Time Spread Backtesting Concepts (Part 3)

Today I conclude this brief mini-series detailing background concepts about time spreads.

Theta is one parameter I found insidious in manual backtesting. 2020-2021 time spreads generally have a lot of “jump.” They seem to hit profit targets quickly and sometimes completely out of the blue (e.g. with PnL small or negative just a day or two beforehand). 2017 time spreads, in contrast, move very slowly. Weeks go by without any significant profit and loss is more common. Perhaps because I monitored the TD ratio per guidelines shown here, I did not think to track theta itself.

2017 volatility is extremely low and I eventually realized that position theta is extremely low with these guidelines, too. Over a given period, the market can be expected to move within a probability cone. When theta is much lower, profit will not accumulate to offset this movement. Without normalizing theta by adjusting spread width, these guidelines really describe entirely different strategies for 2017 and 2020/2021. As shown in the table here, width will affect MR, which can then be normalized as discussed in that final paragraph.

Eventually, I would like to do a study with no profit targets or stop-losses. Track MFE with DTE, MAE with DTE, and then visualize to check for optimal values. This should be done in walk-forward fashion to avoid generalized curve-fitting. Maybe every month I visualize a chart of MAE/MFE over the previous six months to see what values are optimal based on recent history. These values may or may not be stable going forward.

To get started, something simpler like backtesting with a straight 10% profit target and -20% max loss could be done. I should then try to generate a variety of combinations to verify the strategy as profitable in all cases. Other pairs could be 10%/-10%, 15%/-20%, 20%/-20%, 20%/-15%, etc. Of course, the higher the number the longer the trades. For this reason, some measure of PnL%/day also makes sense…

…and by now I have lost the “simpler” part. Keeping complexity out is certainly one of the larger challenges here.

Rewind: start with +10%/-20%. I can then compare strike selection from -5% to ATM to +5% by increments of 1%, 2%, or 2.5% to assess directional bias. Transaction fees should be included, and avoiding less-liquid strikes is a possibility.

As one last piece of theoretical complexity, I suspect an X% change in horizontal skew has less effect on PnL as DTE decreases. Lower DTE means less extrinsic value remains in the short option to be affected by IV change in the first place. Tracking horizontal skew % may therefore be misleading unless done with regard to DTE.