An Arbitrage Strategy for Trading Indices

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 Quote) (SPY) = SPX
• 40 Powershares QQQ(QQQQ Quote) (QQQQ) = NDX
• 100 Diamonds(DIA Quote) (DIA) = DJIA
• 10 iShares Russell 2000(IWM Quote) (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 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 or other premium services from TheStreet.com, please click here.