What are the different types of quantitative risk analysis techniques?

I believe Sensitivity Analysis is a pivotal quantitative risk assessment method in project management. It systematically evaluates the impact of changing individual variables, helping pinpoint the factors most affecting project outcomes. By highlighting vulnerabilities and key drivers, it enables focused risk management strategies. This approach, through a methodical examination of influential aspects, aids decision-makers in optimizing resource allocation and refining mitigation plans, contributing to more resilient and informed project management.

An important aspect that’s very easy to overlook is always aligning the sensitivity analysis with the business or project goals. That way you can help to determine what goals may be harder to achieve or what goals have a higher sensitivity and plan accordingly.

Sensitivity analysis tests the impact of changing variables on outcomes, similar to adjusting lighting in a photograph. In economics, it helps understand which factors affect results the most. For instance, in a lemonade stand, it examines how altering costs or prices influences profits. This analysis guides decision-making by highlighting key drivers of success.

A análise de sensibilidade muitas vezes está ligada a robustez de um modelo ou projeto. E me arrisco a dizer, que o dizem sobre analise de sensibilidade esta muito ligado ao tema de Gestão de Risco de Modelos. Hoje no Brasil podemos observar as citações resumidamente das atribuições de risco de modelo pela resolução 4557/17. Mas como microeconomista/microeconometrista, digo que análise de sensibilidade não está apenas olhando para o modelo e se seus resultados estão sendo afetados. Na ciência econômica existe, por exemplo, a já tão consagrada e muito conhecida, análise de elasticidade, tanto direta quanto cruzada, elasticidade é sinônimo de sensibilidade, resposta, reação de uma variável, em face de mudanças em outras variáveis.

Sensitivity analysis is often linked to the robustness of a model or project. And I dare say, what they say about sensitivity analysis is very linked to the topic of Model Risk Management. Today in Brazil we can see the summary citations of model risk assignments by resolution 4557/17. But as a microeconomist/microeconometricist, I say that sensitivity analysis is not just looking at the model and whether its results are being affected. In economic science, there is, for example, the already well-established and well-known elasticity analysis, both direct and crossed. Elasticity is synonymous with sensitivity, response, reaction of a variable, in the face of changes in other variables.

VaR vs Expected Shortfall (CVaR). VaR represents the maximum potential loss at a certain confidence level, with a probability of 1–α, where α is the chosen significance level. It answers the question: "What value of a given portfolio is at risk? ES, also known as Conditional Value at Risk (CVaR), represents the expected loss when it exceeds the limit set by VaR. It focuses on the tail end of the distribution of returns. It answers the question: "If things go bad, what could the expected loss be? VaR provides the maximum loss over a specific confidence interval and ES (CVaR) calculates the average loss beyond this threshold. As for the best risk measure for investments, it depends on the specific needs and risk tolerance of the investor.

I believe Scenario Analysis is a vital quantitative risk assessment tool that involves examining diverse future scenarios to assess their impact on a project. By exploring various possibilities and evaluating potential risks and opportunities, this method aids strategic planning and proactive risk management. It provides a comprehensive view of how key variables can influence outcomes, helping organizations adapt and enhance the robustness of their plans in the face of uncertainties.

Scenario analysis resembles planning for different situations during a road trip. In economics, it evaluates how various events or conditions can affect plans. Prior to a capital raise, scenarios are created for best, worst, and moderate cases. This approach enables banks/lenders to anticipate potential outcomes, manage risks, and make informed choices.

A análise de cenários se tornou uma técnica indispensável em avaliação quantitativa de risco. Os cenários nada mais são que possibilidades esperadas, ou seja, caminhos possíveis que os dados poderão tomar. Numa análise de cenários sempre vai existir no mínimo 3 caminhos e/ou cenários: 1 - Cenário base (base line / benchmark); 2 - Cenário Otimista (positivo / up) 3 - Cenário Pessimista (negativo / down) Esta é a fundamentação básica de uma análise de cenários. Para isto os profissionais e pesquisadores utilizam diversas técnicas e modelos para tentar desenhar, no mínimo, esses 3 caminhos/cenários. Com isto, é possível estimar as possibilidades ruins, boas e estáveis.

Scenario analysis has become an indispensable technique in quantitative risk assessment. Scenarios are nothing more than expected possibilities, that is, possible paths that the data could take. In a scenario analysis there will always be at least 3 paths and/or scenarios: 1 - Base scenario (base line / benchmark); 2 - Optimistic Scenario (positive / up) 3 - Pessimistic Scenario (negative / down) This is the basic foundation of a scenario analysis. For this, professionals and researchers use different techniques and models to try to design, at least, these 3 paths/scenarios. With this, it is possible to estimate the bad, good and stable possibilities.

Monte Carlo simulation involves running multiple random scenarios, akin to guessing party guest numbers. In economics, it quantifies uncertainties by generating numerous possible outcomes based on historical data. For investments, it models different returns to assess risks and make sound decisions. This technique provides a range of potential results while factoring in probabilities and helps manage uncertainty.

