Introduction

Understanding the behavior of asset return distributions is pivotal for accurate risk assessment and volatility measurement. While the normal distribution, also known as the Gaussian distribution, is often used as a benchmark, it’s crucial to recognize that real-world financial data frequently deviate from this idealized model. This chapter delves into the reasons behind these deviations, shedding light on the complexities that challenge the assumptions of normality.

Asset return distributions form the foundation of risk assessment and decision-making in finance. The normal distribution, characterized by its bell-shaped curve, assumes that most observations cluster around the mean with a symmetrical spread. However, financial markets are influenced by multifaceted factors that introduce deviations from this ideal distribution.

Factors Leading to Deviations

1) Fat Tails and Skewness: Financial data often exhibit “fat tails,” meaning that extreme events occur more frequently than predicted by the normal distribution. These tails reflect market shocks and unexpected events that can lead to significant price movements. Skewness, where the distribution is asymmetrical, further compounds deviations.

• Example: Black Swan events, such as the 2008 financial crisis, led to unprecedented market movements that the normal distribution failed to predict.

2) Volatility Clustering: Financial markets display periods of high and low volatility. This clustering of volatility is in stark contrast to the normal distribution’s assumption of constant variance.

• Example: During times of economic uncertainty, market volatility tends to increase, affecting asset returns in ways not accommodated by the normal distribution.

3) Leverage and Non-Stationarity: Leverage amplifies the impact of market movements. Additionally, financial time series are often non-stationary, with changing statistical properties over time.

• Example: High leverage in certain sectors can exacerbate price fluctuations, leading to non-normal behavior in asset returns.

Implications

Deviation from the normal distribution has profound implications for risk management and valuation. When modeling risk or estimating option prices, assuming a normal distribution can underestimate the probability of extreme events. Portfolio diversification strategies may not provide the expected risk reduction if extreme events are more frequent than assumed.