Introduction

Understanding the distribution of returns is essential in assessing the risk associated with financial assets. In this chapter, we will explore the comparison between the normal distribution and the actual distribution of returns for risky financial assets, particularly equities. While the normal distribution serves as a foundational model in finance, real-world returns often deviate from this idealized pattern. By delving into this comparison, we gain insights into the implications for risk assessment and the challenges posed by non-normality.

Comparing Normal Distribution with Actual Returns

The normal distribution, characterized by its bell-shaped curve, assumes that returns are symmetrically distributed around the mean. However, the distribution of returns for equities and other risky assets typically exhibits properties such as skewness and kurtosis. Skewness refers to the asymmetry of the distribution, where one tail is longer than the other. Kurtosis measures the tail heaviness of the distribution, indicating the likelihood of extreme events.

For instance, let’s consider a hypothetical example of an equity’s monthly returns. While the normal distribution assumes that extreme events are rare, real-world equities may experience significant price movements due to earnings surprises, market shocks, or other factors. As a result, the distribution of equity returns often displays fat tails, indicating a higher probability of extreme events than predicted by the normal distribution.

Implications for Risk Assessment

The assumption of normality significantly simplifies risk assessment and portfolio management. However, the deviation of real-world returns from the normal distribution challenges traditional risk models. Inaccurate risk assessment could lead to underestimation of potential losses during periods of high volatility.

Consider a portfolio manager using the standard deviation as a measure of risk. If returns exhibit fat tails, the standard deviation might not adequately capture the risk of extreme events. This could result in the portfolio being inadequately hedged against severe market downturns.