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.

Butterfly Skepticism (Part 3)

On my mind this morning is skepticism regarding the protective put (PP).

I have seen the PP lauded by many traders as a lifesaving arrow to have in the quiver.

One trader described this to me with regard to a butterfly trading plan. Part of the plan provides for the following adjustment:

1. If NPD is at least 10 with market at least -1.6 SD intraday then record NPD.
2. Buy PP(s) to cut NPD by 75%.
3. On a subsequent big move, if NPD again reaches value recorded in Step 1 then repeat Step 2.
4. If market reverses to the high of purchase day, then close PP(s) from Step 2.

Upon further questioning, I got some additional information. He learned it from a guy who claims to have “mentored” many traders. The mentor (teacher) claims to have seen many lose significant money in big moves and therefore recommends this to avoid windfall losses. The teacher has shown numerous historical examples where this adjustment would keep people in the trade (not stopped out at maximum loss) and often wind up profitable. Further prodding revealed uncertainty over whether these “numerous” examples amount to more than a handful of instances. Of the several times the adjustment has been presented, he acknowledged the possibility that many could have been repetition of the same [handful of] instance[s]. He is uncertain whether anyone has presented big losing trades more than once.

Much of this casts doubt over the sample size behind this adjustment. We certainly wouldn’t want to fall prey to that described in this this second-to-last paragraph.

As described in this third paragraph, the PP is simply an overlay added later in the trade. This strategy also has its own catchy name and is marketed. In order to backtest, we could study the profitability of long puts purchased on days the market is down at least 1.6 SD (also explore the surrounding parameter space as discussed in the fourth complete paragraph here).

From a backtesting perspective, intraday is a huge wrinkle. Technically, I’d need intraday data to identify exactly when the market was down 1.6 SD in order to purchase the PP at the correct time. As mentioned in the second-to-last paragraph here, this is arguably another reason why certain trading plans cannot be backtested: data not available.

I will continue next time.

Constant Position Sizing of Spreads Revisited (Part 4)

Today I will conclude this blog digression by deciding how to define constant position size, which I believe is important for a homogenous backtest.

The leading candidates—all mentioned in Part 3—are notional risk, leverage ratio, and contract size.

Possible means to achieve—both mentioned in Part 2—are fixed credit and fixed delta.

I thought it might be the case that fixed delta results in a fixed leverage ratio. I suggested this in the last paragraph of Part 1 where I asked whether fixed delta would lead to a constant SWUP percentage. For naked puts under Reg T margining, gross requirement is notional risk. For spreads under Reg T margining, notional risk is spread width x # contracts and while notional risk may be fixed, the SWUP percentage varies.

Speaking of, we also have Reg T versus portfolio margining (PM) to complicate things. Both focus on a fixed percentage down (e.g. -100% for Reg T vs. -12% for PM) on the underlying. However, PnL at -12% can vary significantly with underlying price movement. PnL for spreads at -100% will not change as the underlying moves around because the long strike—at which point the expiration risk curve goes horizontal to the downside—is so far above.

Implied volatility (IV) also needs to be teased out since it will affect some of these parameters but not others. Given fixed strike price, IV is directly (inversely) proportional to delta (relative moneyness). For naked puts assuming constant contracts and fixed delta, IV is inversely proportional to notional risk and to leverage ratio. IV does not relate to leverage ratio for spreads, which is net liquidation value (NLV) divided by notional risk as defined two paragraphs above in the last sentence.

After spending extensive time immersed in all this wildly theoretical stuff, I seem to keep coming back to notional risk, leverage ratio, and fixed delta. The first two vary with NLV* and with # contracts due to proportional slope of the risk graph. Number of contracts can vary to keep notional risk relatively constant as strike price changes but this applies more to naked puts and less to spreads where spread width is of equal importance.

