Rosella Giacometti

Constructing an index-tracking portfolio involves closely replicating the performance of a benchmark index while minimizing deviations from it. In this paper, we propose a novel enhanced index tracking model that combines a quantile-regression-based deviation measure with linear second-order stochastic dominance (SSD) constraints. The objective is to control the tail risk of the tracking error while guaranteeing an enhancement of the portfolio return distribution relative to the benchmark. The proposed formulation leads to a linear optimization problem that remains computationally tractable under realistic portfolio constraints. The model is empirically evaluated using real-world data to assess the contribution of SSD constraints and to compare its performance with that of classical quantile regression. The empirical results show that both models outperform the benchmark index. However, when the investable universe is restricted through preselection, the proposed model delivers significant improvements in risk-return performance and tail-risk control.

The ESG score of a company is a measure of its commitment to environmental, social and governance investing standards. ESG scores are produced by rating agencies using unique and proprietary methodologies. The complexity of measurement and the lack of widely accepted standards contribute to inconsistencies across agencies. Discrepancies in ratings issued by multiple data providers are particularly relevant in portfolio optimization problems that integrate ESG objectives into the classical risk-reward framework. In this work, we specifically study the impact on portfolio composition by examining Mean-CVaR-ESG optimal portfolios, where the objective function incorporates the portfolio’s ESG score. To address ESG score discrepancies, we introduce a Distributionally Robust Optimization (DRO) reformulation of the Mean-CVaR-ESG model and assess its potential benefits. Our findings reveal a persistent divergence in optimal strategies across the investment horizon when ESG values from different rating agencies are used. We then apply the DRO approach by replacing a single provider’s ESG score with a statistic derived from the scores of five different agencies. Our results show that, in this case, the DRO approach effectively mitigates score discrepancies by significantly reducing optimal portfolio concentration while enhancing the ESG evaluation of optimal portfolios across all rating agencies.

In this paper, we propose a general bi-objective model for portfolio selection, aiming to maximize both a diversification measure and the portfolio expected return. Within this general framework, we focus on maximizing a diversification measure recently proposed by Choueifaty and Coignard for the case of volatility as a risk measure. We first show that the maximum diversification approach is actually equivalent to the Risk Parity approach using volatility under the assumption of equicorrelated assets. Then, we extend the maximum diversification approach formulated for general risk measures. Finally, we provide explicit formulations of our bi-objective model for different risk measures, such as volatility, Mean Absolute Deviation, Conditional Value-at-Risk, and Expectiles, and we present extensive out-of-sample performance results for the portfolios obtained with our model. The empirical analysis, based on five real-world data sets, shows that the return-diversification approach provides portfolios that tend to outperform the strategies based only on a diversification method or on the classical risk-return approach.

We investigate the impact of climate transition risk on the European financial system, evaluating the expected capital shortfall of the major European banks in a climate stress scenario. Following the methodology proposed by Jung et al. [(2021). “Climate stress testing”. FRB of New York Staff Report. (977).], we measure the dynamic transition risk betas and compare them to the non financial corporate loans exposure, obtained from EBA, of each bank towards the energy sector. Furthermore, we estimate the dynamic risk premium associated with the selected climate transition risk factor in order to explain and eventually exploit stock market anomalies. Finally we estimate the countries’ exposures and we find that at the end of 2022, aggregated European CRISK can be quantified in about EUR 165 bn. As far as the climate premium is concerned, we find evidence of a dynamic climate risk premium negatively correlated to transition risk exposure.

In this paper, we propose a general bi-objective model for portfolio selection, aiming to maximize both a diversification measure and the portfolio expected return. Within this general framework, we focus on maximizing a diversification measure recently proposed by Choueifaty and Coignard for the case of volatility as a risk measure. We first show that the maximum diversification approach is actually equivalent to the Risk Parity approach using volatility under the assumption of equicorrelated assets. Then, we extend the maximum diversification approach formulated for general risk measures. Finally, we provide explicit formulations of our bi-objective model for different risk measures, such as volatility, Mean Absolute Deviation, Conditional Value-at-Risk, and Expectiles, and we present extensive out-of-sample performance results for the portfolios obtained with our model. The empirical analysis, based on five real-world data sets, shows that the return-diversification approach provides portfolios that tend to outperform the strategies based only on a diversification method or on the classical risk-return approach.

Passive investment strategies, such as those implemented by Exchange Traded Funds (ETFs), have gained increasing popularity among investors. In this context, smart beta products promise to deliver improved performance or lower risk through the implementation of systematic investing strategies, and they are also typically more cost-effective than traditional active management. The majority of research on index replication focuses on minimizing tracking error relative to a benchmark index, implementing constraints to improve performance, or restricting the number of assets included in portfolios. Our focus is on enhancing the benchmark through a limited number of deviations from the benchmark. We propose a range of innovative investment strategies aimed at minimizing asymmetric deviation measures related to expectiles and quantiles, while also controlling for the deviation of portfolio weights from the benchmark composition through penalization. This approach, as compared to traditional minimum tracking error volatility strategies, places a greater emphasis on the overall risk of the portfolio, rather than just the risk relative to the benchmark. The use of penalization also helps to mitigate estimation risk and minimize turnover, as compared to strategies without penalization. Through empirical analysis using simulated and real-world data, we critically examine the benefits and drawbacks of the proposed strategies in comparison to state-of-the-art tracking models.

We estimate the risk spillover among European banks from equity log-return data via Conditional Value at Risk (CoVaR). The joint dynamic of returns is modeled with a spatial DCC-GARCH which allows the conditional variance of log-returns of each bank to depend on past volatility shocks to other banks and their past squared returns in a parsimonious way. The backtesting of the resulting risk measures provides evidence that (i) the multivariate GARCH model with Student’s t distribution is more accurate than both the standard multivariate Gaussian model and the Filtered Historical Simulation (FHS), and (ii) the introduction of a spatial component improves the assessment of risk profiles and the market risk spillovers.