Focus on the financial crisis since 2007, compared to the Great Depression.
Discussion on how financial theorists use probability models to understand crises.
Historical Narrative of the Crisis
Crises often described using historical narratives.
Key events leading to the financial crisis:
Bubbles in stock, housing, and commodities markets.
Collapse of stock markets in 2000 and subsequent recovery.
2007 failures in mortgage investment firms, bank runs (e.g., Northern Rock).
Government interventions to prevent further crises.
Probability Models vs. Historical Narratives
Financial theorists emphasize accumulation of small events leading to crises.
Importance of understanding underlying probabilities rather than just narrating events.
Core Concepts in Probability and Finance
Key concepts to be discussed:
Variance, covariance, regression, idiosyncratic risk, and systematic risk.
Breakdown of assumptions in financial theory:
Failure of independence.
Occurrence of outliers and fat-tailed distributions.
Historical Context of Probability Theory
Probability theory has origins dating back to the 1600s.
It provides a framework to deal with complexity in financial outcomes.
Example: Weather forecasting models as a comparison to financial forecasting.
Basic Concepts in Finance
Return on Investment
Return is calculated as the change in price plus any dividends received.
Gross return is always positive (between 0 and infinity).
Expected Value
Mathematical expectation of a random variable is a weighted sum of possible values.
Differentiates between discrete and continuous random variables.
Measures of Central Tendency
Mean (arithmetic average) and geometric mean.
Importance of the geometric mean in evaluating investments, especially when returns can be negative.
Variability and Risk Assessment
Variance
Variance measures how much returns deviate from the mean, indicating risk.
Standard deviation is the square root of variance.
Covariance
Covariance measures how two random variables move together.
Independence implies covariance equals zero.
Correlation
Correlation is a scaled version of covariance; ranges from -1 to +1.
Useful for determining relationships between variables.
Independence and Risk Management
Independence is crucial for the application of the law of large numbers in finance.
The breakdown in independence led to underestimating risks in the financial crisis.
Value at Risk (VaR) and CoVaR
VaR is a common risk measure that assumes independence in returns.
CoVaR is a newer measure that accounts for dependencies between portfolios.
Analyzing Historical Data
Stock Market Movements
Discussion of stock market trends from 2000 to 2010.
Example of Apple Inc. as a case study:
Comparison between Apple and S&P 500 performance.
Importance of idiosyncratic risks (e.g., Steve Jobs' health).
Outliers and Distribution Assumptions
Normal Distribution vs. Fat-Tailed Distributions
Traditional finance assumes returns are normally distributed.
Fat-tailed distributions, as discussed by Benoit Mandelbrot, exhibit higher probabilities for extreme outcomes.
Historical examples of extreme market movements (e.g., October 1929, October 1987) challenge normal distribution assumptions.
Conclusion
The financial crises illustrate the limitations of traditional assumptions in finance, emphasizing the need for probabilistic models that account for dependencies and fat tails.