Computing Delta-Hedged Option Returns

I was reading some papers on delta-hedged option returns and came across an intriguing paper that I found quite interesting.

However, I was a bit confused on the authors' methodology of computing option returns for their strategies. For some context, the paper is looking at the returns of a gamma selling option strategy with S&P500 as the underlying. The formula is on page 5 of the paper

Roni Israelov, Harsha Tummala: Which Index Options Should You Sell? SSRN, 28 Jun 2017

They use the following formula:

I found this confusing because I would expect the return of a delta-hedged short option position to be the daily change in price divided by the initial cost of entering the position (just like all other papers I have read on this subject). In this case, they simply divide the daily P&L by the underlying.

Is there something I'm missing?

It sems a plausible though not perfect measure.

The numerator is the dollar p&l of one option hedged with futures.

The notional value of one option is proportional to the S&P level (specifically 250 times S&P futures for CME options, 100 times SPX for CBOE options). The study goes from 1996 to 2015, during which the notional value has changed (increased) considerably.

The division by SPX(t-1) is a normalization to take into account the changing value of 1 option. It is not perhaps a "return" but it is proportional to the return if you assume the capital needed to do this trade is a constant fraction of the notional value of one option.

(In the absence of historical data on margin requirements, which I believe is hard to find, it is perhaps the best you can do. Though it won't impress academics).

• I see, so they basically compute a sort of “normalized” P&L for the option position. So it kind of makes sense. Even if the data for margin requirements isn’t available, wouldn’t it be better to simply use the same numerator divided by the cost of entering the position (short option - delta hedge) at t-1 to get a better approximation of the return? Apr 17, 2022 at 7:09