We propose a novel dynamic bivariate peak over threshold (PoT) model to study the time-varying behavior of joint tail risk in financial markets. The proposed framework provides simultaneous modeling for dynamics of marginal and joint tail risk, and generalizes the existing tail risk literature from univariate dimension to multivariate dimension. We introduce a natural and interpretable tail connectedness measure and examine the dynamics of joint tail behavior of global stock markets: empirical evidence suggests markets from the same continent have time-varying and high-level joint tail risk, and tail connectedness increases during periods of crisis. We further enrich the tail risk literature by developing a novel portfolio optimization procedure based on bivariate joint tail risk minimization, which gives promising risk-rewarding performance in backtesting.

Portfolio Risk Management Software Market size was valued at USD 3.1 Billion in 2023 and is projected to reach USD 12.9 Billion by 2030, growing at a CAGR of 14.3% during the forecasted period 2024 to 2030

Global Portfolio Risk Management Software Market Drivers

Increasing Complexity of Financial Markets: The need for sophisticated portfolio risk management software is driven by the financial markets' increasing complexity, which includes a wide range of investment products, asset classes, and interconnection across the world economy. In volatile market situations, investors and asset managers need advanced tools and analytics to evaluate and reduce risks across their investment portfolios.

Needs for Regulatory Compliance: Financial institutions and investment organizations must improve their risk management processes and transparency in order to comply with strict regulatory mandates and reporting requirements such as Basel III, Solvency II, MiFID II, and the Dodd-Frank Act. Software solutions for portfolio risk management make regulatory compliance easier and enable features like scenario analysis, stress testing, and risk reporting.

Prudent Investing Techniques: The trend toward risk-aware investing techniques like factor investing, tail risk hedging, risk parity, and smart beta emphasizes how crucial it is to manage portfolio risk effectively. With the use of quantitative risk models and optimization strategies made possible by risk management software, investors aim to maximize risk-adjusted returns, reduce downside risk, and control portfolio volatility.

Volatility and Uncertainty in Financial Markets: The requirement for real-time risk monitoring, scenario analysis, and stress testing capabilities provided by portfolio risk management software is driven by increased market volatility, geopolitical instability, and macroeconomic uncertainty. In order to control portfolio performance, investors attempt to evaluate and manage risks associated with systemic events, market shocks, and geopolitical threats.

Put Risk-adjusted Performance First: When assessing investment strategies and portfolio allocations, investors are placing a greater emphasis on risk-adjusted performance metrics including the Sharpe ratio, Sortino ratio, and information ratio. Portfolio risk management software integrates risk metrics with performance attribution and portfolio optimization tools to give investors the ability to track, evaluate, and improve risk-adjusted returns.

The need for ALM, or asset-liability management: Robust asset-liability management (ALM) solutions are necessary for institutional investors, insurance firms, pension funds, and endowments to manage liquidity risk, long-term liabilities, and asset allocation choices. ALM features like cash flow modeling, duration matching, immunization tactics, and liability-driven investing (LDI) approaches are provided by portfolio risk management software.

Technological and analytical advances: The constant progress in data analytics, artificial intelligence (AI), and technology propels innovation in portfolio risk management software. Capabilities for risk modeling, scenario analysis, and decision assistance are improved by features including big data analytics, machine learning, predictive analytics, and natural language processing (NLP).

Cloud-based solutions are in demand: Cloud-based portfolio risk management software solutions being adopted more quickly as cloud computing and software-as-a-service (SaaS) delivery methods gain traction. With web-based interfaces, cloud-based platforms provide scalability, flexibility, and accessibility, allowing users to access analytics and risk management capabilities at any time and from any location.

Emphasis on Enterprise-Wide Risk Management: Businesses want to include risk management procedures into front-, middle-, and back-office operations. By facilitating enterprise-wide risk aggregation, reporting, and governance, portfolio risk management software solutions help enterprises monitor and manage risks holistically across business units and asset classes.

