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.