Annals of Finance最新文献

{"title":"Capital asset pricing model with size factor and normalizing by volatility index","authors":"Abraham Atsiwo,&nbsp;Andrey Sarantsev","doi":"10.1007/s10436-026-00492-1","DOIUrl":"10.1007/s10436-026-00492-1","url":null,"abstract":"<div><p>The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio, usually taken to be the S&amp;P 500. Winsert size effect in the CAPM, capturing a real-life feature that on average, small stocks (measured by market capitalization) have higher risk and return than large stocks. Testing CAPM involves fitting linear regressions. Our goal is to ensure that regression residuals are independent identically distributed Gaussian. In some cases, we find that including the Volatility Index as a multiplicative factor by these residuals makes them closer to that ideal. In this article, we combine these ideas to create a new discrete-time model, which includes volatility, size factor, and the CAPM. We fit this model using real-world data, prove the long-term stability of this model, and analyze the resulting capital distribution curves.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Leverage, drawdowns and risk relativity","authors":"Hans-Peter Bermin,&nbsp;Magnus Holm","doi":"10.1007/s10436-026-00491-2","DOIUrl":"10.1007/s10436-026-00491-2","url":null,"abstract":"<div><p>We develop a continuous-time framework in which the risk associated with leverage is parameterized by a dimensionless drawdown-risk index relative to an arbitrary reference asset. We further show that the growth-optimal Kelly portfolio is the unique portfolio whose relative drawdown-risk index is invariant to the reference asset. Additionally, we characterize when portfolios have equal relative drawdown-risk indices and how these indices transform under changes of reference asset. Finally, for a prescribed positive risk target, we derive the portfolio that maximizes instantaneous logarithmic outperformance relative to an arbitrary benchmark: a linear combination of the benchmark and the growth-optimal Kelly portfolio.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10436-026-00491-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pricing basket options with the first three moments of the basket: log-normal models and beyond","authors":"Dongdong Hu,&nbsp;Hasanjan Sayit,&nbsp;Frederi Viens","doi":"10.1007/s10436-026-00489-w","DOIUrl":"10.1007/s10436-026-00489-w","url":null,"abstract":"<div><p>Options on baskets (linear combinations) of assets are notoriously challenging to price using even the simplest log-normal continuous-time stochastic models for the individual assets. The paper (Borovkova et al. 2007) gives a closed form approximation formula for pricing basket options with potentially negative portfolio weights under log-normal models by moment matching. This approximation formula is conceptually simple, methodologically sound, and turns out to be highly accurate. However, it involves solving a system of nonlinear equations which usually produces multiple solutions and which is sensitive to the selection of initial values in the numerical procedures, making the method computationally challenging. In the current paper, we take the moment-matching methodology in (Borovkova et al. 2007) a step further by obtaining a closed-form solution for this nonlinear system of equations, by identifying a unary cubic equation based solely on the basket’s skewness, which parametrizes all model parameters, and we use it to express the approximation formula as an explicit function of the mean, variance, and skewness of the basket. Numerical comparisons with the baskets considered in Borovkova et al. (2007) show a very high level of agreement, and thus of accuracy relative to the true price of the basket option. In the second half of the paper, we apply the same moment-matching approach to the case of a class of time-changed models, ones where the log-normal assets in the basket are subordinated by a common random time change, and we obtain a closed-form approximation formula for basket option prices under these models also. Our formula in the time-changed case also involves a system of nonlinear equations that needs to be solved. We simplify this system of equations and eventually reduce the basket option pricing problem under these models into the problem of finding a root of a real-valued function on the real line. While this equation, which depends explicitly on the moment-generating function of the time-mixing distribution, need not have explicit solutions, we show that in examples of distributions popular in the literature, the equation can be of polynomial type, or of exponential type, whose numerical resolutions pose no difficulties. Our numerical tests, based on financially realistic parameters, show that such closed-form approximations to basket prices for this class of time-changed models also perform highly accurately.