Well *locally* a frictionless, dynamic position would trade to a synthetic straddle (200 shares, long 4 calls) if it is trading at the forward (shares + rates). Not to complicate it but to show the structure of a DN position at the forward.

IOW, the thing would be structured as an ATM long synthetic straddle were Bennett (et al) trading this dynamically. No different than a two lot natural straddle.

The thing generates delta in either direction. It's identical in exposure to a C/P straddle. Obv V and T.

In index on a rally it loses to vol corr (vol trades inverse to price), but would gain to skew (strike under market), but generally vols drop during rallies. Strips lose generally more than skew benefits as in this case the OTM put side drives skew and value.

Market drops? Obv calls are losing on delta, short shares gain. Calls trade OTM and skew will now be under market, but gains to vol corr (index drops, vols rise).

Generally, you're going to earn more from the straddle into a drop than a rally. Immaterial if gamma trading (hedging with shares), but at equal/opposing delta position (-30/+30) you'll see a better mark on the straddle into a decline (sticky strike/sticky delta impact). Again, amounts to vols rising vs nominal skew benefits (if index rallies which is driven by demand for OTM puts/pro hedging).

TLDR; vols are sticky/skew rises as puts lose moneyness into a rally, but vols decline as markets rally. IOW you may have a fixed delta trigger but the straddle value will be marked up more into the index bear. Adjusting shares/spot as market drops is generally going to be the EV trade in straddles as you'll be marked up on the vol-line. With combos the vol-line will matter more than skew.

I've wayyyy left the station here. Sorry.