Risk Arbitrage - Profiting from Mergers, Acquisitions and Liquidations

Profiting Risklessly through Special Operations

Profiting Risklessly through Special Operations. Miguel S Salmeron / Getty Images

Arbitrage (sometimes called “risk arbitrage” or “merger arbitrage”) is a special type of investment operation that is meant to generate profit with little or no risk. By taking advantage of special situations that arise in the security markets from time to time, an investor can exploit price discrepancies created by special situations, increasing his net worth regardless of whether the market itself advances.

This article discusses two of the more common arbitrage operations - those arising from mergers and liquidations – as well as the formula necessary to value the potential return on capital employed.

Corporate Mergers and Acquisitions

When a publicly traded company is acquired, the acquiring entity makes a tender offer to the current shareholders inviting them to sell their stock at a price usually above the quoted price on the exchanges or over-the-counter market. As soon as the tender offer is announced, arbitragers will rush in and purchase the security on the open market then turn around and sell it directly to the acquiring company for the higher price.

A Fictional Example of Risk Arbitrage in Mergers and Acquisitions

Acme Industries, Inc. decides to acquire one hundred percent of Smith Enterprises. Smith’s stock trades on the over-the-counter market and is quoted at $15 per share. Acme’s management makes a tender offer in the amount of $25 per share.

This means that for a few, brief moments, an arbitrager can buy shares of Smith Enterprises for $15 each on the open market, turn around and tender (i.e., sell) them to Acme for $25. Through this operation, the arbitrager has made a quick profit of $10 per share from the spread that existed between the market price and the tender price.

It is hardly practical to make a significant profit by attempting to jump into the market the moment a tender offer is announced; very few shares could be acquired before the price had been driven up due to the sudden demand flooding the market from would-be arbitragers. Instead, two methods of risk arbitrage developed which I call pre-emptive and post-tender. In the former type of operation, the arbitrager purchases shares of a company which he believes will be taken over in the coming days or months. If he turns out to be correct, he will fully benefit from the spread between the price he paid and the tender offer. The risk he runs, however, is that a company is not acquired. Since he must rely on rumors and gut feeling to predict which companies will be acquired and for what price, pre-emptive arbitrage is inherently more speculative in nature than its counterpart. As a result, it tends to be far less profitable on the whole.

Post-tender arbitrage, however, deals only with situations where a tender offer has already been announced by a potential acquirer. Despite the $25 standing offer Acme has made for the common stock of Smith Enterprise, it may sell for only $24.00 on the market (the reason for this discrepancy is too complicated and time-consuming to be of value to the average investor).

This difference of $1.00 per share may seem small; looks can be deceiving. Due to the short amount of time, the investment is held, the indicated annual return on such a commitment is remarkably high.

Graham’s Indicated Annual Return Formula for Risk Arbitrage

To calculate the value of a potential arbitrage commitment, Benjamin Graham, the father of value investing created the following formula, which he discussed at length in the 1951 edition of Security Analysis; its creation was heavily influenced by Meyer H. Weinstein’s classic 1931 book, Arbitrage in Securities (Harper Brothers).

Indicated annual return = [GC – L (100% - C)] ÷ YP

Let G be the expected gain in points in the event of success;
L be the expected loss in points in the event of failure;
C be the expected chance of success, expressed as a percentage;
Y be the expected time of holding, in years;
P be the current price of the security

Graham's formula can be used to evaluate the potential return on the risk arbitrage operation in the Acme and Smith merger. The expected gain in the event of success is $1.00 (the spread between the $24.00 quoted price on the open market and the $25 Acme tender offer). If the merger fails to occur, the Smith stock may fall to its pre-tender offer of $15 per share (in many cases, history has proven otherwise; once a company is “in play” as a takeover target, its stock may remain inflated in anticipation of another acquirer materializing. We shall disregard this possibility for the sake of conservatism). Hence, the expected loss in points in the event of failure is $9. Assume there are no antitrust concerns, so the likelihood of consummation is 95%. Also, assume the investor expects to hold his shares for one month (1/12 or 8.33% of a year) until the transaction is complete. The current price of the security is $15 per share. Plugging these into Graham’s formula, the investor gets the following:

Indicated annual return = [1 x .95 – 9 (1.00 - .95)] ÷ .0833 x 24

Indicated annual return = [.95 – .45] ÷ 2

Indicated annual return = 25%

In other words, had the investor been able to earn the same return on his capital for the entire year as he did during the holding period of this investment, he would have earned twenty-five percent. In a world where the historic annual return on long-term equities has hovered around twelve percent, this is mouth watering.


From time to time, corporations will liquidate their operations in whole or part. As the liquidation unfolds, the funds are paid out to the shareholders. An investor that feels he can reasonably estimate the eventual proceeds from the liquidation process can evaluate the potential arbitrage operation with Graham’s formula just as easily as opportunities arising from acquisitions and mergers. There is empirical evidence suggesting that these types of risk arbitrage operations are particularly profitable. According to Christopher Ma, William Dukes and R. Daniel Pace in Why Rock the Boat? The Case of Voluntary Liquidation (The Journal of Investing, Summer 1997, p. 71), “A 1997 study of voluntary liquidations between 1961 and 1985 found that the average annual return for investment in securities from the date of their liquidation announcement until their final liquidating distribution was 44.4%. On average, the liquidation securities substantially outperformed the general market, shareholders recouped their initial investment within one year and the liquidation process was completed in just over two years.”


On the whole, risk arbitrage can be a source of steady and dependable profits over long periods of time. Market conditions, however, will make these operations more or less scarce and more or less attractive. It is the responsibility of the investor to exercise sound judgment and decide at what time and in what amount he is willing to engage in these types of operations. Many institutional investors set aside a portion of their portfolio (ten or twenty percent, for example) that is dedicated to arbitrage commitments, special opportunities, liquidations and other specialized investing practices.