Warrants: A Mathematical Method of Evaluation

Abstract

A WARRANT IS A TRANSFERABLE OPTION conferring on its holder the right to purchase a specified number of shares of the issuer's stock at a stated price (often called price) for a stipulated or an unlimited time. A need exists for an accurate method of evaluating it, not because it is an important security, but because it seems to be improperly evaluated in many instances without reason. Indeed, in a field of endeavor where so much allowance must be made for imponderables, here is a security whose value is simply a function of only one variable, the price of the stock to which it is related, provided the exercising price is constant and the term unlimited or long enough. It can be argued that it is the future price of the stock which concerns the purchaser of the warrant, who will pay up for the warrant of a growth stock, for example. But an option cannot be better than what it confers a claim on. If the stock is particularly attractive, this should also be reflected in its current price; hence there is no reason why a fairly close relationship should not be maintained between the two securities at all times. Admittedly the stock and the warrant are traded separately and probably attract different groups of traders and investors who may assess the same fundamental factors differently; furthermore, factors of supply and demand are different in each case. So in the market place, the relationship between the stock and its related warrant cannot be perfect. It would be surprising if it were. But we are not only interested in how warrants behave, but also how they should behave. In fact, the value of a soundly based, reliable method of evaluating warrants would be to supply us with criteria against which actual market prices can be judged. Our thesis is that there is a mathematical relationship between the price of a stock and that of its related warrant, which can be supported in theory, and which holds within reasonably close limits in many cases in practice. Another objective of this article is to define the principal characteristics of warrants insofar as they might be useful in making investment decisions.

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