Beyond standard deviation: How skewness and kurtosis capture market extremes

Risk management is one of the critical pillars of successful investing because risk and return are inseparable. Every investment decision carries uncertainty, and the challenge lies in balancing the pursuit of returns with the protection of capital. The goal is not merely to chase high gains, but to achieve consistent, sustainable growth while minimising the impact of losses.

Large drawdowns can be damaging. For example, a 50% decline in portfolio value requires a 100% gain to recover to the original level. This simple arithmetic highlights why protecting capital and managing downside risk is essential. Without effective risk management, even strong investment strategies can fail, as severe losses erode both financial resources and investor confidence.

While standard deviation is most widely used tool for measuring risk, it does not fully capture the true nature of investment risk. Financial markets are complex, characterised by asymmetric returns and extreme events that standard deviation alone cannot explain.


To gain a better understanding, investors must look beyond volatility and incorporate additional measures such as skewness and kurtosis. These measures can be calculated using spreadsheet functions, just like averages and standard deviation.

Standard deviation

Risk analysis traditionally begins with standard deviation, a widely accepted measure of volatility. It reflects both diversifiable (asset-specific) and non-diversifiable (market-wide) risks, quantifying how far returns fluctuate around their average.

• Low standard deviation suggests stable, predictable returns.
• High standard deviation indicates greater volatility and uncertainty.

Its simplicity and comparability make it one of the most commonly used risk measures among analysts. By estimating the range within which returns fluctuate, standard deviation provides a probabilistic framework for understanding investment risk.

Limitations of standard deviation

Despite its usefulness, standard deviation has several limitations:

• Equal treatment of gains and losses

Standard deviation penalises both positive and negative deviations equally. An investment that occasionally generates large positive returns may appear just as risky as one that suffers severe losses. This fails to distinguish between volatility that benefits and volatility that harms investors.

• Assumption of symmetry

Standard deviation assumes returns are symmetrically distributed, meaning gains and losses are equally likely and of similar magnitude. In reality, financial markets rarely behave this way. Gains often accumulate gradually, while losses occur suddenly and sharply during crises.

• Underestimation of extremes

Standard deviation assumes extreme outcomes are very rare. Yet real-world markets experience shocks more frequently than models predict. Events such as unexpected policy changes, election results, or commodity price spikes demonstrate that extreme returns occur far more often than statistical theory suggests.

These limitations highlight why relying solely on standard deviation can lead to an incomplete or misleading picture of risk.

How skewness & kurtosis fit your portfolio

Skewness: Measuring asymmetry

Skewness complements standard deviation by measuring the asymmetric pattern of returns. It helps investors understand whether extreme outcomes are more likely to be large gains or large losses.

• Positive skewness: higher likelihood of outsized gains.
• Negative skewness: greater probability of severe losses.
• Zero skewness: no bias toward gains or losses.

Example: Consider two mutual funds with identical average returns (10%) and identical standard deviations (19.9%). The following are the annual five-year returns of the two funds

• Fund A returns: –20%, 4%, 12%, 21%, 33%
• Fund B returns: 40%, 16%, 8%, –1%, –13%

Based solely on standard deviation, both funds appear equally risky. However, Fund A experienced a severe negative return of –20%, while Fund B generated an extreme positive return of 40%. Skewness reveals the difference: Fund A has negative skewness (higher crash risk), while Fund B has positive skewness (greater upside potential).

This example illustrates how skewness provides insights that standard deviation cannot, distinguishing between downside risk and upside opportunity.

Kurtosis: Measuring extremes

While skewness measures the direction of extreme returns, kurtosis measures their frequency and severity.

• High kurtosis: more prone to extreme outcomes, whether gains or losses.
• Low kurtosis: fewer extremes, more stable return behaviour.

Standard deviation assumes extreme returns are rare, with only about a 0.3% probability of falling outside the expected range. In practice, however, extreme events occur far more often. High kurtosis signals that tail risks (extreme outcomes) are more common than traditional models suggest.

For investors, this means that assets with high kurtosis may deliver unusually large gains but also carry a higher probability of severe losses. Recognising this helps in assessing whether an investment aligns with one’s risk tolerance.

Combining skewness and kurtosis

Neither skewness nor kurtosis alone provides a complete picture of risk:

• Skewness alone shows whether extremes lean positive or negative, but not how often.
• Kurtosis alone shows how frequent extremes are, but not their direction.

By combining both, investors gain a more comprehensive assessment:

• Skewness identifies the direction of risk (upside vs downside).
• Kurtosis measures the intensity and frequency of extreme outcomes.

Together, these tools allow investors to select assets that align with both risk tolerance and return expectations (See table). This holistic approach leads to more informed, resilient investment decisions, ensuring portfolios are better prepared for both gradual market trends and sudden shocks.