MILLBURN, N.J. ( Stockpickr) -- An active topic of discussion on RealMoney has taken place for some time concerning the impact of leveraged -- long and short -- ETFs, collectively referred to as ultras, upon the broader markets. Jim Cramer, Eric Oberg and I have argued that ultra activities are a proximate cause for market volatility and, in a related way, selloffs.To a great extent, the algorithmic and high-frequency traders that I've written about before utilize these instruments, along with their derivative securities, to create and profit from market volatility. I decided to perform some research to determine whether there is a link between ultra activity and market volatility. First, let me describe some of the parameters and assumptions I used in my study. First, I created a database of of trading volumes for the ProShares Ultra S&P 500 ( SSO) and ProShares UltraShort S&P 500 ( SDS) and closing prices for the CBOE Volatility Index ( VIX). I used data for the period from Jan. 1, 2008, through June 15, 2010. It was in the beginning of 2008 that ultras first became popular trading vehicles. I then performed a series of regression analyses to determine the relationship of the movement of volatility to transaction volume in ultras as it pertains to the SPX. VIX was my "Y," and ultras were my "X" for the regressions. I was seeking high levels of R-squared, a statistical measure of how well a regression line approximates the sample data points. The R-squared tells us how much of the return of the Y variable can be explained by the X variable. An R-squared of 1 is a perfect fit. The regressions were run with a 95% confidence level. What is the VIX? The VIX, originally introduced in a paper by Robert Whaley , is a "key measure of market expectations of near-term volatility conveyed by S&P 500 stock index option prices," according to the CBOE, and is widely considered to be the world's "to be the world's premier barometer of investor sentiment and market volatility." Be aware that the VIX is a measure of expected or perceived volatility and not realized or actual volatility. Thus, the VIX is what investors are willing to pay for options, not necessarily what the options are worth.