What would be the correlation coefficient of a security that loses, say, 20% when the market is up 10%? For example, a leveraged inverse ETF… would that mean the correlation is less than -1?

First, I want to say this - it is * very* unlikely you’ll ever be asked to calculate correlation coefficients on the exam. The calculations are complex and difficult. Test questions typically focus on what a correlation coefficient tells us, not how to determine them.

With that being said, the correlation will be very close to -1. I compared SPY (S&P 500 ETF) to SDS (S&P 500 2x inverse ETF) using this website. I don’t know what calculation the website is using, but the data seems to be correct. They determined the correlation to be -.9794 over the past year.

Correlation measures the relationship of market price movements between two different assets. Given these two ETFs move opposite, it’s not surprising the correlation is just below -1. While one moves faster than the other, they still move completely opposite.

I hope this helps!