve the returns of portfolios of trader risk. However we found that the AA ‘struggles’ when presented with too many trader ``experts’’, especially when there are many trades with similar overall patterns. To help overcome this challenge, we have applied and compared the use of Statistically Validated Networks (SVN) with a hierarchical clustering approach on a subset of the data, demonstrating that both approaches can be used to significantly improve results of the AA in terms of profitability and smoothness of returns. ...

Implementing portfolio risk management and hedging in practice ArXiv ID: 2309.15767 “View on arXiv” Authors: Unknown Abstract In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton–Jacobi–Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic control may be undesirable for various business reasons. In this work we present a straightforward approach for thinking of cross-asset portfolio risk management and hedging, providing some implementation details, while rarely venturing outside the convex optimisation setting of (approximate) quadratic programming~(QP). We pay particular attention to the correspondence between the economic concepts and their mathematical representations; the abstractions enabling us to handle multiple asset classes and risk models at once; the dimensional analysis of the resulting equations; and the assumptions inherent in our derivations. We demonstrate how to solve the resulting QPs with CVXOPT. ...