The Warrant Puzzle

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).
Imagine 2 identical stocks. One with a call option outstanding and the other with a warrant outstanding. These respective derivative contracts have the same exact terms (expiration date, expiration style, etc) and the stocks themselves have the same attributes but are distinct entities. 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.
  1. What is worth more — the call option on Stock A or the warrant on Stock B?
    1. Answer
      • The primary difference between warrants and listed call options is the effect of dilution: the warrants, when exercised, are exchanged into new shares to be issued by the company, rather than previously existing shares to be delivered by the counterparty.
      • Think of what happens at maturity. Suppose both companies have soared over the preceding five years. Warrant holders and option holders all want to exercise. Let's say both originally had 10 shares outstanding. The option holder of company A would receive ten percent of the value of the company once he chooses to exercise. But the warrant holder of company B would receive one new share out of the now total eleven shares, so he would have about nine percent of the company.
      • dilution affects the value of the warrant such that it costs less than an equivalent option on a different company that had never issued a warrant.
  1. What if a single company has both a warrant and call option (again identical terms) outstanding…which is worth more?
    1. Answer
      They are worth the same!
      Dilution affects the value of the listed option on the same firm in exactly the same way as it affects the warrant…We can even prove it by arbitrage:
      Let's say the warrant costs less than the option. Then we buy the warrant and sell the call and pocket a small difference in premium. Now, whenever the option holder informs us they want to exercise, we will exercise the warrant. The option holder was expecting existing shares, not new shares, but once the new shares are issued, they are all fungible, meaning exchangeable with each other. And if the option holder allows the options to expire worthless, we too can let the warrant expire worthless. In other words, it is a perfect hedge.
[Kris: Why I Love This Puzzle and how it proves that “selling calls for income” is a nonsense statement. ]
Think of what is happening with a warrant — the warrant issued by the company is converting risk to liquidity. It's part of the cap structure not income.
Assets and liabilities change by the same amount if the warrant is fairly priced.
Ask yourself:
What amount should the stock drop by when the warrant is issued?
  • The stock should drop by the notional amount of warrants issued adjusted by its delta!
But should you use the implied delta or a delta generated by expected realized vol?
  • The importance of this question is made plain when considering the extreme…a warrant issued for zero (ie zero implied vol) has cost the company something even if it generates zero delta!
Finally, there’s an insight germane to all investors even if they never heard of warrants:
This reasoning is yet another demonstration for why “selling calls for income” is a misguided framing…
When a company sells stock, the cash proceeds are not income.
When a company issues warrants, the cash proceeds are not income.
When a company issues bonds, the cash proceeds are not income.
When you sell calls on a company, that is not income.
In all cases, the seller/writer/issuer is simply exchanging a risk (liability) for cash (an asset). In a double-entry accounting framework there has been no exchange of value. There is no income! [If you sold the call for more than it's worth then there's an argument to book the excess premium as income similar to what market makers call “theo”.]