The Hidden Story of S&P 500 Skewness: A Historical Analysis

Have you ever wondered if the returns of the S&P 500 are as symmetrical as they seem? Does skewness change over time, and what does that mean for investors? Let's dive into a slice of S&P 500 skewness history to find out.

The Symmetry Illusion: A Closer Look at S&P 500 Returns

Traditionally, financial experts have assumed log returns of the S&P 500 to be symmetric. However, this assumption may not hold up under scrutiny. By examining daily log returns from 1950 to 2011, we can begin to understand how skewness has evolved throughout this period.

Rolling Through Time: Skewness of the S&P 500

Figure 1 displays the rolling 250-day skewness of the S&P 500. Upon initial observation, it might seem that skewness varies considerably over time; however, Figure 2 presents a more nuanced perspective. This figure shows an informal method for assessing the variability of the skewness statistic, which suggests that there is little reason to believe skewness deviates significantly from zero throughout history.


Figure 1: Rolling 250-day skewness of the S&P 500


Figure 2: Rolling 250-day skewness of the S&P 500 (blue) with variability indication (gold)

Understanding Skewness Variability and Its Impact on Investors

Instead of looking at skewness through time, we can examine its variability within a sample. By doing so, we obtain a single value for the entire dataset and then use bootstrapping to observe the statistic's variability. The resulting distribution may look peculiar (Figure 3), but there is an explanation for this shape.


Figure 3: Bootstrap distribution of skewness for the S&P 500 from 1950 to 2011

The Power of One Datapoint

The peculiar shape of the bootstrap distribution in Figure 3 is due to a single datapoint exerting significant influence on the statistic. In fact, when this influential point—October 19, 1987 (Black Monday)—is removed, the resulting distribution becomes more intuitive (Figure 4).


Figure 4: Bootstrap distribution of skewness for the S&P 500 from 1950 to 2011 except for 1987-10-19

Navigating the World of Skewness: Practical Implications and Applications

So, what does this all mean for investors? Understanding skewness can help you make more informed decisions when constructing and managing portfolios. Let's explore the implications of skewness in various scenarios.

Portfolio Construction and Asset Selection

When building a portfolio, consider incorporating assets with diverse skewness profiles. For instance, some stocks may exhibit positive skewness (large gains, small losses), while others might display negative skewness (small gains, large losses). By diversifying across these spectra, you can potentially reduce overall portfolio risk.

Consider assets like C, BAC, MS, EFA, and EEM as examples of various skewness profiles to include in your portfolio.

Risk Management and Hedging Strategies

Investors must be aware of skewness when assessing risk. An asset with positive skewness may appear less risky due to its infrequent large gains, but it could still lead to significant losses if those events occur more frequently than expected. On the other hand, assets with negative skewness might offer more consistent returns but pose a different set of risks.

Scenario Analysis and Stress Testing

Conduct stress tests on your portfolio using historical events like Black Monday or the 2008 financial crisis to gauge how various assets perform under extreme conditions. This can help you better understand the potential impact of skewness on your investments.

Conclusion: Embracing Skewness in Your Investment Strategy

By understanding and accounting for skewness, investors can make more informed decisions when constructing and managing portfolios. While it might seem like an abstract concept, skewness has real-world implications that can significantly impact your investment outcomes. So, don't ignore the power of skewness—embrace it as a valuable tool in your investing arsenal.

VERIFIED\_CATEGORY: Mathematics/Statistics