Consistent growth in assets under management (AUM) has immensely benefited the Hedge Funds industry over the past five years. Industry servicers invest capital they receive from a variety of investor types across a broad range of asset classes and investment strategies. Operators collect a fee for the amount of money they manage for these clients and a percentage of gains they are able to generate on invested assets. This business model helped industry revenue climb at a CAGR of 7.7% to $127.4 billion over the past five years, including an expected incline of 5.7% in 2024. Despite economic volatility in 2020 due to the pandemic lowering interest rates, an incline in the value of stocks in 2020 positively affected many hedge funds. The S&P 500 climbed 16.3% in 2020, which helped increase AUM. Although industry professionals question the relevance of benchmarking hedge fund returns against equity performance, given that hedge funds rely on a range of instruments other than stocks, the industry's poor performance relative to the S&P 500 has begun to raise concern from some investors. These trends have affected the industry's structure, with the traditional 2.0 and 20.0 structure of a flat fee on total AUM and a right-to-earned profit deteriorating into a 1.4 and 16.0 arrangement. As a result, industry profit, measured as earnings before interest and taxes, has been hindered over the past five years. Industry revenue is expected to grow at a CAGR of 3.1% to $148.5 billion over the next five years. AUM is forecast to continue increasing at a consistent rate, partly due to the diversification benefits that hedge funds provide. Nonetheless, increased regulation stemming from the global financial crisis and an escalating focus on the industry's tax structure has the potential to harm industry profit. Further economic uncertainty stemming from heightened inflation and persistently high interest rates is anticipated to dampen any large-scale growth for the industry as more hedge funds take a hawkish approach in their investment portfolio moving forward. Regardless, the number of new hedge funds is forecast to trend with AUM and revenue over the next five years.

An accurate assessment of tail inequalities and tail asymmetries of financial returns is key for risk management and portfolio allocation. We propose a new test procedure for detecting the full extent of such structural differences in the dependence of bivariate extreme returns. We decompose the testing problem into piecewise multiple comparisons of Cramér–von Mises distances of tail copulas. In this way, tail regions that cause differences in extreme dependence can be located and consequently be targeted by financial strategies. We derive the asymptotic properties of the test and provide a bootstrap approximation for finite samples. Moreover, we account for the multiplicity of the piecewise tail copula comparisons by adjusting individual p-values according to multiple testing techniques. Monte Carlo simulations demonstrate the test’s superior finite-sample properties for common financial tail risk models, both in the iid and the sequentially dependent case. During the last 90 years in U.S. stock markets, our test detects up to 20% more tail asymmetries than competing tests. This can be attributed to the presence of nonstandard tail dependence structures. We also find evidence for diminishing tail asymmetries during every major financial crisis—except for the 2007–2009 crisis—reflecting a risk-return trade-off for extreme returns. Supplementary materials for this article are available online.

Learning about the tail shape of time series is important in, e.g., economics, finance, and risk management. However, it is well known that estimates of the tail index can be very sensitive to the choice of the number k of tail observations used for estimation. We propose a procedure that determines where the tail begins by choosing k in a data-driven fashion using scoring rules. So far, scoring rules have mainly been used to compare density forecasts. We also demonstrate how our proposal can be used in multivariate applications in the system risk literature. The advantages of our choice of k are illustrated in simulations and an empirical application to Value-at-Risk forecasts for five U.S. blue-chip stocks.

In this file we have the input data for calculating the CoVaR (Latin America financial Indices returns), fitted copulas, test statistics, and the LATAM banking system CoVaR.

These materials containing data and code are used to reproduce the paper. (PDF)

This table displays the systemic risk scores of 20 newly established top energy companies throughout the entire sample period.

Quantum-Enhanced Portfolio Scenario Engine Market Outlook

According to our latest research, the global Quantum-Enhanced Portfolio Scenario Engine market size reached USD 1.14 billion in 2024, demonstrating a robust growth trajectory driven by rapid advancements in quantum computing and its integration into financial analytics. The market is projected to grow at a CAGR of 32.7% from 2025 to 2033, reaching a forecasted value of USD 13.21 billion by 2033. This remarkable growth is primarily attributed to the increasing demand for advanced risk management, portfolio optimization, and stress testing capabilities across the financial sector, as institutions seek to leverage quantum-powered solutions for superior scenario analysis and decision-making.

