Risk Management Finals - Summary

Risk Management Finals - Summary

• Value at Risk (VAR): The expected maximum loss over a target horizon within a given confidence interval. Addresses loss exposure and worst-case scenarios. Evolved to meet SEC minimum capital requirements for financial institutions.
• VAR Formula: VAR = μ - ασ (Mean - (Standard Deviation * Z-score))
• Historical Simulation Approach: Uses past data to simulate future performance and estimate VAR. Dependent on sample data.
• Model Building Approach: Suitable for portfolios with varying positions. Follows a specific formula.
• Components of VAR: Time frame (period for which VAR is calculated) and Loss amount (calculated VAR).
• Confidence Level: Shows how reliable the VAR estimate is; higher levels give you more accurate VAR.
• Sample Problem 1 (VAR): A portfolio gain is normally distributed with a mean of $2 million and a standard deviation of $10 million at a 99% confidence level. Result: VaR is -$21,300,000.
• Expected Shortfall (ES): A better measure than VAR, that averages losses worse than VAR.
• Historical Simulation: A statistical method using historical data to estimate value at risk (VaR). Critically, it involves using past data as a guide to what happens in the future
• Bootstrap: A statistical technique that estimates the sampling distribution of a statistic (particularly when the data is non-normal). It repeatedly resamples and recalculates the statistic of interest, approximating the true sampling distribution.
• Monte Carlo: A computational method using repeated random sampling to solve complex problems that are difficult to solve analytically. Helpful for estimating VaR.
• Altman's Z-score: A financial distress prediction model to assess a company's creditworthiness. Based on five key accounting ratios.
• Power Law (Scaling Law): A statistical distribution model where a large number of small events are juxtaposed against a small number of large events. Often used in modeling phenomena like income distribution. An alternative to assuming normal distributions.
• Vasicek Model: A stochastic volatility model used for short-term interest rates. Assumes that interest rates revert to a long-term average.
• Two-Asset Case: A simplified model of the relationship between two assets assuming linearly correlated returns. It illustrates portfolio diversification. This model can help reduce overall portfolio risk. This model is also known as variance-covariance approach and is used as an alternative for calculating risk.
• Delta Balancing / Hedging: A risk management strategy used to reduce price fluctuation impact on a portfolio by managing both the underlying asset and options positions.
• Nonlinear Products: Complex investments that have payoff dependencies on several market variables. (e.g. convertible bonds).

Risk Management - Key Concepts

• Hazard Rate: The instantaneous probability of an event occurring at a given time.
• Conditional Probability: The probability of an event, considering that another event has already occurred or is occurring.
• Unconditional Probability: The probability of an event, regardless of other events.
• Conditional and Unconditional Probability These probability ideas are applied in risk modeling situations.

Portfolio Diversification

• The process of diversifying investments to minimize risk.
• Combining different investments to reduce risk, through diversification of investments in various market variables.

Merton Model

• A model that estimates a company's credit default risk.
• It assumes default occurs when the company’s asset value falls below a threshold.
• Merton's model is a complex calculation to identify accurate results.