Computing Delta-Hedged Option Returns

Question

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?

Answer 1

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).