A Simulação de Monte Carlo é bastante utilizada na avaliação e estimação de cenários, pois usa a distribuição de probabilidade dos dados para gerar inúmeras possibilidades (comportamentos futuros). O Método de Monte Carlo consiste em simular uma amostragem aleatória repetida vezes para obter a probabilidade de ocorrência de uma série de resultados de um evento incerto. Por isso "Simulação" de Monte Carlo. Quando se pensa em cenários, para um evento com característica temporal, se pensa em simulação de monte carlo.

Monte Carlo Simulation is widely used in evaluating and estimating scenarios, as it uses the probability distribution of data to generate numerous possibilities (future behaviors). The Monte Carlo Method consists of simulating random sampling repeatedly to obtain the probability of occurrence of a series of results of an uncertain event. Hence "Monte Carlo Simulation". When you think about scenarios, for an event with a temporal characteristic, you think about Monte Carlo simulation.

Using a decision tree is similar to making a flowchart for decisions. Think of it as picking the best path. If you’re deciding between vacation spots, you start at the top with choices like beach or mountains. Each choice leads to different outcomes with their own probabilities. By following the tree, you can see which option has the highest chance of giving you a great vacation. It's a helpful tool that simplifies choices and shows the likely results, guiding you towards making smarter decisions.

A árvore de decisão é uma excelente ferramenta para a avaliação/estimação de cenários, quando os dados apresentam (não somente) características descritivas. A árvore de decisão é um método bastante robusto e muito utilizado no campo de aprendizagem de máquina e inteligência artificial, pois possibilidade a criação de regras quando as variáveis se relacionam. Tais regras formam os nós e os ramos, originando uma estrutura semelhante a uma árvore. Tais regras são as alternativas que são geradas quando as informações se cruzam, demonstrando as probabilidades condicionadas a esse relacionamento. Em suma, é uma método que mostra os possíveis comportamentos futuros de um evento de interesse.

The decision tree is an excellent tool for evaluating/estimating scenarios, when the data presents (not only) descriptive characteristics. The decision tree is a very robust method and widely used in the field of machine learning and artificial intelligence, as it allows the creation of rules when variables are related. These rules form nodes and branches, creating a structure similar to a tree. Such rules are the alternatives that are generated when information intersects, demonstrating the probabilities conditioned on this relationship. In short, it is a method that shows the possible future behaviors of an event of interest.

The VaR is a very limited risk measure, especially under the normality assumption. Fortunately, the industry and regulators have moved beyond using (a single) VaR.

Value-at-Risk is like a safety net that estimates the maximum amount you could potentially lose on your investments. It helps answer the question, "How much could I lose in a worst-case scenario?". VaR calculates the potential loss based on historical data and statistical analysis. For example, if your VaR is $100 million. VaR helps manage risk by giving you an idea of the potential downside, so you can make informed investment decisions and set appropriate safeguards for your portfolio.

O Valor em Risco é uma métrica consagrada, principalmente no mercado financeiro, como um dos principais métodos de avaliação de risco de mercado. Consistem em estimar, em condições normais de temperatura e pressão, o pior cenário possível de um evento por um período de tempo e nível de confiança. Muitas vezes utilizado para estimar a pior perda de um portfólio ou de um ativo. É uma modelo que se alimenta de volatilidade. O VaR é muito utilizado no setor bancário como métrica de risco de mercado. Muito utilizado no cálculo do RAROC para a estimativa do capital econômico ajustado ao risco, bem como nas estimativas de Ajuste ao Risco no IFRS 17.

Value at Risk is an established metric, mainly in the financial market, as one of the main methods for assessing market risk. They consist of estimating, under normal temperature and pressure conditions, the worst possible scenario of an event for a period of time and level of confidence. Often used to estimate the worst loss for a portfolio or asset. It is a model that feeds on volatility. VaR is widely used in the banking sector as a market risk metric. Widely used in calculating RAROC to estimate capital risk-adjusted economic scenario, as well as in the Risk Adjustment estimates in IFRS 17.

Tendo formação em economia, não poderia deixar de mencionar que as Análises Estáticas Comparativas, bem como as de Equilíbrio Geral são ferramentas muito poderosas para a avaliação e estimação de cenários. Outra ferramenta bastante útil são os Modelo Dinâmico Estocástico de Equilíbrio Geral (DSGE). Esse modelo é uma forma poderosa de se estimar e avaliar Foward-Looking, pois permite simular um sistema artificial em que possibilita entender os choques causados por alterações dentro do sistema, ou seja, estimar e avaliar possíveis cenários onde se tem um sistema estável, um sistema otimista e um sistema estressado (pessimista).

Quantitative risk analysis techniques provide a rigorous and structured approach to risk assessment compared to qualitative methods. They assign numerical values to probabilities and outcomes, offering more precise insights into risk impacts. This is especially useful for complex projects or uncertain situations. Quantitative techniques quantify potential losses or gains, identify interdependencies between risks, model uncertainties, and aid in risk mitigation and contingency planning. These methods help prioritize risks, allocate resources effectively, and guide decision-making under uncertainty. Overall, quantitative risk analysis enhances financial performance and informs strategies for managing complex risks.