In the competitive capital market, it is extremely rare for individuals or any non-bank corporations to uncover a pricing error in market, much less securing a riskless profit from it. This is because such opportunity, if arises, would have been swiftly identified and seized by financial institutions/hedge funds almost instantaneously.
Nonetheless, understanding the application of probabilistic rules and the concept of "total expected values" in creating a textbook riskless investment can be highly beneficial. Through a stylized and purposefully-adapted example, this newsletter highlights the uncertainties that individual investors may face when attempting to construct and implement a risk-free investment strategy.
The Scenario
Assuming the following:
Company A and Company B are listed on the stock exchange. Both companies operate in the same industry and are selling similar products in the local market.
At t=0, there is news about the imposition of a new environmental law in the industry, set to be released next month (at t=1). The new rules may potentially be favorable or unfavorable to the business operations of both Company A and Company B.
The current share prices of both companies at t=0 (see table below) have already factored in this information.
In formulating an investment strategy, Investment Company Z has conducted event studies and tabulated the expected share price movements of both companies, in response to the new rules, as shown in Exhibit A. It is anticipated that, if the news is favorable, the share price of Company A will increase from $12 to $14; conversely, if the news is unfavorable, the share price will decrease from $12 to $10. According to the Law of Expected Values, the expected share prices of both Company A and Company B under both favorable and unfavorable scenarios should equal their respective current prices today.
(Exhibit A)
Company Z then calculated the implied probabilities based on the estimated share price movements in both favorable and unfavorable scenarios, presented in Exhibit B.
(Exhibit B)
Applying the law of expected values reveals an inconsistency in the probabilities of favorable outcomes for an event. Specifically, the share price of Company B has been priced at a lower probability of a favorable outcome (33.3%) compared to Company A's probability (66.7%). These inconsistent probabilities (mutually exclusive & exhaustive) suggested either: (i) Company B share is currently undervalued or (ii) Company A share is overpriced .
If Company B share is currently traded at a lower probability today (t = 0) and the new rules turn out to be favorable, the share price of Company B is expected to increase substantially at t=1. Conversely, if the current share price B has reflected 99% chance of reacting positively to the new rules, it is unlikely for share price to increase on t=1 , as market has already priced in the favorable view of the new law.
Given that the new law will impact both companies equally and assuming Investment Company Z can accurately predict the share prices of companies A and B at t=1, Investment Company Z constructed an arbitrage strategy aiming at securing risk-free profit with no or minimal initial investment. This can be achieved by entering into derivative contracts today (at t = 0):
to short 3 shares of Company A at $12 on t = 0.
to purchase 2 shares of Company B at $18 on t = 0.
The proceeds from the share sales will be used to purchase shares of Company B, allowing Investment Company Z to avoid any cash outlay today.
Upon entering into the derivative contracts, Investment Company Z would assess the potential gains and losses from the share price movements of both companies under two scenarios: favorable and unfavorable outcomes of the new law. Assuming the new law results in a favorable outcome at t=1, Investment Company Z would need to unwind its trade positions by selling shares of Company B at $22. The proceeds would then be used to purchase shares of Company A at the latest bid price of $14, in order to return the borrowed shares to the brokerage firm. Investment Company Z would subsequently retain a net settlement gain of $2.
Company Z's investment strategy, illustrated below, demonstrates a calculated net settlement gain of $2 in both scenarios in Exhibit C.
(Exhibit C)
By applying the concept of disparity in probabilities, Company Z identified an opportunity to take an arbitrage position and earn a risk-free net profit of $2. This profit is assured regardless of whether the new law favors Company A or Company B. However, it is important to acknowledge following uncertainties faced by Company Z at t=0:
While the assets identified may be similar, there is no guarantee that Company Z has accurately predicted the share prices of both companies under favorable and unfavorable outcomes. Any miscalculation could impact the implied probabilities of events underpinning the investment positions.
The opportunity is time-sensitive. Any delay in the news release or deferment of new laws will render the arbitrage opportunity unsuccessful. Hence, the new law must be released and implemented at t = 1.
There is a tradeoff in using derivative contracts that offer high leverage. While they can amplify gains, they also come with high premiums and a significantly higher risk of losing the entire investment.
In this stylized example, Investment Company Z managed to earn a modest arbitrage profit of $2. Without substantial capital in hand, this profit can only be amplified by increasing leverage through derivative instruments.
In reality, one would probably wonder whether it is worth the while for individuals or non-bank corporations to invest considerable effort and time into formulating an arbitrage strategy given the various challenges involved. These include: (1) racing against time in identifying two similar assets with differing price in a competitive capital market; (2) earning net profits which are invariably too small without leveraging on risky derivative instruments; (3) replicating the strategy; and (4 ) failing to fully eliminate the aforementioned uncertainties although after extensive research and mitigating efforts. The answer to this is evident, as already pointed out , right at the beginning of this newsletter.
(Readers are to keep in mind that this newsletter does not constitute investment advice or recommendation of investment strategies.)
We assist companies in :
Valuation of financial instruments (free-standing or embedded derivatives) and unquoted equity investments.
Fund accounting.
Providing consultation service including research study & write-up in supporting the accounting treatment relating to a subject matter in a transaction.
DISCLAIMER: All views, conclusions, or recommendations in this article are reasonably held by LT-Wisepool at the date of issue but are subject to changes without notice to you. Whilst effort has been made to ensure the accuracy of the contents in this article, the articles and information contained in the Newsletters page are not designed to address any particular situation or circumstance. Accordingly, users are advised not to act upon these articles and information without any professional advice or consultation with LT-Wisepool. We will not accept liability for any loss or damage suffered by any person directly or indirectly through reliance upon the articles and information contained in the Newsletters page.
Comments