You are comparing two firms, Bex and Ajax Limited. The profitability of both firms stands to increase from reduction in income tax expenses. The price of Bex shares indicates a probability of 0.88 that income taxes will be reduced within the year. The price of Ajax Limited stock, however, reflects a 0.47 probability that income taxes will be reduced within that time frame. All other information related to valuation indicates that the two stocks appear comparably valued.

Which statement(s) is (are) TRUE?

I. The implied probabilities of 0.88 and 0.47 are inconsistent in that they create a potential profit opportunity.
II. The shares of Bex are relatively overvalued compared to Ajax, as their price incorporates a much higher probability of the favorable event (reduction in income taxes) than the shares of Ajax.
III. The shares of Ajax are relatively undervalued in comparison with the shares of Bex.

Correct Answer: I, II and III

Inconsistent probabilities arise when two or more assets are priced based upon different probabilities assigned to the same event. This creates opportunities for wise investors to take advantage of the inconsistencies.

A term that is often used for this is a pairs arbitrage trade. Pairs arbitrage trade is a trade in two closely related stocks involving the short-sale of one stock and the use of proceeds to purchase more of the other stock.

The theorem known as the Dutch Book Theorem states that inconsistent probabilities create opportunities for profit.

Consider the following scenario: Two stocks, A and B, in the same industry, in which an important announcement is pending, have share-prices which reflect the pending announcement differently. Suppose that an investor feels that stock A has the announcement factored into its price with a probability of 0.7, but stock B has the announcement factored into its price with a probability of just 0.4. Suppose also that the announcement is likely to be favorable for both stocks. One of two scenarios could exist:

1. Stock A is fairly valued and stock B is undervalued.
2. Stock A is overvalued and stock B is fairly valued.

In either case, stock B would seem to offer better value than stock A, and thus the investor, provided that he has confidence in his beliefs, could adopt the aggressive strategy of short-selling stock A and using the proceeds to purchase stock B.

Note that the costs of such a transaction would need to be taken into account in order to assess the viability of the trade. Ultimately, though, investors, through their buy and sell decisions, will eliminate the profit opportunity and inconsistency, as the share prices will alter by taking into account the demand for each stock.