An Arbitrage Strategy for Trading Indices
Scott Rothbort
12/22/08 - 12:14 PM EST
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 |
| 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 |
|
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:
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.
Know what you own: Other index ETFs include the Vanguard Extended Market ETF(VXF Quote), the Vanguard Total Stock Market(VTI Quote) and the iShares MSCI Emerging Markets(EEM Quote).
This was originally published on RealMoney
on Dec. 18, 2008. For more information about subscribing to RealMoney
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