Elliot Book Chapter 10: Risk Modeling Flashcards

Risk models allow professionals to predict how decisions influence the variability of future results.
Modeling methods are categorized into three groups: methods based on historical data, methods based on expert input, and methods combining both.

Empirical Probability Distribution: Also known as $a posteriori$ probability, this is based on actual experience or historical data. It assumes observed values define the probabilities of future variable values.
Theoretical Probability Distribution: Constructed using mathematical formulas as a statistical reference. Risk analysts use this when historical data points are insufficient.
Normal Distribution: Often represents securities and stock prices; it generates a bell-shaped curve with tails extending indefinitely to represent low-probability, high-severity catastrophic events.
Extreme Value Theory (EVT): A statistical tool for estimating extreme deviations from the median. It addresses the tail of a distribution to analyze unlikely but possible downside risks (e.g., $100$ -year floods or earthquakes).
Regression Analysis: Estimates relationships between a dependent variable (the forecast) and an independent variable. It seeks an equation for a line to plot subsequent years, though accuracy decreases when forecasting far into the future.

Preference Among Bets: Converts expert opinion into probabilities by having experts choose sides on a bet regarding specific events. This is useful for political or legal risk where data is scarce.
Judgments of Relative Likelihood: Experts compare potential outcomes as more, less, or equally likely relative to known probabilities. This method is susceptible to unintentional bias toward familiar events.
Delphi Technique: A collaborative strategy to reach a group consensus through anonymous, repeated rounds of questionnaires where responses are refined after each round.

Monte Carlo Simulation: Uses computer programs to randomly select values for variables according to a probability distribution, generating thousands of possible scenarios to create an outcome distribution.
Fuzzy Logic: Assigns values to indefinite data fields for more accurate probability. It converts descriptive language (e.g., "too cold" or "just right") into mathematical equivalents based on degrees of truth rather than binary true/false values.

Decision Tree Analysis: Examines the uncertainties, costs, and gains of decision alternatives to select the most effective strategy. It uses pathways leading to outcomes; quantitative analysis assigns expected values and probabilities to each pathway.
Event Tree Analysis: Analyzes the consequences of accidental events rather than decisions. It follows the progression of an accident through barriers (e.g., alarm systems) that either function or fail.
Barrier logic: In event trees, the pathway splits based on the success or failure of a barrier, with the sum of outcome probabilities totaling $1$ .

Influence diagrams provide a holistic visual graph of factors related to a decision, including uncertainties and interdependencies.
Nodes:
- Decision Nodes: Represented by rectangles.
- Variables: Represented by ovals.
- Benefits/Costs: Represented by diamonds.
Comparison: Unlike decision trees, which are often binary and best for one-time decisions, influence diagrams show an overview of all variables and are suitable for ongoing decision-making processes.

Correlation: A statistical relationship between variables, expressed as a coefficient from $-1$ to $+1$ . Positive correlation means variables move in the same direction; negative means opposite directions.
Covariance: The relative association between variables moving in tandem or independently.
Correlation vs. Causality: Correlation does not imply causality, which measures cause-and-effect influence.
Correlation Matrix: A report showing correlation for pairs of risk sources; it always has a value of $+1$ along the diagonal.

Modern Portfolio Theory (MPT): States that investors can optimize risk and return through diversification.
Efficient Frontier: The collection of security combinations generating the highest expected return for a given level of risk or the lowest risk for a given return.
Nonfinancial Assets: While less liquid and divisible than financial assets, nonfinancial assets (e.g., real estate) provide diversification because they are often largely uncorrelated with financial risk sources.

Value at Risk (VaR): A threshold value representing the probability of a loss on a portfolio exceeding a certain amount over a short horizon. It quantifies potential loss in simple monetary terms.
Conditional Value at Risk (CVaR): Determines the likelihood of a loss given that the loss is greater than or equal to the VaR, effectively addressing the tail of the distribution.
Earnings at Risk (EaR): The maximum expected loss of earnings within a specific degree of confidence (e.g., $95\,\%$ ). It uses Monte Carlo simulations to model the influence of factors like sales and production costs.