Updated for the 2026 CFA® Level I curriculum
Skewness and kurtosis help you see features of a return distribution that the mean and standard deviation leave out. Skewness shows whether unusual observations extend farther to the left or right. Kurtosis shows how much weight lies in the tails, which helps you assess exposure to extreme returns.
For CFA Level I, focus on reading these measures together and explaining what they suggest about investment risk.
Quick Answer
Skewness describes the direction of a distribution’s longer tail. Positive skew means the right tail is longer, while negative skew means the left tail is longer. Kurtosis describes how heavy the tails are relative to a normal distribution. Positive excess kurtosis signals more extreme observations, while negative excess kurtosis signals fewer.
Key Takeaways About Skewness and Kurtosis
Positive skewness means the distribution has a longer right tail.
Negative skewness means the distribution has a longer left tail.
A skewness value near zero suggests approximate symmetry.
A symmetric distribution can still have heavier or lighter tails than a normal distribution.
Raw kurtosis uses 3 as the normal-distribution benchmark.
Excess kurtosis uses 0 as the normal-distribution benchmark.
Skewness shows the direction of unusual outcomes, while kurtosis shows how frequently extreme outcomes may occur.
What You Need to Know for CFA Level I
When you see skewness or kurtosis in a question, you should be able to:
Identify positive, negative, or approximately zero skewness.
Determine which side of the distribution contains the longer tail.
Connect negative skewness with possible extreme losses.
Separate tail direction from tail weight.
Compare raw kurtosis with 3 and excess kurtosis with 0.
Classify a distribution as mesokurtic, leptokurtic, or platykurtic.
Explain the investment implication in plain language.
What Is Skewness?
Skewness measures asymmetry around the center of a distribution. The sign follows the direction of the longer tail.
A positive value means the right tail extends farther. A negative value means the left tail extends farther. A value close to zero suggests the tails are roughly balanced.
The longer tail may sit opposite the side where most observations are grouped. For example, a negatively skewed investment can produce small positive returns during most periods while a few severe losses stretch the left tail. Those losses determine the negative sign.
The mean, median, and mode often follow a predictable order when a distribution is skewed.
Distribution | Typical Relationship |
|---|---|
Positively skewed | Mode < Median < Mean |
Approximately symmetric | Mean ≈ Median ≈ Mode |
Negatively skewed | Mean < Median < Mode |
Extreme observations pull the mean toward the longer tail. The median moves less because it depends on the middle observation, while the mode remains near the most common value.
How to Interpret Positive, Negative, and Zero Skewness
Positive Skewness
Positive skewness means the distribution has a longer right tail. Most observations may sit around lower or moderate values, while a few unusually large positive observations stretch the distribution to the right.
For an investment, this shape suggests the possibility of rare, substantial gains. The skewness value only describes the direction of the tail, so you should still review the average return, dispersion, costs, and overall suitability.
Negative Skewness
Negative skewness means the distribution has a longer left tail. Most returns may appear steady, while a small number of severe negative observations extend far below the center.
This shape deserves attention because ordinary periods may understate the investment’s downside exposure. A strategy can look consistent for a long time and still carry the possibility of a large loss.
Zero or Near-Zero Skewness
A skewness value near zero suggests that the left and right tails are approximately balanced.
You still need to examine kurtosis. Two symmetric distributions can have very different exposure to extreme outcomes, depending on how much probability sits in their tails.
What Is Kurtosis?
Kurtosis describes the weight of a distribution’s tails relative to a normal distribution. Heavier tails indicate that extreme observations occur more frequently. Lighter tails indicate that extreme observations occur less frequently.
For CFA Level I interpretation, keep your attention on the tails and the likelihood of unusually large gains or losses. The peak of the curve may also change, but tail exposure carries the main investment implication.
Kurtosis may be reported using either raw kurtosis or excess kurtosis.
Measure | Normal Distribution Benchmark |
|---|---|
Raw kurtosis | 3 |
Excess kurtosis | 0 |
Excess kurtosis equals raw kurtosis minus 3.
Always identify which convention the question uses before comparing the reported value with the normal benchmark.
Mesokurtic, Leptokurtic, and Platykurtic Distributions
Mesokurtic Distribution
A mesokurtic distribution has the same kurtosis as a normal distribution.
Its raw kurtosis is 3, and its excess kurtosis is 0. It serves as the benchmark for comparing heavier or lighter tails.
Leptokurtic Distribution
A leptokurtic distribution has heavier tails than a normal distribution.
Its raw kurtosis is above 3, and its excess kurtosis is positive. Extreme observations are more frequent, so the distribution carries greater tail exposure than the normal benchmark.
Platykurtic Distribution
A platykurtic distribution has lighter tails than a normal distribution.
Its raw kurtosis is below 3, and its excess kurtosis is negative. Extreme observations occur less frequently than they would under a normal distribution.
Skewness vs Kurtosis: What Is the Difference?
Skewness and kurtosis describe separate parts of a distribution’s shape. Skewness identifies the direction of the longer tail. Kurtosis identifies how much weight sits in the tails.
