Skewness and Kurtosis

Hidden tail risks beyond the bell curve
 

By: Yukoh Shimizu

Most investors are familiar with the idea of the mean and variance (volatility) of return distributions. The mean tells you what the central tendency of the distribution is, and the volatility tells you how dispersed those returns are around the mean. Respectively, these two measures represent the first and second “moments” of the return distribution.
 
Very simply, if we consider our return distribution as little weights on a seesaw, the moments describe how the seesaw is balanced and how the weights are distributed: where the balance point is, how spread out the weights are, whether they are clustered on one side or another.
 
These two moments can tell us a lot about the trade-offs involved in holding various assets. Below we show the average annualized excess mean returns and volatility of various asset classes.
 
Figure 1. Mean Annual Excess Return and Volatility (1997-2025)

Source: Capital IQ, Verdad analysis
 
Astute readers will notice that most assets generally fall along a straight line, which reflects the trade-off investors make between risk and return, which we wrote about in our piece on asset class CAPM.

But the average and volatility of return are not the only moments that investors should care about. Traditional bell-curve assumptions tend to understate the likelihood of extreme outcomes—both sudden windfalls and steep losses—lurking in the “fat tails” of return distributions. When these outsize moves occur, they can blindside investors and unravel portfolios built on incomplete risk assessments.
 
That’s where the third and fourth moments of the distributions, skewness and kurtosis, come into play. Skewness reveals whether extreme returns cluster on the upside (positive skew) or the downside (negative skew), describing the types of surprises you might face. Kurtosis measures how fat or thin the tails of the distribution are: a high kurtosis value suggests a greater likelihood of extreme outliers, while a lower kurtosis value points to fewer extreme events. Considering skewness and kurtosis can offer another lens through which to examine prospective assets.
 
Figure 2. Skewness and Kurtosis by Asset (1997-2025)

Source: Verdad analysis
 
Assets positioned farther to the left have more negative skewness (i.e., greater downside outliers), while higher kurtosis on the vertical axis indicates fatter tails and a higher likelihood of extreme moves.
 
In the top-left, EM bonds and corporate credit show pronounced negative skew and high kurtosis, indicating a strong tendency for abrupt, severe losses. This pattern reflects vulnerabilities such as default risk, liquidity shocks, and capital flight, all of which can amplify downside moves. As high-yield and emerging-market instruments, they are particularly sensitive to shifts in global risk appetite.
 
Equities falls in the middle of the matrix, exhibiting moderate skew and kurtosis levels. While they are not immune to market downturns, their return distributions are more balanced, suggesting they experience fewer extreme tail events compared to the riskier high-yield segment.
 
Equities are not, however, as stable as gold or US Treasurys. These cluster toward the bottom-right quadrant, with near-zero or slightly positive skew and relatively low kurtosis. These characteristics signal fewer extreme moves and, in the case of gold, occasional upside potential. Both act as safe havens, tending to hold their value or even appreciate when market stress rises.
 
As an illustrative example, we can see the evidence of the negative skewness and high kurtosis of assets like EM bonds when we look at the cumulative return and max drawdown chart over time. Despite having relatively innocuous average excess returns (5%) and volatility (10%), EM bonds have experienced four instances in the last ~30 years of drawdowns worse than 25%.
 
Figure 3: Emerging Market Bonds Cumulative Return and Max Drawdown (1997-2025)

Source: Bloomberg, Verdad analysis
 
Measures like skewness and kurtosis can be helpful supplements to average return and volatility when thinking about the role that diversifying assets can play in a portfolio. Delving into skewness and kurtosis enables investors to uncover these nuances and build portfolios that are more resilient to unexpected market swings.