Relative measures of team heterogeneity commonly used in economics and finance tend to capture dominance or concentration—the extent to which one member is superior to all others. We show that, by modifying the denominator, alternative measures can rather capture disparity or spread—the extent to which half the members are superior to the other half. We illustrate empirically the benefits of distinguishing between dominance-heterogeneity and disparity-heterogeneity in characterizing the composition of venture capital syndicates.
How to manage the non-dividend behavior of state-owned enterprises is not only a key part of protecting the interests of small and medium-sized investors, but also an inevitable requirement for implementing the mandatory dividend policy and deepening the reform of state-owned enterprises in transitional economies. This paper takes China as representative of transitional economies, discusses the impact of mixed ownership reform on the dividend behavior of state-owned enterprises from the two dimensions of shareholding ratio and appointed executives, and manually collects data on the nature, shareholding ratio and appointed executives of the top ten shareholders disclosed in the annual reports. The empirical findings are as follows: (1) Appointing executives to state-owned enterprises by non-state-owned shareholders can significantly enhance the cash dividend level of state-owned enterprises, while simply increasing the shareholding ratio of non-state-owned shareholders has no significant effect on the dividend level of state-owned enterprises. (2) After local governments launch debt governance actions, the role of mixed ownership reform in improving the dividend level of state-owned enterprises has weakened. (3) In regions with high marketization level and media attention, local government debt governance has a particularly significant negative moderating effect on the positive correlation between mixed ownership reform and the dividend level of state-owned enterprises. This paper will not only better promote the implementation of various policies of the reform of state-owned enterprises to obtain the best implementation efficiency, but also provide more beneficial enlightenment for the protection of the interests of small and medium-sized investors in transitional economies.
A classic problem in finance is the question of how an investor should optimally allocate wealth over one risky and one risk-free asset. This article reconsiders this theory under the assumptions that (1) the investor’s objective is to maximize the intertemporal growth rate of their wealth, (2) that the investor can make portfolio adjustments only in discrete time, and (3) that the risky asset is defined in each period according to only its mean return and the standard deviation thereof. This problem has been resolved only for continuous time. Here, the discrete time strategy for optimal capital growth is resolved for two different methodologies, and it is shown that the continuous time model is recoverable as a limit version of each of the two discrete time models. Finally, both of the methodologies considered lead to the same first-order Taylor’s approximation formula, which always gives a more accurate approximation to the true optimal discrete time strategy than does the continuous time strategy.
We introduce Onflow, a reinforcement learning method for optimizing portfolio allocation via gradient flows. Our approach dynamically adjusts portfolio allocations to maximize expected log returns while accounting for transaction costs. Using a softmax parameterization, Onflow updates allocations through an ordinary differential equation derived from gradient flow methods. This algorithm belongs to the large class of stochastic optimization procedures; we measure its efficiency by comparing our results to the mathematical theoretical values in a log-normal framework and to standard benchmarks from the ’old NYSE’ dataset. For log-normal assets with zero transaction costs, Onflow replicates Markowitz optimal portfolio, achieving the best possible allocation. Numerical experiments from the ’old NYSE’ dataset show that Onflow leads to dynamic asset allocation strategies whose performances are: a) comparable to benchmark strategies such as Cover’s Universal Portfolio or Helmbold et al. “multiplicative updates” approach when transaction costs are zero, and b) better than previous procedures when transaction costs are high. Onflow can even remain efficient in regimes where other dynamical allocation techniques do not work anymore. Onflow is a promising portfolio management strategy that relies solely on observed prices, requiring no assumptions about asset return distributions. This makes it robust against model risk, offering a practical solution for real-world trading strategies.
