Standard Deviation, Variability and You

The following chart visually shows the variability of S&P 500 since Janaury 2019. Cleary the ‘market’ has been quite volatile in the last few weeks. We’ve has extreme up days and extreme down days. Unfortunately, way too many of the downs rather than ups.

I have used Standard Deviation information as a proxy for Variance for quite some time. Today I took the time to check out a YouTube video to refresh my understand of definition of arithmetic mean, variance, and standard deviation. Check it out if you are interested.

Without getting too deep in the weeds on the details, I’ve used the three arithmetic mean compared to the standard deviation for that data set as a short hand proxy for variability. In essence, one standard deviation gives an indication of what the historical results were approximately two thirds of the time. The closer this number is to the historical mean, the closer I think you could expect the future mean to be to the historical mean.

For reference, two standard deviations provides an indication of the range for the historical mean 95% of the time. Clearly the volatility in the stock market is resulting in return variance significantly beyond what we have experienced in recent time periods.

That about sums up my knowledge and capabilities with statistics. However I’m sure you have seen the chart for unemployment insurance claims that came out last week. Somewhere I saw that the weekly number was 12 standard deviations from the expected variation based on the entire history of that data set.

Clearly these are uncharted times!