No free lunch - even in the warrant market

We've seen in a previous section that the intrinsic value of a warrant is defined as the share price minus the exercise price. If a warrant has an exercise price of 100, and the underlying shares are trading at 120, the warrant has an intrinsic value of 20. This has a value because shares can be bought, via the warrant, for 100, even though the share price in the market is 120.

The warrant's price will rarely be - and never significantly so - lower than its intrinsic value. The reason is that this would create a riskless arbitrage: investors could buy the warrants and exercise them into shares, for less than the shares are trading at in the market.

If a warrant is deep in-the-money, or expires in a very short time, a warrant price may trade at a small discount to its intrinsic value. In theory, this presents an arbitrage opportunity; in practice, any potential profit would be offset by the transaction costs.

The normal situation is for the warrant price to be quite a bit more than the intrinsic value. Why is this? Why are investors willing to pay, sometimes significantly, more than the intrinsic value for a warrant? The reason is time value.

The time value of a warrant

 

A warrant has two components of value:

warrant price = intrinsic value + time value

The time value of a warrant is the residual value of the warrant, not accounted for by the intrinsic value. Therefore -

time value = warrant price - intrinsic value

Or, this can be re-written for quicker calculation as -

time value = (warrant price + exercise price) - share price

Investors are willing to pay a premium (time value) over the intrinsic value because of the remaining life of the warrant. As the exercise price is fixed, any future increase in the share price up to the warrant expiry, will be reflected by commensurate gains in the intrinsic value.

In the example illustrated in the diagram, the current intrinsic value of the warrant is 20. If the warrant was due to expire tomorrow, then like as not the warrant would be priced around 20 as well. But if the warrant still has, say, 4 years before expiry, there's a very good chance that the share price will increase significantly over that time, and the intrinsic value rise to 50, 100, or 200...who knows? In the example, the warrant is priced at 50, which, given that the intrinsic value is 20, gives the warrant a time value of 30. The market is therefore telling us that investors are willing to pay 30 for the potential for futures gains in the share price (and thereby gains in the intrinsic value), before expiry of the warrant.

A note on relationships

With all these terms flying around, it can be difficult to understand what affects what! Walking through this, stage by stage -

1. The shares trade freely in the share market, their price determined by the normal laws of supply and demand.
2. The exercise price is fixed.
3. Intrinsic value is defined as the difference between the share price and the exercise price. Note, intrinsic value itself is not related at all to the price of the warrant - it is purely a function of the share price and exercise price.
4. The warrants trade freely in the warrant market, their price determined by the normal laws of supply and demand.
5. Time value is defined as that component of the warrant price not accounted for by the intrinsic value.

An out-of-the-money warrant

 

If a warrant is out-of-the-money (see diagram), by definition a warrant has no intrinsic value. In this case, the time value component accounts for all the warrant price.

A couple of comments on time value

1. Time value is a tricky thing. How much are investors willing to pay for a warrant with an exercise price of 100 and a life of 3 years? How much for a warrant with a life of 5 years? How much will they be willing to pay this time next year? No one knows.
2. It is not possible to compare warrants knowing only their time values. One warrant with a time value of 20 is not necessarily 'cheaper' than a warrant with a time value of 30. We need to know more information about the relationship between the share, warrant and exercise prices. This brings us on to the topic of the Warrant Premium.

Premium

A pillar diagram

 

With reference to the warrant example in the diagram, there are two methods by which an investor could acquire a share in this company -

1. Directly. The investor simply buys a share at 120 in the share market. (This is represented by the left column).
2. Via the warrants. Alternatively, the investor could buy the warrants (at 50), and exercise them (100) to receive one share. (This is represented by the right column).

Of course, it would not be sensible at the moment to acquire a share via the warrant, as the total cost would be 150, when the shares can be bought directly for just 120. Nevertheless, it is perfectly possible. And the warrant premium measures how much more expensive it is to acquire a share via the warrant, rather than buying a share directly.

Warrant premiums

In this case, the extra cost involved is 30 (150 - 120). There's one more stage we take, to make this figure more useful. The premium cost is expressed as a percentage of the share price to normalise the value. Hence, 30 is 25% of the 120, and so the premium on this warrant is said to be 25%.

The mathematical formula for warrant premium is given by -

premium = 100 x ((warrant price + exercise price) - share price) / share price

The warrant premium is a similar measure to time value, except -

1. Unlike time value, the premium captures the extra information about the state of in or out-of-the-money of the warrant.
2. Warrant premiums can be compared directly with each other. As such, the premium can be regarded, perhaps rather crudely, as measuring the 'expensiveness' of a warrant. For example, a warrant with a premium of 20% can be said to be cheaper than one with a premium of 30%. (This isn't the end of the story regarding warrant valuation, but the premium is a quick, common measure used in the warrant market).

Notes on the warrant premium

A high premium warrant

• Warrants tend to have high premiums when they are deep out of-the-money, and low premiums as they become more in-the-money.
• Warrant premiums, on individual warrants, and in aggregate across the whole warrant market, are a good barometer of the mood of the market. When investors feel bullish premiums tends to rise, when they are bearing, premiums fall.
• The term 'premium' is often used in finance. Be aware that that not all the definitions are the same. For example, an option premium, is not the same as a warrant premium.
• In October 2001, the average premium on warrants listed on the LSE was 47.0%.

Summary

One thing that can remain a puzzle for many investors is the nature of the relationship between a share price and its associated warrant price. How are the two connected? While the intrinsic value is a direct function of the share price and the fixed exercise price, the remaining component of the warrant price - the time value - is more intangible. The unpredictability of time value turns warrant analysis - which would otherwise be an exact science - into an art. Time value analysis is the voodoo heart of warrants.

http://www.incademy.com/courses/Traditional-corporate-equity-warrants/Analysis---time-value-and-premium/10/1068/10002