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.

Risk and Return Analysis for Companies Registered in the Iraq Stock Exchange Based on the Sortino and Sharpe Methods

The research aims to measure the return and risk in the Iraq Stock Exchange according to the modern portfolio theory (MPT) and post-modern portfolio theory (PMPT) and identify its difference. The study was recognized with several questions, the most important of which: "Is there a difference in measuring the return and risk between the modern portfolio theory and the post-modern portfolio theory?" The companies listed on the Iraq Stock Exchange were tested to answer this question. Seventy-two companies registered in the Iraq Stock Exchange from 2006 to 2019 has selected for this research sample. The accreditation was done on many financial and statistical indicators to analyze and interpret the results using Excel. According to the post-modern portfolio theory, the study found an apparent discrepancy in the values of the return and risk indicators compared to the modern portfolio theory due to the different philosophies and calculation methods in the portfolio's construction. This study can facilitate further studies and the investors looking forward to investing in the Iraqi stock exchange.

Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory

The present study aims to develop a risk-based approach to finding optimal solutions for life extension management for offshore wind farms based on Markowitz’s modern portfolio theory, adapted from finance. The developed risk-based approach assumes that the offshore wind turbines (OWT) can be considered as cash-producing tangible assets providing a positive return from the initial investment (capital) with a given risk attaining the targeted (expected) return. In this regard, the present study performs a techno-economic life extension analysis within the scope of the multi-objective optimisation problem. The first objective is to maximise the return from the overall wind assets and the second objective is to minimise the risk associated with obtaining the return. In formulating the multi-dimensional optimisation problem, the life extension assessment considers the results of a detailed structural integrity analysis, a free-cash-flow analysis, the probability of project failure, and local and global economic constraints. Further, the risk is identified as the variance from the expected mean of return on investment. The risk–return diagram is utilised to classify the OWTs of different classes using an unsupervised machine learning algorithm. The optimal portfolios for the various required rates of return are recommended for different stages of life extension.

Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory

The present study aims to develop a risk-based approach to find optimal solutions for life extension management for offshore wind farms based on Markowitz’s modern portfolio theory, adapted from finance. The developed risk-based approach assumes that the offshore wind turbines (OWT) can be considered as cash-producing tangible assets providing positive return from the initial investment (capital) with a given risk attaining the targeted (expected) return. In this regard, the present study performs a techno-economic life extension analysis within the scope of the multi-objective optimisation problem. The first objective is to maximise the return from the overall wind assets, while the latter aims to minimise the risk associated with obtaining the return. In formulating the multi-dimensional optimisation problem, the life-extension assessment considers the results of a detailed structural integrity analysis, free-cash-flow analysis, and probability of project failure, local and global economic constraints. Further, the risk is identified as the variance from the expected mean of return on investment. The risk-return diagram is utilised to classify the OWTs of different classes using an unsupervised machine learning algorithm. The optimal portfolios for the various required rate of return are recommended for different stages of life extension.

14. Investment

Without assuming prior legal knowledge, books in the Directions series introduce and guide readers through key points of law and legal debate. Questions, diagrams and exercises help readers to engage fully with each subject and check their understanding as they progress. Part II of the Trustee Act 2000 gives every trustee the power to make any kind of investment as long as he is absolutely entitled to the assets of the trust, a power that permits trustees to hold investments jointly or in common with other persons. There are no unauthorised types of investment, but it is important to know whether the type of investment chosen was appropriate to the trust on the basis of the ‘standard investment criteria’. This chapter examines the types of investment permitted by the general law, a breach of the duty to invest with appropriate care, the significance of modern portfolio theory to trustee investments and the impact of the Trustee Act 2000 upon trustee investments. It also looks at the historical need for income production and discusses capital gains as investment returns, the standard investment criteria, the need for trustees to obtain and consider proper advice about investments, particular types of investment and investment policy.