Calculating holding period return for short option positions

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Hi! Anyone have some insight into the proper method for calculating the holding period return for a short option position? Would the below example be appropriate:
Day 1: Sold (to open position) 1 SPX contract with a strike of 2000 for $5 for December expiration.
Day 2: Bought (to close position) same 1 SPX contract with a strike of 2000 for $4 for December expiration.
HPR: ($5 - $4)/$5 = 20%
Thank you!
 
You need to consider the fact that option positions contain a lot of leverage, and everything should be viewed in terms of notional value.
Let’s go through an example. Let’s say SPX is at $2000 and I trade some short dated options. I buy one 2000 strike call and sell one 2000 strike put. Let’s say both options cost the same amount of money, so total initial premium is zero. This position has 100% delta.
Now, the price of SPX increases by $10. My position is now worth about $10. What is my percentage return? Is it $10 divided by zero = infinity? Of course not. The fact is, that I replicated the risk and return of holding $2000 of SPX. So, the most accurate way to measure my return is $10/$2000 = 0.5%.
Back to your question: Let’s say SPX = $2000 at trade inception. Your payoff diagram is drawn as if you are making delta bets on this amount. Therefore, you made $1 off a risk equivalent notional of $2000, and your return is 0.05%.
Edit: You could also consider calculating return per unit of initial $delta, since the replicating portfolio for your option position is delta times the number of option contracts. Academically, this makes sense to me. I don’t think most people do this though.
 
Your investment is the price you pay when you close the position: $4. So the holding period return is ($5 − $4) / $4 = 25%.
 
Ohai, thanks for your reply!
Yes, I shared a similar intuition to yours: the gain/loss needs to be tallied against the notional value of the position. In the case of a short put option struck at $2,000, you’re on the hook for, in theory, the full $2,000 should the Index go to zero. With that said, and this is where I ran into a deadend, how do you apply that if you’re short a call struck at $2,000? That is, how do do you estimate notional value… from the way I’ve understood it, technically, the notional value of a short call struck at $2,000 is infinite. Then again it’s the same issue as how you’d determine the HPR.
The initial delta might be one curious way of doing it, and it’d certainly hold for the short call position dilemma just noted.
S2000: Thanks for your comment too! So under this approach, say a contract initially sold for $5 was bought back (to close) at $20. So you’ll record a net $ loss of 15 ($20 less the premium received) and divide that by the closing purchase price of $20 for a -75% HPR?
 
It shouldn’t matter if you have a put or call - notional value is still $2000. If your option is has 50 delta, your exposure is calculated as 50% of $2000.
 
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