One of the primary growth factors for the Quantum-Enhanced Portfolio Scenario Engine market is the rising complexity of global financial markets, which necessitates more sophisticated analytical tools. Traditional computational approaches often struggle with the vast number of variables and scenarios required for comprehensive portfolio management. Quantum computing, with its unparalleled ability to process and analyze massive datasets simultaneously, offers a transformative leap in scenario analysis, enabling financial institutions to simulate thousands of market movements and stress scenarios in real-time. This capability not only enhances the precision of risk assessments but also empowers asset managers to respond proactively to market volatility, thereby driving the adoption of quantum-enhanced engines across banks, hedge funds, and insurance companies.

Another key driver is the intensifying regulatory landscape and the growing emphasis on transparency and compliance in the financial sector. Regulatory bodies worldwide are mandating more stringent stress testing and risk evaluation protocols, compelling institutions to upgrade their portfolio management infrastructure. Quantum-enhanced scenario engines are uniquely positioned to meet these requirements, as they facilitate rapid and comprehensive modeling of extreme market events and tail risks. By providing actionable insights with higher accuracy and speed, these solutions help firms maintain regulatory compliance, safeguard client assets, and build investor confidence, further fueling market expansion.

Technological advancements and increasing investments in quantum computing research are also propelling the market forward. Major technology providers and financial institutions are collaborating to develop scalable quantum algorithms and hardware tailored for financial applications. The emergence of hybrid quantum-classical solutions, which combine the strengths of both paradigms, is accelerating real-world adoption. As cloud-based quantum computing platforms become more accessible, even small and medium-sized enterprises (SMEs) are beginning to explore quantum-enhanced scenario analysis, democratizing access to cutting-edge portfolio management tools and broadening the market base.

From a regional perspective, North America currently leads the Quantum-Enhanced Portfolio Scenario Engine market, accounting for the largest revenue share in 2024, followed by Europe and Asia Pacific. The dominance of North America is underpinned by its advanced financial ecosystem, concentration of leading quantum technology vendors, and early adoption among major banks and asset management firms. Meanwhile, Asia Pacific is witnessing the fastest growth, supported by rapid digital transformation in the financial sector, increasing investments in quantum research, and a burgeoning fintech landscape. Europe remains a critical market, driven by regulatory rigor and a strong focus on risk management innovation. Latin America and the Middle East & Africa are gradually emerging as promising markets, propelled by digitalization initiatives and growing awareness of quantum computing’s potential in financial services.

Component Analysis

The Component segment of the Quantum-Enhanced Portfoli

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Tail Spend Management Solutions Market Size 2025-2029

The tail spend management solutions market size is forecast to increase by USD 482.5 million, at a CAGR of 4.7% between 2024 and 2029.

The market is experiencing significant growth, driven primarily by the increasing emphasis on cost reduction strategies. Companies are recognizing the potential savings that can be achieved by optimizing their spend on low-value, infrequent purchases, also known as tail spend. This trend is further fueled by the increasing adoption of Artificial Intelligence (AI) and Machine Learning (ML) technologies, which enable automated identification and management of tail spend. However, the market is not without its challenges. Data quality issues pose a significant obstacle to effective tail spend management. With a large number of suppliers and transactions involved, maintaining accurate and up-to-date data is essential for identifying opportunities for cost savings and managing risk.
Ensuring data accuracy and completeness requires robust data management processes and technologies, presenting an opportunity for solution providers to differentiate themselves in the market. Companies seeking to capitalize on the opportunities presented by the market must address these challenges head-on, investing in advanced data management capabilities and leveraging AI and ML technologies to gain visibility and control over their tail spend.

What will be the Size of the Tail Spend Management Solutions Market during the forecast period?

Explore in-depth regional segment analysis with market size data - historical 2019-2023 and forecasts 2025-2029 - in the full report.
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The market continues to evolve, with cloud-based supplier performance management systems gaining traction. These solutions enable businesses to automate payment processes, integrating business intelligence and data visualization for value creation. Supplier relationships are strengthened through effective communication and performance monitoring, leading to cost reduction and process improvement. Risk management is a critical component, with demand forecasting and supply chain optimization ensuring business continuity. Contract management solutions facilitate efficient negotiation and compliance, while tail spend optimization uncovers hidden savings opportunities. Ethical sourcing and supplier diversity initiatives are integrated, enhancing corporate social responsibility. Artificial intelligence and machine learning are transforming the landscape, providing predictive analytics for inventory management and spend data analysis.

Procurement automation streamlines workflows, reducing manual tasks and increasing efficiency gains. Purchase order management and reporting and analytics provide real-time spend visibility, enabling informed decision-making. The ongoing unfolding of market activities reveals a dynamic and interconnected ecosystem, where e-procurement platforms, spend analytics, and category management are seamlessly integrated. Strategic sourcing initiatives leverage spend data to optimize contracts and negotiate favorable terms. Invoice processing is automated, ensuring accurate and timely payments to suppliers. The continuous evolution of tail spend management solutions is shaping the future of procurement, with a focus on data integration and supplier relationship management.

The market's ongoing growth and innovation are driving significant value for businesses across various sectors.

How is this Tail Spend Management Solutions Industry segmented?

The tail spend management solutions industry research report provides comprehensive data (region-wise segment analysis), with forecasts and estimates in 'USD million' for the period 2025-2029, as well as historical data from 2019-2023 for the following segments.

Solution

  Spend analytics
  Order management
  Contract management


End-user

  BFSI
  Transportation and logistics
  Healthcare
  Retail
  Others


Deployment Type

  Cloud
  On-Premises


Enterprise Size

  SMEs
  Large Enterprises


Geography

  North America

    US
    Mexico


  Europe

    France
    Germany
    Italy
    UK


  Middle East and Africa

    UAE


  APAC

    Australia
    China
    India
    Japan
    South Korea


  South America

    Brazil


  Rest of World (ROW)

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By Solution Insights

The spend analytics segment is estimated to witness significant growth during the forecast period.

The market is witnessing notable development, fueled by the growing demand for enhanced supplier performance management, payment automation, and business intelligence. Cloud-based solutions are increasingly adopted due to their scalability, flexibility, and cost-effectiveness, enabling companies to optimize tail spend and improve efficiency gains. Supplier relationship management is another crucial area of focus, with

Descriptions of macroeconomic, firm financial and market environment variables.

KFS was written up by fiverocks in May 2020 and has been a home run - up over 5x since his write up at $1.75 per share and exceeding the price target on his initial thesis, which has largely played out.

The company has:

Re-started investor outreach (IR page now revamped, investor days/earnings calls being held) after years of zero outbound IR. (The company was also dark on its financial statements at the time of previous write up).

Sold down several non-strategic real estate assets and re-allocated the funds to purchasing operating companies (both extended warranty and as part of search accelerator program).

Simplified its balance sheet, with debt coming down massively as large amounts were associated with the non-core real estate assets, while the company also bought back the majority of its Trups preferred debt at discount to face value.

Unfortunately, I haven't partaken in most of the investment gains to date, only buying shares late last year. However thanks to the author's yeoman's work in the comments section, I noticed he was continually raising his price target, as the initial thesis was playing out and a new one was emerging.

• Portfolio Optimization
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One of my favourite signals for further investigating an idea on VIC, is when the author of an idea continues to pound the table on an idea that has already multi-bagged, given they have every incentive to hit that author exit recommendation button and take the W. It worked out well for me on XPEL, HMHC and HQI, where I either didn't take a position on initial recommendation (or took a very small position), but still managed to make some money, thanks to the respective author's subsequent cheerleading, as the thesis played out and evolved.

Thanks to fiverock's cheerleading on KFS, its clear after looking into the company that there is still plenty of meat left on the bone, as the thesis evolves from the complex to the simple thesis outlined by management, towards a potential compounding machine at a very reasonable starting valuation, as the company continues to build out its search accelerator business.

Summary of current business

KFS's much simplified business now consists of two operating segments - 1) the Extended Warranty Business (68% ebitda) and 2) Search Accelerator (32% ebitda). I'll cover the extended warranty briefly, but its search accelerator business that really has the potential to make the stock a multi-bagger from here.

Extended Warranty business:

Kingsway's Extended warranty business operates under four different companies - three targeting the automotive sector (87% ebitda - IWS, PWI and Penn) and one targeting mechanical (13% of ebitda - Trinity).

