S&P 500 ETF (SPY) - Calculating Edge on a Bullish Spread

SPY is trading $122.62, up 0.3% with IV30™ down 2.9%. The LIVEVOL™ Pro Summary is below.



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I found SPY using our Reports Tab (in beta) and searching the Bullish Butterflies Scan. Here's a quick overview of it:

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The Bullish Butterflies Report identifies butterfly spreads with less than 75 days until expiration, where the middle strike has a delta between 25 and 35 and costs less than 20% of its maximum profit potential.
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The scan then sorts by MaxGain/MaxLoss ratio. The snapshot is included (below).



I picked up the SPY in Dec. It looks like a $0.30 bet (MaxLoss) yields a potential $1.70 MaxGain if SPY can find it's way up about 1.5% more by Dec and stay there - note the operative word, it has to STAY THERE.

Let's look to the Options Tab (below).



Just as I snapped the pic, it looks like the prices actually improved by $0.01; so the butterfly can be done for $1.29. I've included the Skew Tab (below) and highlighted the strikes in play.



Finally, let's take a look at the PnL chart of this trade (below).



So, a ~6:1 MaxGain:MaxLoss looks enticing, but the question is, what are the odds that the SPY stays in the profitable range for this trade? i.e. what is the probability that SPY is in ($124.29, $127.71) on Dec 17th?

One way to do this is to use a log-normal distribution and use the ATM vol as the standard deviation; so, in this case: sigma = 15.61%. I've done some rather quick calcs, the results are below:



Hmm... So, ~20% probability that this thing wins, or 1/5. Now the real question, if you assume the probabilities and assumptions are right (and they very well may not be) is this a good trade? Is there edge?

My back of the envelope calc (after taking some numeric integrals) shows that the fair value for this trade (assuming 20% probability that SPY is in the range) is ~$0.18. So, in other words, $0.29 feels too expensive. Hmm... Is this then a sale @ just $0.29?

There's more to this.  This trade doesn't only win if the stock is in the range on Dec. 17th. What about Dec. 16th, or 15th, or...? Adding those values back in, the trade starts to look fairish... What a surprise, the most actively traded options in the country are priced to fair value... But, I bet other thinly traded companies aren't... And that's why we trade them.

This is trade analysis, not a recommendation.

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