How much SPY put options contract do I need?

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Picco

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Consider me having a $450,000 equity portfolio that is assumed to track the SP500 index perfectly. Say current SPY level is 110, and I want to purchase a contract with strike price of 95. How many contracts do I need to purchase to hedge my portfolio? Ignore delta-hedging and all those kind of exotic stuff.
 
Is this correct:
# of contracts needed = 450,000/(110*100) = 41
 
I don’t remember the details very well (though I should)
I think there is a multiplier in there somewhere for the S&P, which is $250 per point on the S&P.
So your portfolio is equivalent to 450,000 / 250 = 1800 S&P “shares” at 110.
Most option contracts are for 100 shares, but the S&P may be special. So that would be 18 contracts, unless there is some special rule about S&P contracts.
(I’m embarrassed that I am not more confident about remembering those details, so if someone wants to correct me, I’m happy to have my memory refreshed).
 
Ah, I see my mistake. (Portfolio Value)/(S&P index price) = (# shares).
I shouldn’t have divided by the multiplier, but by the price (as with any other stock). I knew something wasn’t feeling right there.
 
There are 3 ways to hedge: Options on SPX futures, options on the SPX index directly, and options on SPY. I would buy options on the SPX cash directly (cash settled market). Why buy options on SPY when you can buy options directly on the index?
250 is the multiplier on SPX futures, the option on the SPY or SPX cash is 100.
If you bought options on the SPX, you would only need 4 contracts (450,000/1100*100). Also, keep in mind this hedge really only protects approx $388,600 of the value of the portfolio (due to difference between strike and market)
 
Although minis would increase transaction costs and introduce basis risk between futures and cash.
 
Also, many people actually own SPY, so it makes sense to hedge it with SPY options. For these SPY fund owners, it’s also worth considering that it has tracking error with respect to SPX.
 
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