Area | Skewness | Kurtosis |
|---|---|---|
What it measures | Asymmetry | Tail weight |
Main question | Which tail is longer? | How frequent are extreme observations? |
Positive value | Longer right tail | Heavier tails when using excess kurtosis |
Negative value | Longer left tail | Lighter tails when using excess kurtosis |
Investment relevance | Direction of unusually large outcomes | Frequency of unusually large outcomes |
Main exam risk | Reversing the tail direction | Using the wrong normal benchmark |
A distribution can be negatively skewed and leptokurtic at the same time. In that case, its longer tail sits on the downside, and extreme observations occur more frequently than a normal model would suggest.
How to Interpret Skewness and Kurtosis in Investment Returns
Mean and standard deviation describe the center and spread of returns. Skewness and kurtosis add information about the shape of the distribution and the behavior of its tails.
Consider two funds with similar average returns and standard deviations. One may have a long left tail with frequent extreme losses, while the other may have balanced, lighter tails. Their central statistics look similar, but their downside exposure differs considerably.
Use the following process when interpreting the measures:
Check whether skewness is positive, negative, or near zero.
Identify which side contains the longer tail.
Connect that tail with unusually large gains or losses.
Confirm whether the reported kurtosis is raw or excess.
Compare the value with 3 for raw kurtosis or 0 for excess kurtosis.
Combine the two results into a clear investment interpretation.
Negative skewness highlights the direction of downside extremes. Positive excess kurtosis tells you those extreme observations may occur more often than a normal distribution predicts. Together, the measures provide a fuller view of tail risk.
Sample Skewness and Excess Kurtosis Formulas
The CFA Level I learning outcome emphasizes interpretation and evaluation. These formulas are most useful as a reference for understanding how the measures are constructed.
Sample Skewness
Sample Excess Kurtosis
Formula Symbols
Where:
Number of observations =
Individual observation =
Sample mean =
Sample standard deviation =
The third power in the skewness formula preserves the sign of each deviation. Large negative deviations therefore pull skewness below zero, while large positive deviations push it above zero.
The fourth power in the kurtosis formula makes every contribution positive and gives greater weight to observations far from the mean. A series with more extreme deviations will therefore produce a higher kurtosis value.
When using software or a financial calculator, check whether the output reports raw kurtosis or excess kurtosis before interpreting it.
Worked Interpretation Example
Suppose two funds report similar average returns and standard deviations over the same period:
Fund A: Skewness = −1.1, excess kurtosis = +2.0
Fund B: Skewness = +0.2, excess kurtosis = −0.3
Fund A
Fund A has negative skewness, so its longer tail sits on the left. Its most extreme observations are therefore more likely to be large negative returns.
Its excess kurtosis is +2.0, which is above the normal benchmark of 0. The distribution has heavier tails, so extreme outcomes occur more frequently than a normal model would suggest.
Together, these figures show meaningful exposure to rare, severe losses.
Fund B
Fund B has skewness of +0.2, which is close to zero. Its distribution is approximately symmetric, with a slight extension to the right.
Its excess kurtosis is −0.3. The tails are slightly lighter than normal, so extreme observations occur somewhat less frequently.
Interpretation
The shape measures separate the two return profiles even though their means and standard deviations are similar. Fund A carries greater downside tail exposure. Fund B has a more balanced distribution with slightly lighter tails.
An analyst would combine these findings with expected return, overall volatility, liquidity, fees, and the investor’s objectives before making a recommendation.
Common Exam Traps
Looking at where most observations sit instead of identifying the longer tail.
Reading negative skewness as a longer right tail.
Treating positive skewness as proof of superior investment performance.
Assuming a near-zero skewness value means the distribution is normal.
Comparing excess kurtosis with 3.
Comparing raw kurtosis with 0.
Describing kurtosis only through the height of the curve’s peak.
Reporting the statistic without explaining what it means for investment risk.
Practice Question
A return distribution has skewness of −0.8 and excess kurtosis of +1.5. Which statement most accurately describes the distribution?
It has a longer left tail, with heavier tails and more extreme observations than a normal distribution.
It has a longer right tail, with heavier tails and more extreme observations than a normal distribution.
It has a longer left tail, with lighter tails because its excess kurtosis is below 3.
Correct Answer: A
A skewness value of −0.8 means the distribution has a longer left tail. Its most extreme observations therefore occur on the negative side.
Excess kurtosis of +1.5 is above the normal benchmark of 0. The distribution has heavier tails, so extreme observations are more frequent than under a normal distribution.
Option B. reverses the direction of the skew.
Option C. compares excess kurtosis with 3, which is the benchmark for raw kurtosis.
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FAQs About Skewness and Kurtosis
What Is the Difference Between Skewness and Kurtosis?
Skewness measures asymmetry and identifies the direction of the longer tail. Kurtosis measures tail weight and indicates how frequently extreme observations may occur.
Together, they show both where unusual outcomes are concentrated and how significant the tail exposure may be.
Is Normal-Distribution Kurtosis 3 or 0?
A normal distribution has raw kurtosis of 3 and excess kurtosis of 0.
Before interpreting a reported value, check which convention the question or software output uses.
What Does Negative Skewness Mean for Investment Returns?
Negative skewness means the distribution has a longer left tail. The investment may produce ordinary or positive returns during most periods while remaining exposed to occasional severe losses.
The statistic highlights the direction of tail risk and should be considered alongside return, volatility, kurtosis, and the investor’s objectives.