PENDEKATAN METODE MARKOWITZ UNTUK OPTIMALISASI PORTOFOLIO DENGAN RISIKO EXPECTED SHORTFALL (ES) PADA SAHAM SYARIAH DILENGKAPI GUI MATLAB

A portfolio is a combination of two or more securities as investment targets for a certain period of time with certain conditions. The Markowitz method is a method that emphasizes efforts to maximize return expectations and can minimize stock risk. One method that can be used to measure risk is Expected Shortfall (ES). ES is an expected measure of risk whose value is above Value-at-Risk (VaR). To make it easier to calculate optimal portfolios with the Markowitz method and risk analysis with ES, an application was made using the Matlab GUI. The data used in this study consisted of three JII stocks including CPIN, CTRA, and BSDE stocks. The results of the portfolio formation with the Markowitz method obtained an optimal portfolio, namely the combination of CPIN = 34.7% and BSDE = 65.3% stocks. At the 95% confidence level, the ES value of 0.206727 is greater than the VaR value (0.15512).

PENDEKATAN METODE MARKOWITZ UNTUK OPTIMALISASI PORTOFOLIO DENGAN RISIKO EXPECTED SHORTFALL (ES) PADA SAHAM SYARIAH DILENGKAPI GUI MATLAB

A portfolio is a combination of two or more securities as investment targets for a certain period of time with certain conditions. The Markowitz method is a method that emphasizes efforts to maximize return expectations and can minimize stock risk. One method that can be used to measure risk is Expected Shortfall (ES). ES is an expected measure of risk whose value is above Value-at-Risk (VaR). To make it easier to calculate optimal portfolios with the Markowitz method and risk analysis with ES, an application was made using the Matlab GUI. The data used in this study consisted of three JII stocks including CPIN, CTRA, and BSDE stocks. The results of the portfolio formation with the Markowitz method obtained an optimal portfolio, namely the combination of CPIN = 34.7% and BSDE = 65.3% stocks. At the 95% confidence level, the ES value of 0.206727 is greater than the VaR value (0.15512).

The Risk of Miscomputing the Value at Risk / O Risco de Calcular mal o Valor em Risco

Este artigo explora como o VaR (Value at Risk), que é a métrica de risco financeiro mais popular, é comumente calculado e usado. Ainda persiste um grande mal-entendido sobre essa técnica no setor financeiro, do que ela é, para que serve, como é usada e até mesmo quem deve usá-la. Embora o VaR não seja mais uma novidade, em muitas organizações, tanto na academia quanto na indústria, ele ainda é implementado da forma como foi concebido na década de 1990 como um primeiro esforço para quantificar o risco financeiro.Dado que o VaR é fortemente apoiado pela Teoria Moderna de Portfólio (Modern Portfolio Theory -MPT), e que esta, por sua vez, foi elaborada sob a suposição de que as oscilações dos sinais financeiros se comportam sob uma Distribuição de Probabilidade Normal, é assim que ainda é calculado em muitas organizações que o aplicam para controlar o negociação de ativos financeiros à vista e derivativos. Neste artigo, o uso da distribuição t de Student em escala (Scaled t-Distribution) é discutido como a melhor opção para modelar a série temporal de retornos financeiros. Os retornos modelados com essa distribuição, por sua vez, permitem que o Value at Risk seja calculado com maior precisão. Além disso, com essa distribuição, pode-se calcular a métrica de risco criada como uma grande melhoria para o VaR: The Expected Shortfall (ES), também conhecido como VaR Condicional (CVaR).Para demonstrar que a distribuição t de Student em escala é melhor para modelar sinais financeiros nos retornos de ações e, portanto, para o cálculo de VaR e ES, três gráficos de distribuições de probabilidade diferentes são gerados e sobrepostos: A distribuição empírica, a distribuição Normal e a distribuição t de Student em escala, calculadas com a técnica de estimativa de máxima verossimilhança (Maximum Likelihood Estimation).Isso é feito para cada uma das seis ações analisadas neste estudo: O FAANG (Facebook, Apple, Amazon, Netflix, and Google), mais aquele recentemente adicionado ao SP 500: Tesla.

Scenario-based risk evaluation

Risk measures such as expected shortfall (ES) and value-at-risk (VaR) have been prominent in banking regulation and financial risk management. Motivated by practical considerations in the assessment and management of risks, including tractability, scenario relevance and robustness, we consider theoretical properties of scenario-based risk evaluation. We establish axiomatic characterisations of scenario-based risk measures that are comonotonic-additive or coherent, and we obtain a novel ES-based representation result. We propose several novel scenario-based risk measures, including various versions of Max-ES and Max-VaR, and study their properties. The theory is illustrated with financial data examples.

Expected Shortfall Reliability—Added Value of Traditional Statistics and Advanced Artificial Intelligence for Market Risk Measurement Purposes

The Fundamental Review of the Trading Book is a market risk measurement and management regulation recently issued by the Basel Committee. This reform, often referred to as “Basel IV”, intends to strengthen the financial system. The newest capital standard relies on the use of the Expected Shortfall. This risk measure requires to get sufficient information in the tails to ensure its reliability, as this one has to be alimented by a sufficient quantity of relevant data (above the 97.5 percentile in the case of the regulation or interest). In this paper, after discussing the relevant features of Expected Shortfall for risk measurement purposes, we present and compare several methods allowing to ensure the reliability of the risk measure by generating information in the tails. We discuss these approaches with respect to their relevance considering the underlying situation when it comes to available data, allowing practitioners to select the most appropriate approach. We apply traditional statistical methodologies, for instance distribution fitting, kernel density estimation, Gaussian mixtures and conditional fitting by Expectation-Maximisation as well as AI related strategies, for instance a Synthetic Minority Over-sampling Technique implemented in a regression environment and Generative Adversarial Nets.

Implementation of a Commitment Machine for an Adaptive and Robust Expected Shortfall Estimation

This study proposes a metaheuristic for the selection of models among different Expected Shortfall (ES) estimation methods. The proposed approach, denominated “Commitment Machine” (CM), has a strong focus on assets cross-correlation and allows to measure adaptively the ES, dynamically evaluating which is the most performing method through the minimization of a loss function. The CM algorithm compares four different ES estimation techniques which all take into account the interaction effects among assets: a Bayesian Vector autoregressive model, Stochastic Differential Equation (SDE) numerical schemes with Exponential Weighted Moving Average (EWMA), a Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) volatility model and a hybrid method that integrates Dynamic Recurrent Neural Networks together with a Monte Carlo approach. The integration of traditional Monte Carlo approaches with Machine Learning technologies and the heterogeneity of dynamically selected methodologies lead to an improved estimation of the ES. The study describes the techniques adopted by the CM and the logic behind model selection; moreover, it provides a market application case of the proposed metaheuristic, by simulating an equally weighted multi-asset portfolio.