Skewness and Kurtosis: Distribution
When we talk about investments, our minds often jump to average returns. We want to know how much money we can expect to make. But astute investors know that the average tells only part of the story.
To truly understand the potential risks and rewards of an investment, we need to understand the shape of its returns distribution.
This is where two powerful statistical concepts come in: Skewness and Kurtosis.
Think of a bell curve, the symmetrical shape we often associate with normal distribution. Most traditional financial models assume returns follow this perfect bell.
However, in the real world, investment returns rarely conform to such neat patterns. They can be lopsided, have fat tails, or be incredibly pointy. Understanding these deviations is crucial for making informed financial decisions.
Skewness: Is the Distribution Lopsided?
Skewness measures the asymmetry of a distribution. In simpler terms, it tells us if the returns are more clustered on one side of the average than the other, or if there are more extreme returns in one direction.
Positive Skewness (Right-Skewed)
Imagine a distribution where the tail is longer on the right side. This means there are a few unusually large positive returns that pull the average up. For investors, this can be an attractive characteristic. It suggests a higher probability of small losses or moderate gains, with a smaller chance of large losses, but a welcome possibility of significant gains. Think of a lottery ticket – many small losses, but the rare, massive win. In finance, early-stage venture capital investments or innovative growth stocks often exhibit positive skewness. Many might fail or offer small returns, but a few can deliver explosive, life-changing gains.
Negative Skewness (Left-Skewed)
Now imagine the tail stretching out to the left. This indicates a higher probability of experiencing a few unusually large negative returns that drag the average down. While there might be many small gains, the risk of a significant loss is present. For investors, this is generally undesirable. It implies that while most of the time things might be okay, there's a lurking danger of a substantial hit. A common example in finance is selling uncovered call options. You collect small, consistent premiums (small gains) most of the time, but face the risk of theoretically unlimited losses if the underlying asset's price skyrockets (rare, huge loss). Certain mean-reversion trading strategies can also exhibit negative skewness, generating many small wins but being susceptible to infrequent, massive losses if prices trend strongly against the position.
Zero Skewness
A perfectly symmetrical distribution, like our ideal bell curve, has zero skewness. This means positive and negative deviations from the mean are equally likely.
Kurtosis: Are the Tails Fat or Thin?
Kurtosis, on the other hand, measures the tailedness of a distribution. It tells us about the presence of extreme outliers – how often do unusually large or small returns occur? It also speaks to the peakedness of the distribution.
Leptokurtic (Positive Kurtosis)
A leptokurtic distribution has fatter tails and a sharper, taller peak than a normal distribution. This means there's a higher probability of extreme events (both positive and negative) occurring. For investors, this is often associated with higher risk. While you might see more significant gains, you also face a greater chance of substantial losses. Assets with jump risk or those highly susceptible to market shocks often exhibit leptokurtic returns. Cryptocurrencies, low-cap equities or volatile commodity prices are classic examples. Their returns often show periods of relative calm interspersed with sudden, dramatic price swings, both up and down, that are far more frequent than a normal distribution would predict. The daily returns of major stock market indices (like the S&P 500) also tend to be leptokurtic, especially during financial crises, where extreme events occur more frequently.
Platykurtic (Negative Kurtosis)
A platykurtic distribution has thinner tails and a flatter, more spread-out peak than a normal distribution. This suggests fewer extreme outliers. Returns are more uniformly distributed, meaning there's a lower probability of experiencing very large gains or losses. This can indicate a more stable and predictable asset, though perhaps with lower potential for outsized returns. Highly diversified, low-volatility bond funds or money market accounts might exhibit platykurtic characteristics, as their returns tend to be very tightly clustered around the mean with rare, large deviations.
Mesokurtic (Zero Kurtosis)
A normal distribution is mesokurtic, meaning its kurtosis is zero. It serves as our baseline for comparison.
Why Do Skewness and Kurtosis Matter for Investments?
Ignoring skewness and kurtosis can lead to a dangerously incomplete picture of an investment portfolio:
- Risk Management: Standard deviation, a common risk measure, only tells you about the typical dispersion of returns. It doesn't differentiate between a distribution with frequent small losses and rare, huge gains (positive skewness) versus one with frequent small gains and rare, huge losses (negative skewness). Understanding skewness allows you to assess the likelihood of extreme negative events. Kurtosis helps you quantify the probability of those extreme events, both good and bad. This is particularly critical when stress-testing portfolios for Black Swan events.
- Portfolio Construction: If your portfolio is heavily weighted towards negatively skewed assets, you're exposing yourself to greater downside risk than a simple standard deviation might suggest. Similarly, a portfolio with a high degree of leptokurtosis means you need to be prepared for more volatile swings. Diversifying across assets with different skewness and kurtosis characteristics can help create a more robust and predictable portfolio.
- Performance Evaluation: When evaluating a fund manager, simply looking at average returns isn't enough. A manager who achieves high average returns but with significant negative skewness might be taking on excessive tail risk that could eventually lead to a disastrous drawdown, wiping out years of gains.
- Tailoring to Your Risk Tolerance: If you're highly risk-averse, you might prefer assets with positive skewness and platykurtic distributions – those that offer a good chance of modest gains and a lower probability of extreme losses. Conversely, if you have a higher risk tolerance and are seeking outsized returns, you might accept some negative skewness or leptokurtosis, but you should do so with a full understanding of the potential implications.
Understand the whole story
While average returns and standard deviation are essential, a deeper dive into the shape of returns distributions through skewness and kurtosis provides a more nuanced and powerful understanding of investment characteristics.
Don't just look at the average; understand the whole story of an investments behavior.