Silver’s Extreme Moves Happen WAY More Than You Think

Key Concepts

• Normal Distribution: A symmetrical probability distribution, often called the bell curve, where most outcomes cluster around the average.
• Standard Deviation (Sigma): A measure of the amount of variation or dispersion of a set of values. A higher standard deviation indicates greater variability.
• Tail Events: Extreme, infrequent occurrences that lie far from the average in a distribution.
• Empirical Data: Data obtained through observation or experimentation, as opposed to theoretical models.
• Six Sigma Event: An event that is six standard deviations away from the mean. In a normal distribution, these are extremely rare.

Silver Returns & Deviation from Normality

The video focuses on demonstrating that silver’s daily returns do not follow a normal distribution, despite exhibiting a bell-curve shape in a histogram of historical data. While a bell curve is present, the frequency of extreme events (tail events) is significantly higher than predicted by a normal distribution model.

Visualizing the Difference: Histograms & Zoom Levels

The presenter utilizes a visual comparison of silver’s actual daily returns (represented by a gray histogram) against a theoretical normal distribution (represented by a blue line). The analysis begins with a broad view of all daily returns since 1970. Initially, returns around the average are slightly more probable in silver’s actual data, which isn’t particularly noteworthy. However, the key difference emerges when examining the tails of the distribution – the areas representing events two, three, and especially four or more standard deviations from the mean.

Through successive zoom levels, focusing on the negative and positive tails, the disparity between the empirical data (gray line) and the normal distribution (blue line) becomes increasingly pronounced. The blue line, representing the normal distribution, flattens out dramatically in the tails, predicting extremely low probabilities for these events. Conversely, the gray line shows a substantially higher probability of these extreme events occurring in silver.

Frequency of Six Sigma Events

The core argument centers on the frequency of “six sigma” or greater events – those occurring six or more standard deviations from the mean.

• Normal Distribution Prediction: In a normal distribution, a six sigma event is predicted to occur once in 500 million days, equating to approximately once every 2 million years. As the presenter states, “probably you wouldn't live to see it.”
• Silver’s Empirical Reality: However, based on historical data, silver experiences six sigma events (positive or negative) approximately once every 407 days, or roughly once every 19 months. This represents a dramatically higher frequency than predicted by the normal distribution model.

Implications & Supporting Evidence

This observation has significant implications for risk management and modeling of silver’s price behavior. The video demonstrates that relying on a normal distribution to assess risk in silver would severely underestimate the likelihood of extreme price swings. The presenter’s evidence is entirely data-driven, based on a comprehensive analysis of silver’s daily returns since 1970, visualized through histograms and comparative zoom levels. The presenter doesn’t offer explanations why silver deviates from normality, only that it demonstrably does.

Technical Vocabulary

• Histogram: A graphical representation of the distribution of numerical data.
• Empirically: Based on observation or experience rather than theory or pure logic.
• Trading Day: A day on which a financial market is open for business.

Conclusion

The video effectively illustrates that silver’s returns are not normally distributed. The frequency of extreme events, particularly those at the six sigma level or beyond, is far higher than predicted by a normal distribution model. This finding underscores the importance of using appropriate statistical models when analyzing and managing risk associated with silver investments, and highlights the limitations of assuming normality in financial markets. The presenter’s use of visual aids and specific data points (frequency of six sigma events) strengthens the argument and provides actionable insights for investors and analysts.