Stock market traders who trade because of information they possess reveal that information to the rest of the market in the process of bidding: if the information is positive they bid up the price, and if it is negative they lower it. New information constantly develops and is brought to the market in this way, and because it influences prices, it ultimately influences the allocation of investments by firms. Using a new approach, we estimate the flow of this information and the price of that information (different from the stock price), and thus the total value of that information, for each stock, and then sum up this value across all stocks, obtaining an estimate of the total value of the dynamic flow of information in the stock market as a whole. This requires digesting the records of millions of stock orders (including cancelled orders, not just executed trades) to construct the dynamic limit order book and estimate the information flow and value from its structure. Our results support the notion that the cross-correlation of price impact across stocks is consistent with the capital asset pricing model: there is a single systematic component of price impact, and this is driven by the volatility of the systematic component of the stock market. This result suggests that by separating the underlying information into two components, systematic and idiosyncratic, informed traders distinguish between productive assets that have a systematic impact on the economy and those that can be diversified.
We aim to address the challenge of identifying an ideal long-term arbitrage strategy that can adapt to an individual’s market perspective. In this research, we expand upon the existing body of knowledge regarding optimal asset allocation by employing a reinforcement learning algorithm rooted in a Markov Decision Process. The state space of this process is defined by estimating a Hidden Markov Chain (HMC), which serves to characterise the market dynamics. Our agent acquires knowledge about the market at each time step through this characterisation, employing the MAP algorithm to determine an optimal strategy. We then extend the agent’s state space to incorporate a physical risk index and a climate transition risk index. After showing the current limits to the integration of such indices, we explore three possible scenarios for the materialisation of climate risks on market regimes, which could be integrated into climate stress tests, and analyse the behaviour of our agent in each of these scenarios. This article therefore illustrates the relevance of estimating an HMC to construct resilient allocation strategies that could be used in climate stress tests that make assumptions about the impact of climate change on volatility.
We propose a novel sentiment-based index of global financial stress for the period between January 2004 and July 2025. It builds on the dictionary comprising English terms related to financial instability and selected with the aid of more than 200 large language models. The index represents the first principal component from the data series measuring the intensity of search in Google for these terms. It notably spikes with the GFC in September–October 2008, the outbreak of COVID-19 in March 2020, the onset of the Ukrainian conflict in February 2022 and the turmoil in the US banking sector in March 2023. The index is not driven by the extant financial stress or uncertainty measures, exhibiting moderate predictive power for some of them. Furthermore, it produces a detrimental effect on global real economic activity when the latter is in decline. The index Granger causes the worldwide frequency of currency crises, while exhibiting bidirectional linkages with the frequency of banking crises, triple episodes involving banking, currency and debt crises, and the implementation of macroprudential policy measures. Finally, we show that the dictionary underlying our global index can apply to elaborate country-level financial stress indices, using the USA and the UK as an example.
We develop a discrete-time Markov process model for group lending with joint liability to analyze repayment dynamics, income sustainability, and optimal contract design in microfinance. Borrower groups transition between application, beneficiary, delay, and re-application states, with transition probabilities determined by repayment success, delay persistence, partial repayments, and re-entry mechanisms. Using the stationary distribution of the resulting Markov chain, we derive closed-form expressions for expected discounted group income under both full and partial repayment regimes. The analysis shows that expected income increases with repayment success, re-entry probability, and partial repayment effectiveness, while higher delay persistence and default risk substantially reduce long-run wealth. We derive an endogenous optimal interest rate satisfying a lender break-even condition with operational costs and joint-liability spillovers. The resulting pricing rule generalizes zero-net-present-value loan rates to environments with delay risk and burden sharing. A sensitivity analysis indicates that larger borrower pools reduce equilibrium interest rates through risk sharing, whereas higher default burdens and costs necessitate higher rates. The modelling approach provides a tractable analytical basis for pricing and sustainability in joint-liability microfinance lending.
We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that is expressed in terms of a characteristic function. We provide examples of models in which the characteristic function can be computed analytically and, thus, the value of European options is explicit. Numerical implementation to produce the implied volatility is also presented.
