So, I gained a lot of followers this week, and I figured that I would do a quick post on a seemingly mundane topic: delta. I primarily trade skew, and delta can be really hard to manage. What is my damn delta? ¯\\_(ツ)_/¯ 1/(n!)

Vanna, the primary measure of your skew risk, can be viewed 2 ways (not going to mention partial derivs here to keep it simple):
1) how much your vega changes for a $1 move in the underlying
2) how much your delta changes for a 1vol move (e.g. vol from 38% to 39%) 2/(n!)

(both ways are equiv, and u shld convince yourself that they have the same units). From (2), we can see one natural heuristic: when flat price(fp)/vol corr is the same sign as my vanna, then I am synthetically long gamma, and when signs are diff, then synth short gamma 3/(n!)

Why? Well think about long gamma: when fp rallies, I gain delta (and need to sell to lock it in), and vice versa for when fp falls. Let's take case where fp/vol > 0 and vanna > 0. We have the following:
fp increases -> vol increases -> delta increases (long vanna) 4/(n!)

Similar when fp decr (exercise for reader). Not always true that fp incr -> vol increases, but that's more about how fp/vol corr *realizes* (much like realized vol in VRP). When fp/vol corr < 0 and vanna > 0 (e.g. long calls or short puts), then you are synth short gamma 5/(n!)

FYI, I am not saying a simple long OTM call position is short gamma! I'm saying that the vanna exposure creates a similar dynamic to being short gamma. So, changes to vol will offset some of your gains from being long gamma with a long OTM call. 6/(n!)

The farther out in tenor you trade, the bigger the effect (because vega is larger when TTM is larger). Anyway, this change in vega can be a big deal because, let's say the mkt doesn't move at all, but vols decrease (and you're long OTM calls "delta neutral"). 7/(n!)

Well, now you are short the underlying, and need to buy some delta (ok if fp hasn't moved, but this is rarely the case). This is why I joke that CL OTM calls are actually short delta. Very frequent dynamic is that fp increases, but the call price decreases! 8/(n!)

These are usually secondary considerations if you're trading the front, but for a skew trader, they are often the diff between making money and losing. Finally, I'll post later about this, but you should almost never trade just the und to rebalance greeks w/ a skew pos. 9/(n!)

You need to rebalance delta, vega, and gamma simultaneously, so you end up trading calls, puts, call spreads, put spreads (not delta hedged) in order to rebalance them together (e.g. if I want to buy vol and delta, then I'll buy calls live, i.e. with no delta hedge). 10/(n!)

No wonder you end up with so many strikes on the book! Anyway, hope this advanced topic wasn't too boring or stupid. Even if you don't trade it, I think it helps to have intuition for how vol affects your greeks. Have a nice weekend! fin/(3↑↑↑↑3)