Butterfly Skepticism (Part 4)

Today I want to complete discussion of the protective put (PP) butterfly adjustment.

I might be able to come up with some workaround (as done in this second paragraph) for PP backtesting. I could look at EOD [OHLC] data and determine when the low was more than 1.6 SD below the previous day’s close. In this case, I could purchase the put at the close. This would bias the backtest against (not a bad thing) the adjustment in cases where the close was more than 1.6 SD below because the put would be more expensive.

Unfortunately, I am not sure this particular workaround would work. If the close is less than 1.6 SD below then the backtested PP would be less expensive than actual. Furthermore, if I waited until EOD then the NPD and corresponding PP(s) to purchase would be different. This would distort the study in an unknown direction. I could track error (difference) between -1.6 SD and closing market price. Positive and negative error might cancel out over time. If I had a large sample size then this might or might not be meaningful.

At best, this workaround seems like a questionable approximation of an adjustment strategy that is precisely defined.

Before dismissing the PP out of frustration, let’s step back for a moment and piece together some assumptions.

First, I believe the butterfly can be a trade with somewhat consistent profits and occasionally larger losses. Overall, I’m uncertain whether this has a positive or negative expectancy (hopefully to be determined as I begin to describe here).

Second, as butterflies are held longer, I believe profitability will be decreased. I have seen some anecdotal (methodology incompletely defined) research to suggest butterflies are more profitable when avoiding periods of greatest negative gamma.

Third, I have seen anecdotal (methodology incompletely defined) research to suggest PPs as unprofitable whether:

• purchased in high or low IV
• purchased at specified deltas
• purchased for specified amounts
• held to expiration, managed at specified profit targets, or managed at 50% loss

Fourth, this adjustment will require any butterfly to be held longer on average. The additional time will be needed to recoup the PP loss. The result will be, as described per second assumption above, decreased average profitability.

In my mind, combining the first and fourth assumptions does not bode well.

The big unknown involves the magnitude of the largest losses and in what percentage of trades those largest losses occur.

Interestingly, the trader who explained this to me said PP will lose money in most cases. What it can prevent is a massive windfall loss. Being forthright [about the obvious?] may give the teacher more credibility. Without backtesting, though, I think it leaves us with more than reasonable doubt over whether this approach tends toward profit or loss.