Weighting An Options Pair Trade

A question for the mailbag

Friends,

An option trader pinged me about a trade between a correlated pair of names whose IV ratio was trading at an extreme level compared to the ratio of realized volatilities that the pair has experienced in the past.

This trader is experienced. He understood that pitting vanilla options against one another invites path dependence. It’s worth spelling that out with a demonstration:

Imagine both assets are trading for $100 so you buy the 100 strike straddle in asset A and short the 100 strike straddle in asset B. Once these assets start bouncing around the moneyness of the straddle positions will get out of sync. After a week if both assets realize the same volatility but the path of A means it’s up 5% and the path of B means its up only 2% then you will have more gamma and theta in B because the straddle is closer to at-the-money (ATM). The further you get from a strike the more your exposure “goes away”. Far OTM options spit off smaller greeks and are less sensitive to changes in underlying price or volatility.

Let’s get to the question.

He was theta-weighting the trade instead of vega-weighting the trade. He wanted to know if I would do the same.

I’ll give examples of how each approach will end up weighting the legs, how I’d weight the trade, how to map weightings to the nature of a relationship, and even what greeks depend on.

By the time you finish this post, you will be able to understand the risks of different weightings and how to compute weightings in your head knowing nothing else except spot prices and ATM vols.