Risk and Payoff Structure of Covered Calls with Extra Short Calls

# Analysis of Unbalanced Covered Calls


# Analysis of Unbalanced Covered Calls












Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events.

I couldn't find any reference to this strategy (unbalanced is an adjective I chose, referring to the non-equivalent legs), it looks favorable because of the amount of premium that can be collected.

So the covered call -10 ATM calls +1000 shares

and the additional naked calls

-10 ATM calls

This is considered because of margin requirement for the naked calls isn't as much as completely covering them.

For example purposes, 65 strike is used and assume symbol shares were purchased at or near 65

The risk profile of a normal covered call looks like this: The green line represents profit/loss at expiration, the "hockey stick" risk profile you may be familiar with.

Do note: the premium collected here represents a maximum 7% gain on the entire position, which is mainly the shares.

Also note: the normal covered call becomes loss making at underlying price $60.55 (by expiration), this represents at 6.8% decline in the underlying asset. This represents 6.8% of downside protection.

The risk profile of an unbalanced covered call looks like this:

Do note: the premium collected here represents a maximum 10% gain on the entire position, and the symbol would have to decrease or increase by 2 strikes on expiration (63/65 strike) or increase by for you to get the same 7% gain that the normal covered call would have provided in its best scenario.

Also note: the unbalanced covered call becomes loss making at underlying price $58.33 (by expiration), this represents a 10% decline in the underlying asset and 10% of downside protection. This is sort of favorable because all of the time premium will still be collected and more calls can be written for the next option series after expiration, so total account equity will still grow despite losses in the underlying.

Again, the green line represents profit/loss at expiration day.

Given the extra downside protection, and potential need for a stop order if the asset price rises too high, is the added risk of the naked leg justified? Mainly, what other variables should be considered in this analysis, especially related to the theoretically unlimited loss on asset price rise and how fast the delta will increase on the naked leg.

This is similar to the risk profile of a diagonal, except that the underlying is still stock so after expiration, one could write new options at any strike price without changing margin considerations. (in a diagonal, the long leg's strike has to be subtracted from the short legs strike, resulting in potentially massive margin implications)

Thanks for any insight

## Answer by r2k0 (score 1)

https://quant.stackexchange.com/a/14242

Selling 2 ATM calls against 100 underlying shares result in Delta neutral.

> "Given the extra downside protection, and potential need for a stop order if the asset price rises too high, is the added risk of the naked leg justified?"

The risk is if the move is more than extrinsic premium collected. One thing to watch out this type of trade is skewness. There are better ways to manage if the price move more than extrinsic premium collected depending on your risk tolerance.

## Answer by Bob Baerker (score 0)

https://quant.stackexchange.com/a/58415

The reason that you couldn't find any reference to this strategy is because you are looking at a synthetic position that contains more legs than necessary.

If you buy 1,000 shares and sell 10 ATM 65 calls, you have executed a covered call. This position is synthetically equivalent to selling 10 short 65 puts. Now you sell an additional 10 short ATM 65 calls and you have created a short straddle that looks like this:

The risk profile of a naked straddle is not similar to the risk profile of a diagonal spread. A diagonal spread is a kissing cousin to a covered call, often called the Poor Man's Covered Call, and it's risk profile is 'curvier' than that of a covered call because the options have different expirations (the long leg still has time premium remaining at near term expiration and it varies as the underlying's price varies). Compare the following two graphs: