Risk Management

Sizing the bets in a focused portfolio ArXiv ID: 2402.15588 “View on arXiv” Authors: Unknown Abstract The paper provides a mathematical model and a tool for the focused investing strategy as advocated by Buffett, Munger, and others from this investment community. The approach presented here assumes that the investor’s role is to think about probabilities of different outcomes for a set of businesses. Based on these assumptions, the tool calculates the optimal allocation of capital for each of the investment candidates. The model is based on a generalized Kelly Criterion with options to provide constraints that ensure: no shorting, limited use of leverage, providing a maximum limit to the risk of permanent loss of capital, and maximum individual allocation. The software is applied to an example portfolio from which certain observations about excessive diversification are obtained. In addition, the software is made available for public use. ...

Navigating Market Turbulence: Insights from Causal Network Contagion Value at Risk ArXiv ID: 2402.06032 “View on arXiv” Authors: Unknown Abstract Accurately defining, measuring and mitigating risk is a cornerstone of financial risk management, especially in the presence of financial contagion. Traditional correlation-based risk assessment methods often struggle under volatile market conditions, particularly in the face of external shocks, highlighting the need for a more robust and invariant predictive approach. This paper introduces the Causal Network Contagion Value at Risk (Causal-NECO VaR), a novel methodology that significantly advances causal inference in financial risk analysis. Embracing a causal network framework, this method adeptly captures and analyses volatility and spillover effects, effectively setting it apart from conventional contagion-based VaR models. Causal-NECO VaR’s key innovation lies in its ability to derive directional influences among assets from observational data, thereby offering robust risk predictions that remain invariant to market shocks and systemic changes. A comprehensive simulation study and the application to the Forex market show the robustness of the method. Causal-NECO VaR not only demonstrates predictive accuracy, but also maintains its reliability in unstable financial environments, offering clearer risk assessments even amidst unforeseen market disturbances. This research makes a significant contribution to the field of risk management and financial stability, presenting a causal approach to the computation of VaR. It emphasises the model’s superior resilience and invariant predictive power, essential for navigating the complexities of today’s ever-evolving financial markets. ...

Constrained Max Drawdown: a Fast and Robust Portfolio Optimization Approach ArXiv ID: 2401.02601 “View on arXiv” Authors: Unknown Abstract We propose an alternative linearization to the classical Markowitz quadratic portfolio optimization model, based on maximum drawdown. This model, which minimizes maximum portfolio drawdown, is particularly appealing during times of financial distress, like during the COVID-19 pandemic. In addition, we will present a Mixed-Integer Linear Programming variation of our new model that, based on our out-of-sample results and sensitivity analysis, delivers a more profitable and robust solution with a 200 times faster solving time compared to the standard Markowitz quadratic formulation. ...

Fast calculation of Counterparty Credit exposures and associated sensitivities using fourier series expansion ArXiv ID: 2311.12575 “View on arXiv” Authors: Unknown Abstract This paper introduces a novel approach for computing netting–set level and counterparty level exposures, such as Potential Future Exposure (PFE) and Expected Exposure (EE), along with associated sensitivities. The method is essentially an extension of the Fourier-cosine series expansion (COS) method, originally proposed for option pricing. This method can accommodate a broad range of models where the joint distribution of involved risk factors is analytically or semi-analytically tractable. This inclusivity encompasses nearly all CCR models commonly employed in practice. A notable advantage of the COS method is its sustained efficiency, particularly when handling large portfolios. A theoretical error analysis is also provided to justify the method’s theoretical stability and accuracy. Various numerical tests are conducted using real-sized portfolios, and the results underscore its potential as a significantly more efficient alternative to the Monte Carlo method for practical usage, particularly applicable to portfolios involving a relatively modest number of risk factors. Furthermore, the observed error convergence rates align closely with the theoretical error analysis. ...

Predicting risk/reward ratio in financial markets for asset management using machine learning ArXiv ID: 2311.09148 “View on arXiv” Authors: Unknown Abstract Financial market forecasting remains a formidable challenge despite the surge in computational capabilities and machine learning advancements. While numerous studies have underscored the precision of computer-generated market predictions, many of these forecasts fail to yield profitable trading outcomes. This discrepancy often arises from the unpredictable nature of profit and loss ratios in the event of successful and unsuccessful predictions. In this study, we introduce a novel algorithm specifically designed for forecasting the profit and loss outcomes of trading activities. This is further augmented by an innovative approach for integrating these forecasts with previous predictions of market trends. This approach is designed for algorithmic trading, enabling traders to assess the profitability of each trade and calibrate the optimal trade size. Our findings indicate that this method significantly improves the performance of traditional trading strategies as well as algorithmic trading systems, offering a promising avenue for enhancing trading decisions. ...

Real-time VaR Calculations for Crypto Derivatives in kdb+/q ArXiv ID: 2309.06393 “View on arXiv” Authors: Unknown Abstract Cryptocurrency market is known for exhibiting significantly higher volatility than traditional asset classes. Efficient and adequate risk calculation is vital for managing risk exposures in such market environments where extreme price fluctuations occur in short timeframes. The objective of this thesis is to build a real-time computation workflow that provides VaR estimates for non-linear portfolios of cryptocurrency derivatives. Many researchers have examined the predictive capabilities of time-series models within the context of cryptocurrencies. In this work, we applied three commonly used models - EMWA, GARCH and HAR - to capture and forecast volatility dynamics, in conjunction with delta-gamma-theta approach and Cornish-Fisher expansion to crypto derivatives, examining their performance from the perspectives of calculation efficiency and accuracy. We present a calculation workflow which harnesses the information embedded in high-frequency market data and the computation simplicity inherent in analytical estimation procedures. This workflow yields reasonably robust VaR estimates with calculation latencies on the order of milliseconds. ...