I want to say that for naked puts, the answer is fixed notional risk (strike price x # contracts), but we also need to keep delta fixed to maintain moneyness. With fixed credit, changing the latter would affect slope and leverage ratio. This is how I described the research plan originally and we will see whether an optimal delta exists or whether results are similar across the range. In the midst of all this mental wheel spinning, I seem to have gotten this right for naked puts without realizing it.

I guess I have also lost sight of the fact that this post is not even supposed to be about nakeds (see title)!

Getting back to constant position sizing of spreads, I think we can focus on notional risk and moneyness but we should also factor in SWUP. As the underlying price increases (decreases), spread width can increase (decrease) and we will normalize notional risk by varying contract size. Short strikes at fixed delta will be implemented and compared across a delta range.

Which is what I had settled on before (for spreads)…

[To reaffirm] Which is what I had settled on before (for naked puts)…

As I unleash a gigantic SIGH, I question whether any of this extensive deliberation was ever necessary in the first place?

I think at some level, this mental wheel spinning is what I missed as a pharmacist. The complexity fires my intellectual juices and is great enough to require peer review/collaboration to sort through. Once that is done, selling the strategy is an entirely separate domain suited to different talents, perhaps.

I left a job of the people (co-workers/customers) for a job that begs for people, which I have really yet to find. Oh the irony!

* By association, this is why I stressed magnitude of drawdown as a % of initial account value (NLV) in previous posts.

Constant Position Sizing of Spreads Revisited (Part 3)

Happy New Year, everyone!

The current blog mini-series has been a tangent from the automated backtester research plan. Today I will discuss whether fixed notional risk—with regard to naked puts and spreads—is even important.

This issue is significant because it seems like fixed notional risk is the “last man standing” since I initially mentioned it in Part 1. I have reassessed the importance of so many concepts and parameters in this research plan. The fact that they get misunderstood and reinterpreted is testament to how theoretical and highly complex they are. Especially from the perspective of avoiding confirmation bias, I believe this is all debate that must be had, and a main reason why system development is best done in groups as a means to check each other.

The reason fixed notional risk may not matter is because leverage ratio can vary. I also mentioned this in the third-to-last paragraph here. Leverage ratio is notional risk divided by portfolio margin requirement (PMR). Keeping PMR under net liquidation value and meeting the concentration criterion are essential to satisfy the brokerage. Leverage ratio can be lowered by selling the same total premium NTM. This will affect the expiration curve by decreasing margin of safety as it lifts T+x lines. Analyzing this, somehow, might be worth doing if backtesting over a delta range does not provide sufficient comparison.

Whether “homogeneous backtest” should mean constant leverage ratio throughout is another highly theoretical question that is subject to debate. Keeping allocation constant, which I aim to do in the serial, non-overlapping backtests, is one thing, but leverage can vary in the face of fixed allocation. I discussed this here in the final four paragraphs. In that example, buying the long option for cheap halves Reg T risk but dramatically increases the chance of blowing up (complete loss) since the market only needs to drop to 500 rather than zero. While the chance of a drop even to 500 is infinitesimal, theoretically it could happen and on a percent of percentage basis, the chance of that happening is much greater than a drop to zero.

Portfolio margin (PM) provides leverage because the requirement is capped at T+0 loss seen 12% down on the underlying. In the previous example, 500 represents a 50% drop. Even under PM, though, leverage ratio can vary because of what I said in second-to-last sentence of paragraph #4 (above).

When talking just about naked puts, much of this question about leverage seems to relate to how far down the expiration curve extends at a market drop of 12%, 25%, or 100%. This brings contract size back into the picture because contract size is proportional to downside slope of that curve.

With verticals, though, number of contracts is less meaningful because width of the spread is also important. The downside slope will be proportional to number of contracts. The max potential loss of the vertical depends not only on the downside slope, but for how long that slope persists because the graph only slopes down between the short and long strikes.

Either way, you can see how number of contracts gets brought back into the discussion and could, itself, be mistaken as being sufficient for “constant position size.”

I certainly was not wrong with my prediction from the second paragraph of Part 1.