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For your current put positions, are you hedging these positions by
buying puts on applicable indexes? (similar to recommendation in the Cohen book)

Yup, some.
Not according to Cohen's formula.

Since I have very strong ideas about the fundamental value of all the firms
against which I write puts, I'm not particularly concerned if their prices go down.
I just take the stock, and (more often than not) replace it with fresh puts.
I'm worried only about lasting deterioration their business prospects.
Merely low prices don't bother me that much; this too shall pass.

So, I buy only a relatively small number of index puts for disaster insurance.
Usually they are a dead loss. That's not why I buy fewer, it's just an observation.
I try to buy them when the index is at fresh highs and the VIX (cost of
index options) is very low (hmmmm...)
The outcome here is that if the market really crashes, I have a huge
windfall at exactly the right time to do a little shopping.
I'd love to get some Colgate or Hershey at half off.

As for scale, the face value of all the puts I write if exercised
simultaneously is typically a little more than the size of my cash pile backing them.
(not what I recommend, but it's what I do much of the time).
So I kinda sorta plan on having enough puts to cover the difference, give or take.
e.g., if I have $100 cash and write $120 in puts I wouldn't mind buying disaster puts with a face value of $20.

Right now it's kind of moot since option premiums are so low that there
aren't many tickers I'd want to hold as short puts, and what I have is running off.
At the moment I'm left holding rather more disaster puts than I need.

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