In a covered call strategy, should I hold the call or sell/roll if the delta becomes too small?

Question

I am tweaking a covered call algorithm. The short leg consists of out of the money call options. The goal is to collect the tim premium, but an equally favorable circumstance is when the call decreases in value due to the lower price of the underlying asset in the normal course of market fluctuations. The short leg can easily go from a 10% gain to a 60% gain because it shifts further out of the money, at this point the price decrease becomes much slower, as it will take several more standard deviations to take the 60% gain to an 80% gain, this is where I am contemplating closing the short leg in favor of selling the call that is now closer to the money.

Are there any caveats of doing this? My risk profiles do not intuitively show me the caveats of rolling the short leg in the middle of a covered call.

Upon getting the second set of short options (and closing the first set of short options) , they will still be covered by a long leg. If price decreases, the short options approach $0 (100% gain), if price stagnates, the short options approach (100% gain), if price increases I will collect only the time premium from the short options and my maximum gain with the long leg is limited.

Am I missing something? Insight appreciated

Answer 1

"I am contemplating closing the short leg in favor of selling the call that is now closer to the money. Are there any caveats of doing this?"

• The biggest caveat is the obvious issue of whip-saw. Where right after you roll down, the market turns up again.
• Also, if you are starting with an out of the money call (delta < 50), and the stock declines, you will likely be losing more on the covering stock than you will be making in premium collection on the short call.

You can get as complex as you like by considering vol and theta, etc...

Your choices in this strategy basically are:

1. close the short call option
2. roll in the same month
3. roll to a future month.

The easiest way to compare these options, and make a decision, is to look at the holding period return implied by collecting the premium for these options, and then choosing the one with the highest annualized return. Then consider the risk as a tie-breaker.

So if you might roll down in the same month, and the implied annual return is 24%, for example, and the alternative is rolling out to the next month at the same strike, with an annualized return of 29%. (assuming that both strikes are within your risk criteria) This lets you make an apples-to-apples comparison of your choices.

As a practical matter, (and depending on the term structure of volatility and the time to expiration ) often rolling out to a later month is the optimal choice, given a specific set of risk constraints.