In the context of micro-finance, a group of individuals undertake business projects that may interfere with one another. A contagious default happens if one person's project failure leads to the default of another group member. In this paper, we apply a probabilistic approach to analyze the impact of such contagion among investment group members. Firstly, a general formula is provided to compute the group survival probability with the presence of contagion effect. Then, special cases of this probability model are examined in detail. In particular, we show that if the investment group is homogeneous, defined in the paper, then including more members into the group will eventually lead to default with probability 1. This differs from the non-contagious scenario, where the default probability decreases monotonically with respect to the group size. Afterwards, we provide an upper bound of the optimal group size under the homogeneous setup; so, one can run a linear search within finite time to locate this optimizer.
This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock capitalization processes, we establish a conditional McKean-Vlasov system to study the market dynamics coupled to the expected trading volume of investors. We show that optimal arbitrage can be characterized as a solution of a Cauchy PDE constructed by the volatility terms in the market model. The structure of the market dynamics can be relaxed, and we provide a theoretical framework to study a general mean-field system, where the interaction is characterized by a joint distribution of wealth and strategies. In this setting, the optimal relative arbitrage constitutes the strong equilibrium of an extended mean-field game. We provide conditions for the existence and uniqueness of the mean-field equilibrium. We further prove the propagation of chaos result for the finite-player game counterpart, and demonstrate that the Nash equilibrium converges to the mean field equilibrium when the population grows to infinity.
Many countries impose regulatory restrictions on lending rates known as interest rate caps. In most cases, these restrictions apply to the effective (rather than nominal) interest rate, a measure which incorporates all commissions and fees associated with a loan. Because the effective interest rate is the internal rate of return (IRR) of the loan's cash flow stream, this regulatory rule becomes ambiguous for loans that do not have a conventional IRR. This paper resolves this ambiguity. We begin by clarifying the concept of IRR. We axiomatize the conventional definition of IRR (as a unique root of the IRR polynomial) and demonstrate that any extension to a larger domain necessarily violates a natural axiom. Building on this result, we show that there is a unique extension of the interest rate cap to all loans consistent with a set of economically meaningful axioms. The rule we characterize takes the form of a net present value test. This result is general, and applies to any setting where one wishes to extend an IRR-based threshold rule to arbitrary cash flows. Applications include lending and deposit rates regulation, investment screening, and capital budgeting, where the standard decision rule accepts a project if its IRR exceeds the hurdle rate.
This paper introduces an interval-valued extension of the internal rate of return (IRR). This extension is motivated by the inability to assign to an investment project a particular rate of return satisfying a set of reasonable axioms. We demonstrate that there exists an essentially unique extension consistent with a natural set of axioms. Notably, in the most significant case, the extension maps a project to an interval with the lower and upper bounds defined by the minimal and maximal roots of the IRR polynomial, respectively. This result effectively reconciles several existing generalizations of the IRR, all of which yield values within this interval. The interval-valued IRR preserves the essential properties of the conventional IRR, thereby enhancing the ranking of investment projects by their rate of return. Furthermore, it serves as a robust extension of the IRR for measuring portfolio performance and making accept/reject investment decisions.
We present a lattice-based algorithm to price both European and American-style derivatives under the same fractional Brownian motion environment in which Hu and Oksendal (2003), Necula (2004), and Zhuang and Song (2023) obtain explicit-form formulas for European options. To manage the path-dependency induced by the asset value process, we apply a procedure recalling the forward shooting grid method. Hence, we discretize the asset evolution by constructing a grid made up of a limited number of representative buckets at each time step. For each bucket in the grid, we establish a binomial dynamics to identify the successors at the next observation epoch. Since the grid is composed by representative buckets, it may occur that successors do not appear in the grid. In these cases, we invoke interpolation techniques to proceed backward on the grid and compute the derivative price at inception. Numerical investigations show the accuracy and efficiency of the proposed model.