\u0000</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10436-026-00489-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Heterogeneity within teams: dominance or disparity?","authors":"Anna Calamia,&nbsp;Suting Hong,&nbsp;Pierre Mella-Barral","doi":"10.1007/s10436-026-00490-3","DOIUrl":"10.1007/s10436-026-00490-3","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Short-rate-dependent volatility models","authors":"Tim Leung,&nbsp;Matthew Lorig","doi":"10.1007/s10436-026-00488-x","DOIUrl":"10.1007/s10436-026-00488-x","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kelly trading and expected utility","authors":"Hans-Peter Bermin","doi":"10.1007/s10436-026-00487-y","DOIUrl":"10.1007/s10436-026-00487-y","url":null,"abstract":"<div><p>We study intertemporal hedging of parameter risk in a continuous-time portfolio problem with stochastic investment opportunities. Under Brownian uncertainty, we derive conditions under which an optimal expected power-utility strategy has a maximal instantaneous Sharpe ratio, or equivalently is a Kelly strategy. In general, the optimal power-utility strategy is not a Kelly strategy, because it contains an intertemporal hedge against fluctuations in the maximal instantaneous Sharpe ratio. Nevertheless, under relevant collinearity or diagonal conditions, each component of the optimal strategy can be expressed as a scaling of the corresponding component of the growth-optimal Kelly strategy. In this sense, the power-utility strategy provides a parsimonious modification of Kelly leverage, although the adjustment need not be economically small in multi-asset environments. The modification is consistent with time-diversification and provides a possible channel through which relative risk aversion inferred from observed leverage may depend on the investment horizon.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10436-026-00487-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Markov-Modulated ESG Rating Dynamics under Exogenous Environmental Regimes","authors":"Lucianna Cananà,&nbsp;Salvatore Vergine","doi":"10.1007/s10436-026-00486-z","DOIUrl":"10.1007/s10436-026-00486-z","url":null,"abstract":"<div><p>ESG ratings are increasingly used to assess firms’ sustainability profiles and to support investment, risk-management, and disclosure decisions. This paper investigates whether ESG rating dynamics depend on firm-level carbon emission intensity. We propose an exogenous-regime Markov-modulated model in which ESG rating transition probabilities vary across regimes defined by a carbon-emission-intensity index. The index is based on total CO<span>(_2)</span> emissions normalized by revenue, which controls for firm size and allows environmental conditions to be compared across companies operating at different scales. This index is discretized through a likelihood-based change-point procedure, and the resulting regime process is modeled as a Markov chain. We apply the model to annual Refinitiv ESG rating categories for 100 firms over 2015-2024. The empirical results show that ESG ratings are highly persistent, but their transition dynamics differ across environmental regimes. The regime-dependent modeling is statistically supported and improves one-step-ahead forecasting accuracy relative to the homogeneous Markov-chain benchmark, with the two-threshold model providing the best overall performance.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Risk minimization for markets driven by pure-jump additive processes via Malliavin–Mancino–Taylor type formula","authors":"Yunosuke Mukai,&nbsp;Ryoichi Suzuki,&nbsp;Nino Nagata","doi":"10.1007/s10436-026-00485-0","DOIUrl":"10.1007/s10436-026-00485-0","url":null,"abstract":"<div><p>We study quadratic risk minimization for discounted exponential asset prices driven by time-inhomogeneous pure-jump additive processes whose compensator factorizes through a deterministic time change and a family of Lévy kernels. Using Malliavin–Skorohod calculus on the canonical jump space, we derive a second-order Taylor–Clark–Haussmann–Ocone representation and combine it with the Galtchouk–Kunita–Watanabe decomposition to obtain an explicit representation of the risk-minimizing hedge ratio in incomplete markets. For exponential jump amplitudes, the denominator admits a cumulant representation, yielding closed-form expressions for this denominator in a model bank of time-varying jump kernels, including Merton, Kou, Variance Gamma, CGMY, Normal Inverse Gaussian, and double phase-type specifications. We also treat fixed- and floating-strike lookback options. A market-data-calibrated benchmark application to Henry Hub natural gas futures illustrates how the representation can be implemented from observed daily futures returns. In this calibrated experiment, the full second-order hedge reduces the terminal hedging error variance by 83.1% relative to the first-order truncation and performs competitively against stationary Kou and Black–Scholes benchmark hedges. These results lead to a practically computable second-order approximation for risk-minimizing hedges.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10436-026-00485-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An effective interest rate cap: a clarification","authors":"Mikhail V. Sokolov","doi":"10.1007/s10436-026-00484-1","DOIUrl":"10.1007/s10436-026-00484-1","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148299895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How to effectively protect the interests of small and medium-sized investors in transitional economies: empirical evidence based on China’s mixed ownership reform","authors":"Jianxiong Hu","doi":"10.1007/s10436-026-00483-2","DOIUrl":"10.1007/s10436-026-00483-2","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"22 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}