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With the great success of my ETF Covered Call strategy, I’ve decided to expand onto a mathematical model surrounding arbitrage around S&P 500 index. With the volatility in today’s market as it is, it makes sense to explore this theorem and cook up a new recipe for success.

The ingredients: SSO (Ultra S&P 500 Proshares) & SDS (Ultra Short S&P 500)

Take two inversely leveraged S&P 500 ETFs and apply at a 3:2 ratio. In this example, I would buy 300 shares of SDS and buy 200 shares of SSO.

The table below shows results of what would happen if the S&P 500 climbed or dropped 1%, 2%, 3% respectively to each ETF.

S&P Arbitrage

S&P 500 - Down 3% Down 2% Down 1% - Up 1% Up 2% Up 3%
                 
SSO $86.40 $(5.18) $(3.46) $(1.73)   $1.73 $3.46 $5.18
                 
SDS $55.00 $3.30 $2.20 $1.10   $(1.10) $(2.20) $(3.30)
                 

Unfortunately, this table is where the simplicity ends because the next step involves looking at options for 30, 60 and 90 days out on both of these leveraged ETFs and solving a 3 by 3 matrix for the optimum positive return.

The end result is to essentially arbitrage the S&P 500 and always earn a positive return whether the index drops or rises. It is always easier to see the solution in my head than to spend a great deal of time writing it down then translating it for a primitive computing device ;)

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I’ll keep tweaking the recipe and hopefully publish some results in the future. With the holidays around the corner and a couple of multi million dollar projects on my plate, it’ll be difficult to get this problem wrapped up anytime soon.

If there are any mathematicians out there interested in the problem I think I’ve provided enough clues but let me know if you want to have at it.