Merger Arbitrage. Kirchner Thomas

the collar. Exhibit 2.7 shows an example of a merger agreement that forces arbitrageurs to do a little extra math. An arbitrageur has to calculate the reference values for the collar from the information in the merger agreement. The value is fixed at $18.06 per share in the collar, and the exchange ratio can fluctuate between 0.4509 and 0.4650. The two reference prices are calculated as

Exhibit 2.7 Acquisition of Windrose Medical Properties by Health Care REITMerger agreement, section 2.2

      (c) Conversion of Shares. Each Share issued and outstanding immediately prior to the Merger Effective Time (other than Shares to be cancelled in accordance with Section 2.2(b)) shall be converted into a fraction of a duly authorized, validly issued, fully paid and non-assessable share of common stock, par value $1.00 per share, of Parent (a “Parent Share” and collectively, the “Parent Shares”) equal to the quotient determined by dividing $18.06 by the Parent Stock Price (as defined below) and rounding the result to the nearest 1/10,000 of a share (the “Exchange Ratio”); provided, however, that if such quotient is less than 0.4509, the Exchange Ratio will be 0.4509 and if such quotient is greater than 0.4650, the Exchange Ratio will be 0.4650. For the purposes of this Section 2.2, the term “Parent Stock Price” means the average of the volume weighted average price per Parent Share on the NYSE, as reported on Bloomberg by typing “HCN.N <EQUITY> AQR <GO>”, for ten (10) trading days, selected by lot, from among the fifteen (15) consecutive trading days ending on (and including) the date that is five trading days prior to the Effective Times.

This is an uncharacteristically narrow collar. As long as Health Care REIT's stock price remains between $38.84 and $40.05, Windrose's shareholder will receive $18.06 worth of Health Care REIT's stock. The range for this collar is less than 5 percent of the buyer's stock price. Typical are ranges of 10 or 15 percent. It can be seen from chart in Figure 2.6 that Health Care REIT was fluctuating quite wildly during the merger period and exceeded the upper limit of the collar by the time of the closing on December 20, 2006.

Figure 2.6 Fluctuation of Health Care REIT's Stock Price Prior to the Merger

      Arbitrageurs must hedge mergers with collars dynamically. If the merger is hedged with a static ratio and the stock price of the acquirer moves, the arbitrageur will incur a loss. For example, 10 days after the announcement, Stifel traded below $29 and an arbitrageur investing at that time would have hedged with a ratio of 0.2586. By January 2013 and until the closing, Stifel stock traded above $35. Therefore, at the time of the closing, the arbitrageur would have received only 0.2143 shares. The arbitrageur would have had an excess short position of 0.0443 shares. With Stifel worth $38.75 on the day of the closing of the merger, an arbitrageur would have had to purchase these extra short shares at a cost of $1.717 per share of KBW. This would have reduced the profitability of the arbitrage by about 10 percent, and led to a loss. Conversely, if an arbitrageur enters into a position when it trades at the upper bound of the collar and the stock price declines, there will be an insufficient number of shares sold short. This underhedging results in the short position not generating enough return to offset losses on the long position of the arbitrage. The correct way to hedge a collar is dynamically, in the same way that an option collar is hedged by an option market maker.

      In the case of the Windrose/Health Care REIT merger, the collar is very tight and the hedge ratio does not change very much. It would be possible to enter an arbitrage position with a static hedge ratio and assume the modest risk that the position needs to be adjusted once the exact conversion ratio is known. An arbitrageur will weigh the potential transaction costs of such a strategy against the spread that can be earned. However, such a narrow collar is an exception rather than the norm, so this question hardly ever arises.

A more accurate method for hedging transactions with collars is delta hedging. Both discontinuities in the payoff diagram of collars lead to optionality (see Figure 2.7). The discontinuity to the left of a fixed-value collar resembles the payoff diagram of a short put position, whereas the discontinuity to the right resembles a long call position. In a delta-neutral hedge, the arbitrageur calculates the sum of the deltas of these two options and shorts the number of shares given by that net delta. A drawback of delta-neutral hedging is that it requires constant readjustment with fluctuations in the stock price and as time passes. However, for wide collars with exchange ratios that change significantly, delta-neutral hedging is the best method to hedge. For further details on the concept of delta hedging, the reader should consult texts dealing with options.

Figure 2.7 Optionality in Mergers with a Fixed-Value Collar

Fixed share collars are less common than fixed-value collars. One recent example of this rare structure is shown in Exhibit 2.8. It is the September 2010 acquisition of AirTran Holdings, Inc. by Southwest Airlines Co.

Exhibit 2.8 Acquisition of AirTran Holdings, Inc. by Southwest Airlines Co

      […]Subject to the terms and conditions of the Merger Agreement, which has been approved by the boards of directors of the respective parties, if the Merger is completed, each outstanding share of AirTran common stock (including previously unvested restricted shares of AirTran common stock) will be converted into the right to receive a fraction of a share of Southwest common stock equal to the Exchange Ratio (as defined below) (the “Base Per Share Stock Consideration” and, as the same may be adjusted as discussed below, the “Per Share Stock Consideration”) and $3.75 in cash, without interest (the “Base Per Share Cash Consideration” and, as the same may be adjusted as discussed below, the “Per Share Cash Consideration”). The Per Share Stock Consideration and the Per Share Cash Consideration are collectively referred to herein as the “Merger Consideration.”

      The Exchange Ratio will be determined as follows:

      1. In the event that the average of the last reported sales prices for a single share of Southwest common stock on the New York Stock Exchange (the “NYSE”) for the 20 consecutive full trading days ending on (and including) the third trading day prior to the closing date of the Merger (the “Southwest Average Share Price”) is less than $10.90, the Exchange Ratio will equal (A) $3.50 divided by (B) the Southwest Average Share Price, rounded to the nearest thousandth.

      2. In the event that the Southwest Average Share Price is equal to or greater than $10.90 but less than or equal to $12.46, the Exchange Ratio will be 0.321.

      3. In the event that the Southwest Average Share Price is greater than $12.46, the Exchange Ratio will equal (A) $4.00 divided by (B) the Southwest Average Share Price, rounded to the nearest thousandth.

      In addition, in the event that the Southwest Average Share Price is less than $10.90, Southwest may elect to deliver, as Merger Consideration, an additional amount of cash, an additional number (or fraction) of shares of Southwest common stock, or a combination of additional cash and additional number (or fraction) of shares of Southwest common stock (which shares will be valued based on the Southwest Average Share Price) such that, after giving effect to such election, the aggregate value of the Merger Consideration (valuing Southwest common stock based on the Southwest Average Share Price) is equal to $7.25.

      Based on the closing price of Southwest common stock on the NYSE on September 24, 2010, the last trading day before public announcement of the merger, the Merger Consideration represented approximately $7.69 in value for each share of AirTran common stock. […]

      This collar is straightforward. If Southwest Airlines' share price falls below $10.90, shareholders of AirTran will receive more shares so that the value they receive remains $3.50. This is a very risky transaction to enter for a buyer, and probably one of the reasons for its rarity. If Southwest Airlines' share price were to suffer a sudden sharp drop, it will have to issue more shares in the merger. The additional issuance dilutes existing