Kurtosis and Skewness in Finance

In finance, understanding the distribution of data is crucial for risk management and investment decision-making. While standard deviation measures the spread or volatility of data around its mean, skewness and kurtosis provide insights into the shape of the distribution, revealing characteristics beyond volatility alone.

Skewness

Skewness describes the asymmetry of a probability distribution. A symmetrical distribution, like the normal distribution, has a skewness of zero. A positive skew (right skew) indicates that the tail on the right side is longer or fatter than the tail on the left. This implies that there are more extreme positive values. In financial terms, a positively skewed asset may exhibit occasional large positive returns, though negative returns are more frequent.

Conversely, a negative skew (left skew) indicates a longer or fatter tail on the left side, suggesting more frequent large negative returns. Investors often dislike negative skew because it implies a higher probability of substantial losses. Assets with embedded insurance-like features, such as out-of-the-money put options, tend to exhibit negative skew.

Mathematically, skewness is the third standardized moment of a distribution. A simple interpretation is that it quantifies the degree of asymmetry around the mean.

Kurtosis

Kurtosis describes the “tailedness” of a probability distribution. It measures the concentration of values in the tails compared to the rest of the distribution. A distribution with high kurtosis (leptokurtic) has heavier tails and a sharper peak than the normal distribution, implying a higher probability of extreme values (both positive and negative). A distribution with low kurtosis (platykurtic) has thinner tails and a flatter peak.

Excess kurtosis is kurtosis relative to the normal distribution, which has a kurtosis of 3. Therefore, excess kurtosis is calculated as kurtosis minus 3. A positive excess kurtosis indicates a leptokurtic distribution, while a negative excess kurtosis indicates a platykurtic distribution.

In finance, leptokurtic distributions are often associated with higher risk. Assets with high kurtosis are more likely to experience extreme price swings, which can lead to significant gains or losses.

Mathematically, kurtosis is the fourth standardized moment of a distribution.

Applications in Finance

Skewness and kurtosis are valuable tools in portfolio management and risk assessment. For example:

• Risk Management: Identifying assets with significant negative skewness can help investors manage downside risk. Similarly, understanding kurtosis helps estimate the likelihood of extreme events, which is crucial for stress testing portfolios.
• Option Pricing: Skewness and kurtosis can affect option prices. Option pricing models that assume a normal distribution may underestimate the prices of options on assets with non-normal distributions.
• Hedge Fund Analysis: Hedge fund strategies often exhibit non-normal return distributions. Analyzing skewness and kurtosis can help investors understand the risk profiles of these funds.
• Investment Strategy: Some investors actively seek assets with positive skewness, aiming to capture the upside potential while mitigating downside risk.

By incorporating skewness and kurtosis into their analysis, financial professionals can gain a more complete understanding of the risks and opportunities associated with different investments, leading to more informed and effective decision-making.