A Little Puzzle About Warrants

A little puzzle about warrants from the book Financial Hacking.

Here are a few reasons to bother pic.twitter.com/0mwT8GBEiD

— Kris (@KrisAbdelmessih) April 17, 2023

Warrants are just call options issued by the company itself (as opposed to a call option written in a listed market by an arbitrary counterparty).

— Kris (@KrisAbdelmessih) April 17, 2023

Imagine 2 identical stocks. One with a call option outstanding and the other with a warrant outstanding. These contracts have the same exact terms (expiration date, expiration style, etc) and the stocks themselves have the same attributes but are distinct entities.

— Kris (@KrisAbdelmessih) April 17, 2023

(This is not a trick — you can accept the assumptions — the terms of the contracts and the behavior of the 2 different stocks is identical.)

— Kris (@KrisAbdelmessih) April 17, 2023

Question 1: What is worth more — the call option on Stock A or the warrant on Stock B?

[screenshot answer] pic.twitter.com/gtPVp406h2

— Kris (@KrisAbdelmessih) April 17, 2023

Then the more “devious” question.

Question 2: What if a single company has both a warrant and call option (again identical terms) outstanding…which is worth more?

[screenshot answer] pic.twitter.com/8wWCEwRnJ0

— Kris (@KrisAbdelmessih) April 17, 2023

I’ll mention one more thing that doesn’t have to do with the book. Again, this concept of “selling calls for income”.

— Kris (@KrisAbdelmessih) April 17, 2023

If you overwrite calls each month on a stock you own you are doing something very similar to just selling a portion of your position every month. If you own 100 shares of X, and you sell a .20 delta call, you theoretically liquidate 20% of your position.

— Kris (@KrisAbdelmessih) April 17, 2023

It may not feel like that because usually the calls expire worthless but look at 2 approaches:

— Kris (@KrisAbdelmessih) April 17, 2023

Strategy #1: You sell 20% of your holdings a month instead of selling calls Your position shrinks by 20% each month. In 10 months your position is .80¹⁰ or 10% of what you started with. Zeno’s paradox aside, in about a year you are out of your position.

— Kris (@KrisAbdelmessih) April 17, 2023

Strategy #2: You overwrite .20 delta calls every month

Most months you keep the call premium, approximately 1 in 5 months, your entire position gets called away.

The relative performance of the 2 strategies is going to depend on the volatility and path of the stock! pic.twitter.com/QkSHGzJd2y

— Kris (@KrisAbdelmessih) April 17, 2023

It’s tempting to think “well if I get assigned on those .20d calls less than 1-in-5 times then I’m selling the calls for more than they are worth”.

Sorry. That’s not the full test.

— Kris (@KrisAbdelmessih) April 17, 2023

Think of the scenario where you sell 20% instead of selling the call option — then the stock drops to zero. You will never have been assigned on your call but that call-overwriting strategy will have much worse results than the “sell a portion of your holdings” strategy.

— Kris (@KrisAbdelmessih) April 17, 2023

What did the performance disparity depend on?

The volatility.

— Kris (@KrisAbdelmessih) April 17, 2023

know it’s hard to believe — but calls are puts and puts are calls and this demonstration didn’t rely on the put-call parity formula to make the point. Mayim gives an intuitive proof of p-c parity as well.https://t.co/tJMu1vemZ5

— Kris (@KrisAbdelmessih) April 17, 2023

How does the warrant example reinforce "selling calls is not income?"

See screenshot pic.twitter.com/AAVbA8gXwL

— Kris (@KrisAbdelmessih) April 17, 2023

Generalizing... pic.twitter.com/pNCA1p5YkP

— Kris (@KrisAbdelmessih) April 17, 2023