This paper distinguishes itself from previous studies and contributes to the literature by estimating a green premium using a factor model framework. Specifically, we propose a two-factor model, where bond returns are explained not only by a systemic market risk factor but also by a systemic green risk factor. Using the Fama and MacBeth regression approach on a sample of Euro-denominated green and conventional bonds over the period 06.11.2014–30.06.2021, we estimate the green premium disentangling its two components: the sensitivity to systemic greenness (i.e. magnitude of risk) and the price of green risk. Three main results emerge from our research. First, we find that the price of green risk is significant and positive albeit small. Second, the sign of the green premium is substantially driven by the issuer macro sector rather than by the green label, being on average negative for Financial bonds and positive for Government and Non-Financial ones, whereby this difference can be explained by a more direct exposure to green systemic risk in the latter two cases. Third, looking at the dynamics of the green risk price we find it decreases to almost zero as the bond market reaches a new normal, but it becomes negative during Covid-19 pandemic, suggesting greenness is considered a benefit in periods of financial distress caused by negative economic shocks.
This paper develops a theoretical model incorporating return uncertainty to examine the interaction between monetary policy and capital regulation on bank risk-taking. Even without aggregate risk, uncoordinated policies can elevate systemic risk. Bank decisions depend on both monetary policy rates and capital requirements. The analysis shows that restrictive monetary policy, when not aligned with capital regulation, amplifies bank risk-taking through a risk appetite channel, where high interest rates and stringent capital thresholds jointly increase systemic risk. A numerical example with realistic parameters illustrates these effects. Aligning these policies mitigates excessive risk-taking and supports financial stability.
Small and medium enterprises (SMEs) play a central role in driving economic development and innovation. Access to finance is central for their growth and sustainability, particularly as they navigate the multifaceted challenges posed by climate change. Small and medium enterprise access to finance is challenging to quantify accurately. Utilizing composite indicators offers a potential solution, albeit one requiring meticulous design and implementation. Through this paper, we show how to improve the robustness to methodological assumptions of the European Investment Fund Small and Medium Enterprise Access to Finance Index, enhancing its reliability and depth of analysis. A robust index is central for conveying a clear message and standing up to scrutiny, because its results remain stable regardless of the specific formula used to compute it. The second aim of the paper is to design a robust index for SME green performance and support. The index aims at measuring both the performance of SMEs in adopting sustainable and green practices and the support they receive from public policies to facilitate these efforts. The third aim of the paper is to propose a new conceptual framework linking SME access to finance and green performance and support. We aim at offering a holistic approach to understand the interplay between financial access and green business practices and enhance SME competitiveness, sustainability, and economic resilience in EU27.
This paper introduces a novel voting-based approach to forecasting the equity premium, emphasizing directional consistency and robustness to structural change. Using a comprehensive dataset of 155 macroeconomic, financial, and technical predictors spanning January 1960 to December 2022, we develop a two-step framework that combines statistical screening with voting-based model weighting. Empirical results show that our method consistently outperforms traditional forecast combination techniques as well as several sophisticated alternatives-including LASSO, Elastic Net, and dynamic factor models. It nearly doubles out-of-sample forecast accuracy relative to standard benchmarks and delivers substantial economic gains for mean-variance investors, as measured by improvements in Certainty Equivalent Returns. Notably, the method excels during recessionary periods by adaptively emphasizing predictors-such as interest rates, volatility, and labor market indicators-whose importance rises in turbulent conditions. These results underscore the method's advantages in high-noise, high-uncertainty environments, making it a valuable tool for asset allocation, risk management, and policy analysis.
Economic sanctions have recently become a prominent tool in international policymaking. However, the mechanisms through which sanctions are transmitted and their impact on the domestic financial sector remain unclear. This paper employs a calibrated New Keynesian small open economy model to analyze the transmission channels of sanctions-induced terms of trade shocks and their impact on the economy. The rise in the domestic prices of imports is a crucial channel through which trade restrictions affect the economy due to the production sector’s reliance on imported investment goods. The findings indicate that both export and import sanctions lead to similar outcomes: a fall in investment caused by a 10
