An Arbitrage Strategy for Trading Indices

Editor's note: This was originally published in two parts on RealMoney. It is being republished as one article as a bonus for TheStreet.com readers.

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 "How to Build Your Own Trading Model in 8 Steps ," 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:

Regression Statistics Multiple R 0.99741 R Square 0.99482 Adjusted R Square 0.99479 Standard Error 12.79523 Observations 491   Anova df SS MS F Significance F Market Cap. ($mill.) Regression 3 15,325,275.10 5,108,425.03 31,202.61 0 $ 8,250 Residual 487 79,730.61 163.72 - - N/A Total 490 15,405,005.71 - - - N/A - Coefficients Standard Error t Stat P-value Lower 95% Upper 95% - Intercept (131.66354) 5.13262 (25.65233) 0.00000 (141.74834) (121.57874) - 1,759.37 (0.00845) 0.00629 (1.34321) 0.17983 (0.02081) 0.00391 - 12,474.52 0.08685 0.00145 59.88824 0.00000 0.08400 0.08970 - 787.42 0.59637 0.01531 38.94880 0.00000 0.56628 0.62645 Source: LakeView Asset Management, LLC

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