FinPT: Financial Risk Prediction with Profile Tuning on Pretrained Foundation Models ArXiv ID: 2308.00065 “View on arXiv” Authors: Unknown Abstract Financial risk prediction plays a crucial role in the financial sector. Machine learning methods have been widely applied for automatically detecting potential risks and thus saving the cost of labor. However, the development in this field is lagging behind in recent years by the following two facts: 1) the algorithms used are somewhat outdated, especially in the context of the fast advance of generative AI and large language models (LLMs); 2) the lack of a unified and open-sourced financial benchmark has impeded the related research for years. To tackle these issues, we propose FinPT and FinBench: the former is a novel approach for financial risk prediction that conduct Profile Tuning on large pretrained foundation models, and the latter is a set of high-quality datasets on financial risks such as default, fraud, and churn. In FinPT, we fill the financial tabular data into the pre-defined instruction template, obtain natural-language customer profiles by prompting LLMs, and fine-tune large foundation models with the profile text to make predictions. We demonstrate the effectiveness of the proposed FinPT by experimenting with a range of representative strong baselines on FinBench. The analytical studies further deepen the understanding of LLMs for financial risk prediction. ...

Detecting Depegs: Towards Safer Passive Liquidity Provision on Curve Finance ArXiv ID: 2306.10612 “View on arXiv” Authors: Unknown Abstract We consider a liquidity provider’s (LP’s) exposure to stablecoin and liquid staking derivative (LSD) depegs on Curve’s StableSwap pools. We construct a suite of metrics designed to detect potential asset depegs based on price and trading data. Using our metrics, we fine-tune a Bayesian Online Changepoint Detection (BOCD) algorithm to alert LPs of potential depegs before or as they occur. We train and test our changepoint detection algorithm against Curve LP token prices for 13 StableSwap pools throughout 2022 and 2023, focusing on relevant stablecoin and LSD depegs. We show that our model, trained on 2022 UST data, is able to detect the USDC depeg in March of 2023 at 9pm UTC on March 10th, approximately 5 hours before USDC dips below 99 cents, with few false alarms in the 17 months on which it is tested. Finally, we describe how this research may be used by Curve’s liquidity providers, and how it may be extended to dynamically de-risk Curve pools by modifying parameters in anticipation of potential depegs. This research underpins an API developed to alert Curve LPs, in real-time, when their positions might be at risk. ...

Combining Reinforcement Learning and Barrier Functions for Adaptive Risk Management in Portfolio Optimization ArXiv ID: 2306.07013 “View on arXiv” Authors: Unknown Abstract Reinforcement learning (RL) based investment strategies have been widely adopted in portfolio management (PM) in recent years. Nevertheless, most RL-based approaches may often emphasize on pursuing returns while ignoring the risks of the underlying trading strategies that may potentially lead to great losses especially under high market volatility. Therefore, a risk-manageable PM investment framework integrating both RL and barrier functions (BF) is proposed to carefully balance the needs for high returns and acceptable risk exposure in PM applications. Up to our understanding, this work represents the first attempt to combine BF and RL for financial applications. While the involved RL approach may aggressively search for more profitable trading strategies, the BF-based risk controller will continuously monitor the market states to dynamically adjust the investment portfolio as a controllable measure for avoiding potential losses particularly in downtrend markets. Additionally, two adaptive mechanisms are provided to dynamically adjust the impact of risk controllers such that the proposed framework can be flexibly adapted to uptrend and downtrend markets. The empirical results of our proposed framework clearly reveal such advantages against most well-known RL-based approaches on real-world data sets. More importantly, our proposed framework shed lights on many possible directions for future investigation. ...

Proofs that the Gerber Statistic is Positive Semidefinite ArXiv ID: 2305.05663 “View on arXiv” Authors: Unknown Abstract In this brief note, we prove that both forms of the Gerber statistic introduced in Gerber et al. (2022) are positive semi-definite. Keywords: Gerber Statistic, Positive Semi-Definite, Risk Management, Dependence Modeling, General (Risk Measurement) Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 2.0/10 Quadrant: Lab Rats Why: The paper is dense with advanced linear algebra proofs, demonstrating matrix transformations and series expansions to establish positive semidefiniteness, which is a purely theoretical property with no practical implementation details provided. It contains no backtesting, datasets, or statistical metrics, focusing solely on the mathematical validity of the Gerber statistic. flowchart TD A["Research Goal<br/>Prove Gerber Statistic is PSD"] --> B["Analyze Structure<br/>1-form and 2-form"] B --> C["Mathematical Derivation<br/>Matrix Factorization & Boundaries"] C --> D["Computational Verification<br/>Symbolic/Numerical Analysis"] D --> E["Key Findings<br/>Both forms are Positive Semi-Definite"] E --> F["Outcomes<br/>Validated for Risk Management & Dependence Modeling"]