Standard Deviation and Its Limitations: An Analysis in the Financial Context

In our previous article, we discussed the concept of standard deviation as a crucial measure for evaluating the risk of an asset or portfolio. However, it is important to recognize that standard deviation has its limitations, particularly in extreme and unpredictable situations, such as financial crises and highly improbable events.

A notable mention comes from Nassim Taleb's book, "The Black Swan." Taleb argues that highly improbable and impactful events, termed "Black Swans," have a significant effect on financial markets but cannot be adequately captured by standard deviation. These events, such as financial crises or market collapses, have such a profound impact that they distort traditional risk analysis based on standard deviation.

To illustrate numerically how such events deviate from the average and our prediction models, consider some practical examples from our local stock market (Ibovespa). Over a long-term period of the past 10 years (2013–2023), the standard deviation for the Ibovespa is 25% annually, and on a daily basis, it is 1.57% (a linear approximation is not suitable here).

With such measures converted to daily deviations, you might recall trading days with significant fluctuations that likely exceeded these measures. For instance, the "Joesley Day" (May 18, 2017), when the Ibovespa dropped 8.8%, would theoretically occur once every 905 years if assuming a normal distribution. Notably, "Joesley Day" was not even the worst performance day for the Ibovespa; on March 12, 2020, during the COVID crisis, the index fell 14.78%.

Moreover, during periods of crisis, the correlations between assets tend to approach 1.0. This means that asset price movements become more aligned, making diversification based solely on standard deviation less effective. In other words, assets that might be combined in a portfolio and show relatively distinct movements end up falling similarly.

Therefore, while standard deviation is a valuable tool for risk assessment, it is essential to acknowledge its limitations. Investors should be aware of the potential for extreme and unpredictable events and consider additional strategies, such as "Stress Testing," which allows investors to evaluate the resilience of their portfolios against extreme events and protect the portfolio with "hedges," provided they are not excessively costly.

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