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.
[…]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 shareholders and leads to a drop in the share price with the issuance of even more shares. It risks triggering a downward death spiral in the share price. In order to minimize the risk of unanticipated dilution, the merger agreement allows Southwest Airlines to deliver additional cash in lieu of stock. As discussed earlier, arbitrage activity always exerts some selling pressure on an acquirer's stock, so that the possibility of this effect should not be ignored. Only buyers who acquire target companies that are small relative to their own size should use fixed-share collars, because the dilution would remain insignificant even for a sharp drop in share prices, and no death spiral would be triggered. If Southwest Airlines accepted a fixed-share collar, it must have been very confident that its share price would remain strong.
The number of shares to be issued as long as Southwest Airlines' share price is in the collar is fixed at a ratio of 0.321 of Southwest shares for each share of Airtran owner. For prices above the upper and below the lower bounds of the collar, it is the dollar value of the consideration that is fixed rather than the number of shares, so that the exchange ratio varies.
This transaction can be hedged only through a delta-neutral hedging strategy.
Figure 2.8 shows the implied options in a fixed-rate collar. The combination of a long call with a low strike price and a short call with a higher strike price yields such a payoff diagram. This combination is also known as call spread or bull spread. An arbitrageur who wants to hedge a fixed-rate collar needs to calculate the delta for each option, sum the deltas, and then short the net delta in the form of shares of the target firm.
Figure 2.8 Optionality in Mergers with a Fixed-Share Collar
Chapter 3
The Role of Merger Arbitrage in a Diversified Portfolio
Portfolio theory reduces investments to two dimensions: risk and return. Both variables are forward looking and hence difficult to assess without perfect foresight. Therefore, analysis relies on historical relationships that are extrapolated to the future. It is assumed, or rather hoped, that the historical relationships will also hold in the future. This may or may not be the case.
Risk is a variable that is particularly difficult to define. The most common substitute for risk is price volatility. An asset's historical price fluctuations are observed, and it is assumed that these historical fluctuations incorporate all the risks that stockholders faced in the past. This historical volatility is then used in forward-looking analysis, and it is assumed that any risks that this stock faces have already occurred in the past and hence are incorporated in the historical volatility. The length of time over which historical volatility is calculated is the most important determinant of whether there is any validity to this approach. It clearly makes no sense to produce 10-year forecasts based on historical volatilities observed over only one or two years.
More fundamentally, it is a strong assumption that all risks inherent in a stock have already manifested themselves in the past. The economy evolves constantly and markets are in flux; assuming that future fluctuations will somehow resemble those of the past is not obvious. However, it is the only practical approach that can be taken when forecasts are made.
