Trino-Manuel Ñíguez

Finite multivariate Gram-Charlier expansions integrate to one by construction but are hard to keep nonnegative everywhere. We study the positive counterpart of the bivariate modified multivariate Gram-Charlier (MmGC) density, the positive MmGC (PMmGC) distribution, obtained by squaring its Hermite polynomial. It is a proper density for every parameter vector and retains closed-form moments, coskewness, cokurtosis and an exact portfolio distribution. We embed it in a twostage TGARCH framework with constant or dynamic conditional correlation. A grid-based analysis at published MmGC estimates quantifies how much of the support a finite linear expansion covers with a nonnegative density. Applied to daily returns on the S&P 500 paired with the SOX semiconductor index, gold and Brent crude oil (1990-2025), the PMmGC fits the tails better and attains a higher likelihood than the positivity-restricted MmGC in every configuration, at an identical parameter count. A test of independence of the PMmGC innovations shows that higher-order spillovers matter most where correlation is weakest: for gold and oil they leave portfolio Value-at-Risk almost unchanged but roughly double the probability of a joint 1% loss and raise conditional Value-at-Risk (CoVaR) by 11-20%, whereas for the highly correlated semiconductor index correlation captures almost all joint tail risk.

We develop a cubic-augmented framework for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) in which the higher moments of returns are recovered in closed form from a cubic representation of the quantile function, and cubic-coefficient forecasts are mapped into tail-risk forecasts through two parallel routes. The framework is evaluated out of sample on eight MSCI equity indices, four developed and four emerging, over 6,880 daily observations from January 2000 to May 2026, using a rolling-window protocol with 1,000 evaluation windows at the five-day and one-day horizons. Coverage and expected-shortfall backtests show that the CAViaR-Cubic and Robust-Cubic specifications deliver correctly calibrated VaR and ES forecasts in the overwhelming majority of markets, at both coverage levels and horizons, whereas at the daily 1% level the Gaussian threshold-GARCH (TGARCH-N) benchmark is rejected in every market. The cubic forecasts dominate TGARCH-N on calibration and loss, and match the skewed-t specifications on loss while outperforming them on tail calibration, without requiring a parametric density. The results establish the cubic quantile approach as a new, stable and reliable route to VaR and ES forecasting.

We develop a distribution-based framework for ranking …nancial assets when performance measures are estimated with uncertainty and are statistically dependent across assets. The method transforms pairwise comparisons of estimated performance measures into domination probabilities, which de…ne a stochastic matrix whose Perron-Frobenius eigenvector provides a complete ranking and, after normalization, a long-only eigenportfolio. For Sharpe ratio estimators, we initially derive closed-form domination probabilities from their joint asymptotic distribution under temporally independent and identically distributed multivariate returns. The associated covariance matrix incorporates correlations, coskewness, and cokurtosis. We further extend the framework to serially dependent returns, to alternative performance measures, including the modi…ed Sharpe ratio and the VaR ratio, and to conditional and …nite-sample Edgeworth-corrected domination probabilities. An empirical application to S&P 500 constituents shows that the proposed eigenportfolio generally outperforms Sharpe ratio benchmarks across di¤erent frequencies. Block-bootstrap evidence supports the robustness of the selection and performance results.

We present a polynomial expansion of the standardized Student-t distribution. Our density, obtained through the polynomial adjusted method in Bagnato, Potí, and Zoia (2015. “The Role of Orthogonal Polynomials in Adjusting Hyperbolic Secant and Logistic Distributions to Analyse Financial Asset Returns.” Statistical Papers 56 (4): 1205–12340), is an extension of the Gram–Charlier density in Jondeau and Rockinger (2001. “Gram-Charlier Densities.” Journal of Economic Dynamics and Control 25 (10): 1457–1483). We derive the closed-form expressions of the moments, the distribution function and the skewness–kurtosis frontier for a well-defined density. An empirical application is also implemented for modeling heavy-tailed and skewed distributions for daily asset returns. Both in-sample and backtesting analysis show that this new density can be a good candidate for risk management.

Purpose: The authors apply their method to analyze which portfolios are capable of providing superior performance to those based on the Sharpe ratio (SR).Design/methodology/approach: In this paper the authors illustrate the use of conditional copulas for identifying differences in alternative portfolio performance strategies. The authors analyze which portfolios are capable of providing superior performance to those based on the SR.Findings: The results show that under the Gaussian copula, both expected tail ratio (ETR) and skewness-kurtosis ratio portfolios exhibit remarkably low correlations respecting the SR portfolio. This means that these two portfolios are different respecting the SR one. The authors also find that copulas which focus on either the upper tail (Gumbel) or the lower tail (Clayton) render significant differences. In short, the copula analysis is useful to understand what kind of equity-screening strategy based on its corresponding performance measure (PM) performs better in relation to the SR portfolio.Practical implications: Copula methods for evaluating relative tail forecasting performance provide an alternative tool when forecast differences are very small or found non statistically significant through standard tests.Originality/value: Our copula methods to evaluate models' performance differences are significant because when models' performance is rather similar, conclusions on statistical differences, can be defective as they may hinge on the subsample type or size used, leading to inefficient investment decisions. Our method based in copula is novel in this research topic.

The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of dynamic equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio of cryptocurrencies by implementing backtesting techniques and for different risk measures: value-at-risk, expected shortfall and median shortfall. The results support our proposal showing that the SNP-DCC model has better performance for lower confidence levels than the SNP-DECO model and is more appropriate for portfolio diversification purposes.

The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of Dynamic Equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio on cryptocurrencies by implementing backtesting techniques and for different risk measures: Value-at-Risk, Expected Shortfall and Median Shortfall. The results support our proposal showing that the SNP-DCC model has better performance for a smaller confidence level than the SNP-DECO model, although both models perform similarly for higher confidence levels.

In this paper we show that flexible probability distribution functions, in addition to being able to capture stylized facts of financial returns, can be used to identify pure higher-order effects of investors' optimizing behavior. We employ the five-parameter weighted generalized beta of the second kind distribution—and other density functions nested within it—to determine the conditions under which risk averse, prudent and temperate agents are diversifiers in the standard portfolio choice theory. Within this framework, we illustrate through comparative statics the economic significance of higher-order moments in return distributions.