KFS likes the extended warranty business, due to its lack of capital intensity + the sticky nature of relationships with customers (for example, the automotive extended warranties are mostly sold by credit union/dealer partners with credit union in particular exhibiting little churn). Furthermore, the nature of claims are fairly predictable, typically relating to mechanical failure (eg, transmission issues), with high quality data and little tail risk, resulting in predictable and recurring revenues.

Whilst KFS has in the recent past been able to acquire extended warranty businesses at attractive valuations, they see current valuations as probably too high to contemplate acquisitions here in near future and will be focusing on organic growth.

Search Accelerator:

KFS's search accelerator business 'officially' commenced as a separate operating segment with the purchase of the Ravix business (accounting/HR outsourcing) in 2021, under Timi Okah, their first operator-in-residence. KFS CEO JT Fitzgerald is quite experienced with the search fund model, having been a post-MBA search fund CEO himself, while also being an active investor in the space . Since the acquisition of Ravix, KFS has also purchased CSuite (financial executive search) and SNS (nurse staffing). There are also 4.5 operators-in-residence (OIRs) that are currently searching for businesses to acquire (the 0.5 being Charles Joyce, who is working on initiatives to improve search efficiency and OIR recruitment at holdco level, but is also interested in acquiring a business at some point).

Before describing the current state of affairs for KFS's search accelerator business, I think its worthwhile to give a brief history of the search fund model, its history of lucrative returns and why I believe KFS's search accelerator is well-positioned to perform well.

Search Funds (also knows as 'Entrepreneurs through acquisition' or ETA) are typically set up by freshly minted, high potential MBAs who have the ambition of running their own company, but are lacking in both financial resources and experience. Typically at least some of the search fund principals will have experience in both search funds and/or running a business and in addition to investing are also there to provide mentorship and guidance to the searcher. Whilst the asset class has grown rapidly since the early 80s, professional search investors are still a relatively small group and mostly know each other.

In terms of size, KFS is looking to purchase businesses with ebitda between $1.5mn-$3mn- at the sweet spot of being too small for a mid-market PE fund, whilst also being out of reach for majority of ex-HNWI individuals. In terms of types of business they are looking to acquire, KFS (and search funds in general) look to acquire businesses with predictable, recurring revenues and low operational complexity (given they will be managed by rookie CEOs).

Searchers are typically looking to purchase businesses from owners approaching retirement age, who are looking for both exit liquidity and succession planning (JT has used the phrase 'succession capital' to describe the solution that searchers like KFS are providing to retiring entrepreneurs.) Deals can be sourced in multiple ways including business brokers, cold approaching and purchase of databases. Its typically a very time consuming process, with several rocks needing to be turned over, and can take take anywhere up to two years.

In terms of deal economics, at KFS the OIRs are given a very modest salary and resources to initiate their search (at more traditional search funds, the searchers have to raise a fund to cover search costs, typically upto two years). On consummation of a deal, the searcher is given some equity in the business, with this amount increasing over time, and the amount typically linked to certain return goals. It's also typically structured in such a way that KFS's equity is preferred and they need to be made whole on their investment (+ modest single digit return), before the searcher participates in any upside. While the searcher CEO is paid a salary, it is usually fairly modest and given the typical talent level, well below their opportunity cost if they had entered the corporate world post-MBA, so the carried interest is really their main way of making bank and aligning the incentives between searcher and KFS. It makes more financial + reputational sense for a searcher/OIR to either end or extend their search than consummate a mediocre/bad deal.

Searchers typically look to create value in the business once acquired, either by pursuing additional revenue channels, cutting costs and/or investing in the business. Given that the previous owner is typically approaching retirement age, in several instances the company is a lifestyle business and not necessarily cost or revenue-optimised, so there is usually some low hanging fruit to improve profitability. Early signs at Ravix look promising (although its probably too soon to judge).

Stanford Business School releases a study every couple of years on the financial performance of search funds. The most recent study was 2022, which looked at the performance of 546 search funds in US and Canada between 1984 to 2021. In total, the aggregate pre-tax IRR and MOIC of all funds in the study was 35% and 5.2x, respectively, with this number including 1) search funds that failed to consummate an acquisition (34% of total funds) and 2) search funds that produced a loss (27% of funds that consummated an acquisition), so potential returns could be higher if these left tail outcomes can be mitigated (in the most recent investor day, JT discusses how he believes the KFS model can avoid some of the pitfalls associated with traditional search funds).

