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.

We also know that there is an inverse relationship between the direction of market and VIX movement. When markets rise, the VIX falls. When markets fall, the VIX rises.

Volatility vs. All SPX Ultra Volume

My belief is that absent the uptick rule, long or short ultras become interchangeable. Thus, we should look at the total impact of all ultras combined. I began by running a regression of VIX closing prices vs. total ultra volume. Here are the statistical results:

In order to better understand the relationship between the VIX and ultra volumes, I have prepared a graph to visualize the correlation. This graph and others in this article normalized the ultra volumes and VIX levels by unitizing all series of values by their mean values over the period of time that the data series covers. Here is the graph of the total ultra volume and the VIX:

Volatility Separately vs. Short or Long Ultra Volume

While I surmised that the total ultra activity was the cause of volatility, it is worthwhile separating the analysis into two separate components. Thus, I ran two other analyses.

First was the VIX vs. the short ultra (SDS). Here are results of the regression analysis:

Here is the graphic representation of the VIX and SDS volumes:

Second was the VIX vs. the long ultra (SSO). Here are the results of the regression analysis:

Here is the graphic representation of the VIX and SSO volumes:

Conclusion

I have long held the belief that the ultras were a component of volatility. This indeed appears to be the case.

We have some very strong data that indicates that the VIX is highly influenced by volumes in the Ultras. Specifically, the R-squared was:

  • 0.70 for the Total Ultra Analysis
  • 0.43 for the Short Ultra Analysis
  • 0.73 for the Long Ultra Analysis
  • The peaks and spikes in volume and volatility can be violent and should not be ignored. There is a causal relationship between the ultra volume and the VIX spikes and peaks.

    What surprised me was that the short ultras by themselves had a far less impact on volatility than all ultras or the long ultras. I was also surprised by the magnitude of impact of the long ultras on volatility.

    I think that more work still need to be done. Specifically, I want to perform a similar analysis using the dollar value rather than the trading volume of ultras. also, as I have written before, there are other factors that influence market volatility. I believe that contract volumes and dollar equivalent values of SPX e-mini futures contracts may make up the balance of volatility not derived by activity in the ultras.

    But make no mistake: Ultras do impact implied volatility and, by extension, market prices.

    -- Written by Scott Rothbort in Millburn, N.J.
    At the time of publication, Rothbort was long CBOE, although positions can change at any time.

    Scott Rothbort has over 25 years of experience in the financial services industry. He is the Founder and President of LakeView Asset Management, a registered investment advisor specializing in customized separate account management for high net worth individuals. In addition, he is the founder of TheFinanceProfessor.com, an educational social networking site; and, publisher of The LakeView Restaurant & Food Chain Report. Rothbort is also a Term Professor of Finance at Seton Hall University's Stillman School of Business, where he teaches courses in finance and economics. He is the Chief Market Strategist for The Stillman School of Business and the co-supervisor of the Center for Securities Trading and Analysis.

    Mr. Rothbort is a regular contributor to TheStreet.com's RealMoney Silver website and has frequently appeared as a professional guest on Bloomberg Radio, Bloomberg Television, Fox Business Network, CNBC Television, TheStreet.com TV and local television. As an expert in the field of derivatives and exchange-traded funds (ETFs), he frequently speaks at industry conferences. He is an ETF advisory board member for the Information Management Network, a global organizer of institutional finance and investment conferences. In addition, he is widely quoted in interviews in the printed press and on the internet.

    Mr. Rothbort founded LakeView Asset Management in 2002. Prior to that, since 1991, he worked at Merrill Lynch, where he held a wide variety of senior-level management positions, including Business Director for the Global Equity Derivative Department, Global Director for Equity Swaps Trading and Risk Management, and Director for secured funding and collateral management for the Global Capital Markets Group and Corporate Treasury. Prior to working at Merrill Lynch, within the financial services industry, he worked for County Nat West Securities and Morgan Stanley, where he had international assignments in Tokyo, Hong Kong and London. He began his career working at Price Waterhouse from 1982 to 1984.

    Mr. Rothbort received an M.B.A., majoring in Finance and International Business from the Stern School of Business, New York University, in 1992, and a B.Sc. in Economics, majoring in Accounting, from the Wharton School of Business, University of Pennsylvania, in 1982. He is also a graduate of the prestigious Stuyvesant High School in New York City. Mr. Rothbort is married to Layni Horowitz Rothbort, a real estate attorney, and together they have five children.