Let's say there is a discrepancy is the market with respect to implied spot-vol beta (implied skew) and the actual beta of ATM vols with spot. Let's say Put vol > Call Vol but the atm vols are rising as spot goes up.
How to formulate a vanilla trade (combination of call,puts and underlying) that will have exposure on (implied beta - realized beta) using which I can take a bet on the arbitrage (statistical) of this pattern reverting to normal (same direction of implied and realized).
To clarify terms , implied beta means the spot-vol correlation that is implied by the price of risk reversals. Realized beta means spot-vol correlation measured from recent market behavio.
I don’t believe a trade can be constructed with positive expectation if the market behavior returns to “normal”. The market is priced such that “normal” behavior is assumed already. The fact that recent behavior is different does not affect anything.
This is analogous to a simple vol trade where recent realized vol is 15% whereas options are priced at 12%. You cannot make money by betting that realized vol will return to 12%, because the market already assumes so.
However you can certainly bet that the abnormal behavior will continue, by trading a risk reversal and rebalancing Vega and spot exposure daily.