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This table presents the descriptive statistics of market indices’ daily returns in the countries where the top energy companies are located. The mean (Mean, in percentage), standard deviation (Std.), skewness (Skew.), kurtosis (Kurt.) are shown from January 1, 2007 to August 31, 2022.

This research extends the conventional concepts of the bid–ask spread (BAS) and mid-price to include the total market order book bid–ask spread (TMOBBAS) and the global mid-price (GMP). Using high-frequency trading data, we investigate these new constructs, finding that they have heavy tails and significant deviations from normality in the distributions of their log returns, which are confirmed by three different methods. We shift from a static to a dynamic analysis, employing the ARMA(1,1)-GARCH(1,1) model to capture the temporal dependencies in the return time-series, with the normal inverse Gaussian distribution used to capture the heavy tails of the returns. We apply an option pricing model to address the risks associated with the low liquidity indicated by the TMOBBAS and GMP. Additionally, we employ the Rachev ratio to evaluate the risk–return performance at various depths of the limit order book and examine tail risk interdependencies across spread levels. This study provides insights into the dynamics of financial markets, offering tools for trading strategies and systemic risk management.

This paper investigates the volatility dynamics and underlying long memory features of four major cryptocurrencies—Bitcoin, Ethereum, Litecoin, and Ripple—which were selected due to their high liquidity, large trading volumes, and historical significance in the digital asset market. The long-range dependence exhibited in cryptocurrency markets is often overlooked. However, based on the strong evidence of persistent dependence in the return series, we adopt advanced volatility models that are capable of accommodating high volatility and heavy-tails, as well as the long memory properties of cryptocurrencies. Specifically, we employ long-memory extensions of the GAS (Long memory GAS) and GARCH (Fractionally Integrated Asymmetric Power ARCH) models, integrating heavy-tailed innovation distributions: the Generalized Hyperbolic Distribution (GHD) and Generalized Lambda Distribution (GLD). Standard GARCH and GAS models are included as benchmarks. The performance of the models are assessed using Value-at-Risk (VaR) estimation, backtesting (in-sample and out-of-sample) and volatility forecasting metrics. The results indicate that long memory models, particularly the FIAPARCH model, consistently outperforms the standard GAS and GARCH models in capturing tail risk and the volatility persistence. These findings emphasize the critical role of long memory in modeling the risk of cryptocurrencies, indicating that accounting for volatility persistence can significantly enhance the accuracy of risk estimates and strengthen risk management practices.

ABSTRACT This article assesses the impact of alternative assets on the performance of Brazilian private pension funds. Few studies touch on this topic in Brazil and most only investigate the addition of alternative assets and their impact on the performance. The market of open private pension funds in Brazil has been growing rapidly in recent years and gaining much relevance, especially after the announcement of the reformulation of the Brazilian pension system. In 2018, the Free Benefit Generating Plan (PGBL) and the Free Benefit Generating Life (VGBL) represented more than 94% of total assets in their sector. The Brazilian specially constituted investment funds (FIEs) of PGBL and VGBL private pension plans are characterized by their dependence on fixed income assets. Brazil currently faces an unprecedent low interest rate scenario - which, following a worldwide panorama, seems to be set for a long time - and pension fund managers must search for alternative investments that aggregate both risk premia and diversification. The results of this study may support managers in this little-discussed matter. We compare the performance of FIEs without additional alternative assets versus the portfolio with alternative assets, adding a hedge fund index, an equity mutual funds index, a commodity index, an electric power index, a public utilities index, a gold index, and a real estate index. Several performance measures were used, considering Brazilian regulations and a rebalancing strategy. Our results showed that almost all alternative assets used in this study improved the performance of the Brazilian FIEs of PGBL and VGBL private pension plans, especially the public utilities index and the hedge fund index. Some even improved the portfolio tail risk.

Data presented as median and interquartile ranges.

The exact wording of the risk categories included in the risk assessment tool.

The proportion of times each level of risk was assigned to each of the risk categories by the assessors (n = 158 pens).

Levels of risk that the assessors were asked to assign to each risk category as described in Table 1.