While the proof is outside the scope of this blog, we will state that implied volatility tends to be more rich than realized volatility. As such, we will tend to be net sellers of volatility. By being net sellers of volatility, we will be net short vega and necessarily net short gamma and net long theta. Being net short vega (and therefore net long theta) also allows us to have a portion of our portfolio function as passive income, with time working in our favor. This is not to say that we will avoid long vega positions (i.e. backspreads), but that if forced to choose between a long and short vega strategy, we would choose the short vega one.

Vega v. Delta

Because we will try and carry short vega, we need to understand our tail risk moving forward. What is our worst case scenario? Carrying net short vega exposes us to sharp upward moves in volatility. When do these types of moves tend to occur? Comparing the SPX to the VIX, for example, we see that volatility tends to spike on rapid moves downward. We can see then that we have delta risk to the downside, and thus if we are net short vega we should also carry some negative delta to offset our vega risk.

Duration

By looking to maintain net positive theta as our primary portfolio metric, we should also look to optimize it. When should we enter or exit positions to maximize our profit if we intend to be net positive theta? Because option decay is initially very slow, and then grows exponentially into expiration, we can infer that the best time to take advantage of decay is sometime in the middle. Taking a look at theta vs. days to expiration (DTE) graphs (easily found online or derived yourself) shows a clear acceleration zone in the 30-60 DTE area. As such, we will look to establish our short short vega positions between 30 and 60 days to expiration, and our long vega positions a bit farther out. Taking on short vega in shorter timeframes may expose us to unacceptable gamma risk and make it more difficult to manage our trades quantitatively. The same idea applies to long vega positions.

Second and Third Order Greeks

As retail traders, the only second order greek we will consider is gamma. With the exception of gamma, I don’t feel it’s necessary to get too bogged down in second order greeks, and perhaps more importantly very few retail brokers (if any) even provide them. If you feel the need to have third order greeks available for making trades, your strategies are well outside the scope of this project.