Week 3 has been a lot of fun. It has been challenging to say the least, but the “learnings” are absolutely worth the effort. At work my team teases me about how often I use standard deviations and Z-scores in our day to day work. It helps me understand not just the item or store metrics but how it fits in the distribution of items or stores metrics. They say it is my hammer, and “when you’re holding a hammer everything looks like a nail!” It seems like the basic “index” math is what makes “Wally World” go round.
The index shows the percent difference from the mean, using the mean as the denominator. This is a good, valid number, but it doesn’t show if that number is expected or is an outlier. For instance, what is a good index? We always look for an index of 120, meaning the number is 20% greater than the mean. Depending on the base that could be good, great or insignificant. When we look at demographics that buy a particular item. An index of the Caucasian customer at 120 is huge, because the mean is in the 70% range, which gives me an actual of 84%. An index of 120 for the Asian customer is different because the average is less than 5%, so the Asian demographic for that item would be 6%.
Therefore, I love Z-scores. A Z-score tells me how many Standard Deviations from the mean an item or store metric would be. The index of 120 might land with a Z-score of 3.5 for that Caucasian customer, meaning it is an outlier, and a Z of 0.5 for the Asian customer, where it is absolutely expected. Another benefit of Z-scores are the fact that they are real relative numbers that I can apply real math to. For instance, I can calculate Z-scores for dollar sales, unit sales, growth, share metrics etc., and then weight and sum them to create a valid cumulative standardized score that I can then rank and study.
This past week we created analysis to measure performance of a stock portfolio vs individual stock performance. The key metric used was the Sharpe Ratio. I knew nothing about this metric, and knowing I was going to have to write a report on my results, I dug in and researched how the math worked and what the metric truly told me. Imagine my surprise when I realized that the Sharpe ratio is simply a slightly modified Z-score. The math is the difference of the mean of the daily return less the return of a risk-free security, then divided by the standard deviation of the daily mean returns. In other words how many standard deviations from the mean is my net return. Just as my example above, the Sharpe Ratio helps me understand the return in terms of the volatility. This was simple and awesome!
I absolutely gloated at work the next day at how a Nobel prize winner used Z-scores as part of his analysis and how it is still used everyday. I should change my name to Thor.
