An Arbitrage Strategy for Trading Indices

Several years ago, I sat down with James Altucher at a Barnes & Noble cafe and discussed some cluster arbitrage strategies I developed that would be suitable for large accounts or funds.

For a few years, I traded several of these cluster arbitrages when I had customer demand. Perhaps that demand will return to LakeView Asset Management as investors seek less risky, transparent and unleveraged arbitrage strategies.

Well, time has passed, and ETFs have become more prominent. My pattern-recognition skills, which I learned many years ago and discussed in this TheStreet University article, still keep my interest alive in developing these strategies.

In the last few months, especially in the recent market downturn, I noticed somewhat parallel percentage moves in the S&P 500 (SPX) and Dow Jones Industrials (DJIA). Hence I decided to run a multiple regression of the SPX (as my "Y") and several indices as my "X's" to see if I could determine a mean-reverting trading pattern. The "X's" were the Nasdaq 100 (NDX), Dow Jones Industrials (DJIA) and Russell 2000 (RUT).

I ran the regression over a period from Jan. 3, 2007, to Dec. 12, 2008. The regression ran at a 95% confidence level and yielded the following output:

One of the most important statistics for a regression is the R Squared. The R Squared is the correlation coefficient for the performance of the Y variable relative to the X variables. An R Squared close to 0 will indicate no correlation, whereas a value of 1 is perfect correlation. In general, look for something that is at least 0.95 and as close to 1.00 as possible.

As you can see from the output, the R Squared for my regression is nearly 1. This indicates to me that we have a well-correlated regression. The way that you can interpret this regression is to say that we can replicate the SPX by using some combination of the NDX, DJIA and RUT. Thus, taking the output from the regression, we can establish that we can apply the following formula to our trading model:

SPX = -131.66354 - .00845 NDX + .08685 DJIA + .59637 RUT

Next, I calculated the Replicated SPX (right side of the equation) for every day in which I had data. I then compared the actual SPX with the Replicated SPX such that Actual SPX minus Replicated SPX equals a premium if positive or discount if negative. Theoretically, if we bought the Replicated SPX package when the actual SPX was at a premium and sold short the actual SPX, we would be buying a risk-free arbitrage. The theory being that at some point the Replicated SPX and Actual SPX would converge in value.

Next I calculated and graphed the daily discount or premium (blue line), the average discount or premium (red line), the average discount or premium plus one standard deviation (green line) and the average discount or premium minus one standard deviation (purple line). This is depicted in the chart below:

Lakeview Asset Management, LLC

As you can see, the blue line trades in a wave-like pattern such that it will trade down from the green line through the red line to the purple line and then back once again up to the green line. Hence, if we bought the Replicated SPX package and sold short the Actual SPX when the premium rose to the green line and held it until it hit the purple line, we would generate a nice arbitrage profit. Once the discount is at the purple line, we close out the original trade and reverse the positions such that we would buy the Actual SPX and sell short the Replicated SPX package. Since Jan. 3, 2007, we would have made four trades, and each would have yielded hefty risk-free gains.

Of course, it is very difficult for the individual investor or professional money manager to buy entire indices. Thus we can do the next best thing which is to use ETFs. There is an ETF for each of those indices in this model. Here are the ETFs and the indices they relate to:

• 10 Spyders (SPY - commentary - Cramer's Take) (SPY) = SPX
• 40 Powershares QQQ (QQQQ - commentary - Cramer's Take) (QQQQ) = NDX
• 100 Diamonds (DIA - commentary - Cramer's Take) (DIA) = DJIA
• 10 iShares Russell 2000 (IWM - commentary - Cramer's Take) (IWM) = RUT

We can simply take these ETFs and substitute them into the Replicated SPX formula above to arrive at a Replicated SPY. Once this is accomplished, we are free to arbitrage.

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Know what you own: Other index ETFs include the Vanguard Extended Market ETF (VXF - commentary - Cramer's Take), the Vanguard Total Stock Market (VTI - commentary - Cramer's Take) and the iShares MSCI Emerging Markets (EEM - commentary - Cramer's Take).

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At the time of publication, Rothbort had no positions in securities mentioned, although positions can change at any time.

Scott Rothbort has over 20 years of experience in the financial services industry. In 2002, Rothbort founded LakeView Asset Management, LLC, a registered investment advisor based in Millburn, N.J., which offers customized individually managed separate accounts, including proprietary long/short strategies to its high net worth clientele. He also is the founder and manager of the social networking educational Web site TheFinanceProfessor.com.

Immediately prior to that, Rothbort worked at Merrill Lynch for 10 years, where he was instrumental in building the global equity derivative business and managed the global equity swap business from its inception. Rothbort previously held international assignments in Tokyo, Hong Kong and London while working for Morgan Stanley and County NatWest Securities.

Rothbort holds an MBA in finance and international business from the Stern School of Business of New York University and a BS in economics and accounting from the Wharton School of Business of the University of Pennsylvania. He is a Term Professor of Finance and the Chief Market Strategist for the Stillman School of Business of Seton Hall University.

For more information about Scott Rothbort and LakeView Asset Management, LLC, visit the company's Web site at www.lakeviewasset.com. Scott appreciates your feedback; click here to send him an email.