Hi, I want to understand a bit more in depth why the Hedge Ratio (or Delta) of a call is positive.
I already understand what it “conceptually” means: short a call, we hedge it with long underlying (& viceversa).
I guess I am trying to understand if there’s any formula where I can see this. Why “positive” hedge ratio means the above?
The delta of a call is positive because the value of a call option increases when the price of the underlying increases.
As for the hedge ratio, think of the ultimate hedge: if you want to hedge a short position in, say, 100 call options, the perfect way to do so is to close out your short position: buy 100 call options. So . . . to hedge a negative delta position you need positive delta, and to hedge a positive delta position you need negative delta.
Always remember the objective of delta hedging: you want a portfolio delta of zero.