Читать книгу Merger Arbitrage - Kirchner Thomas - Страница 9

Stock-for-stock mergers are more complicated than cash mergers. In stock-for-stock mergers, a buyer proposes to acquire a target by paying in shares rather than cash. Sometimes the consideration paid can be a combination of stock and cash. That case is addressed later.

A good example of a stock-for-stock merger announcement is shown in Exhibit 2.2. It is the $4 billion acquisition of Australian gold miner CGI Mining Ltd by Canada's B2Gold Corp, announced in September 2012.

Exhibit 2.2 Merger Announcement for CGI Mining Ltd and B2Gold Corp

VANCOUVER, BRITISH COLUMBIA–(Marketwire – Sept. 19, 2012) – B2Gold Corp. (TSX: BTO)(OTCQX: BGLPF)(PINKSHEETS: BGLPF)(NAMIBIAN:B2G) (“B2Gold”) and CGA Mining Limited (TSX: CGA)(ASX: CGX) (“CGA”) are pleased to announce that they have entered into a definitive Merger Implementation Agreement (“Merger Agreement”) to combine the two companies at the agreed exchange ratio of 0.74 B2Gold common shares for each CGA share held, which represents a purchase price of approximately C$3.18 per CGA share and a premium of 22 % using the 20 day volume weighted average share price of each respective company, and a 26 % premium over the CGA closing share price on September 17, 2012 based on the closing price for the B2Gold shares as of such date. The transaction is valued at approximately C$1.1 billion.

The merger will be implemented by way of a Scheme of Arrangement under the Australian Corporations Act 2001 (“Scheme”). Upon completion of the Scheme, existing B2Gold shareholders and CGA shareholders will own approximately 62 % and 38 %, respectively, of the issued common shares of the combined company.

[…]

Transaction Structure and Terms

[…]

The merger is subject to regulatory, Australian Court, shareholder, and third party approvals, together with other customary conditions. Regulatory approvals include approval by the Australian Foreign Investment Review Board, and ASX and TSX approvals in respect of the issue of new B2Gold shares under the Scheme and as consideration for the cancellation of the CGA options.

A Scheme Booklet setting out the terms of the Scheme, Independent Expert's Report and the reasons for the CGA Directors' recommendations is expected to be circulated to all CGA shareholders. A meeting of CGA shareholders to consider the Scheme is expected to be held later in the year and the Scheme is expected to be implemented shortly thereafter. The Scheme is conditional upon approval by 75 % of the number of votes cast, and 50 % of the number of CGA shareholders present and voting, at the meeting of CGA shareholders.

In addition to the approval by CGA shareholders, the Scheme is conditional upon B2Gold shareholders approving the issuance of B2Gold shares that will be issued in connection with the Scheme and the cancellation of the CGA options by a simple majority of the B2Gold shares that are voted at a shareholder meeting to be held in reasonable proximity to the CGA shareholder vote.

The Merger Agreement also contains customary and reciprocal deal protection mechanisms, including no shop and no talk provisions, matching and notification rights in the event of a competing proposal and a mutual reimbursement fee payable by B2Gold or CGA in specified circumstances.

In this case, B2Gold is the buyer, CGA the target, and the per share consideration is no longer a fixed cash amount but a fixed number of B2Gold shares. Shareholders of CGA will receive 0.74 shares of B2Gold for each share of CGA that they hold. The number 0.74 is referred to as the exchange ratio or conversion factor.

The dollar amount of C$3.18 mentioned in the press release refers to the value of the merger on the day before the announcement. This amount is calculated simply by multiplying the closing price of B2Gold's stock of C$4.30 on September 18, the last trading day before the announcement, by the conversion factor of 0.74. It is not the value that shareholders will receive at the closing of the merger. The value will vary with the stock price of B2Gold. This distinction is important, because unlike in the case of a cash merger, arbitrageurs face an uncertain dollar value at the time of closing that will vary with B2Gold's stock price. Therefore, they cannot just buy the stock of the target CGA and wait for the merger to close.

The naive approach would be to purchase CGA stock and wait for the merger to consummate. The investor would receive 0.74 shares of B2Gold that it would then need to sell at the prevailing market price, which could be higher or lower. There is no arbitrage in such a transaction. Recall that one of the elements of the definition of arbitrage was that a purchase and sale occur simultaneously. Holding a stock and waiting to sell it for a higher price is speculation, not arbitrage.

Instead, arbitrageurs must lock in the value of the transaction through a short sale. For readers new to short sales, a brief explanation is given here. Additional aspects of short sales are discussed in Chapter 14.

Short Sales

Most investors will only buy stocks and sell stocks that they bought previously and hold in their portfolio at the time of the sale. Selling short differs from a normal sale mainly through the timing of the purchase. A short sale is done before the stock is acquired. If a stock declines in value, a short seller will make a profit; if a stock increases in value, the short seller will suffer a loss.

An important component in short selling is the delivery of the stock to the buyer. The buyer is unaware that the stock has been sold short and rightfully expects delivery. In order to make delivery of the stock, the short seller must borrow it from someone who owns it. Most brokerages and clearing firms offer their customers the ability to borrow stock. Online discount brokerages generally have fully automated systems to locate stocks that can be borrowed for their customers. If the stock cannot be borrowed, it cannot be sold short, and the brokerage will inform the customer. In return for lending out the stock, the lender demands a fee, which the arbitrageur must factor into the calculation. This will be discussed later.

The process of closing the short sale – that is, buying back the shares that have been shorted – is a buy-to-cover transaction.

Sometimes the lender of a stock requests its return, for example, if the stock is to be sold. In that case, the customer must either buy to cover or the broker will do a buy-in, meaning that the broker places the buy-to-cover order. If an investor is served with a notice of an upcoming buy-in, it is always better to buy the stock oneself and maintain control over the order than to let the broker execute a buy-in.

Selling short is sometimes portrayed as illegal, dishonest, or un-American. However, in financial markets, arbitrage would not be possible without short selling. Arbitrage involves the simultaneous sale of an asset identical to the one acquired; in many instances, this is possible only through short sales. If there were no arbitrage in financial markets, many products would not be priced correctly, and investors might overpay.

The chief executives of some companies have launched a crusade against naked short selling, which is an illegal activity in which the short seller does not borrow the stock that is sold short. However, regulations to prevent naked short sales are in place already.

One complication in the merger is that even though CGA Mining is an Australian company, it is dually listed in Canada and Australia. An arbitrageur must decide which of the two shares to purchase. A brief glance at the trading volume of the shares on the two exchanges shows that the vast majority of the trading volume occurs in the Canadian market. Another advantage of investing in the Canadian shares is that arbitrageurs do not have to deal with the unfavorable time zone during which the Australian market is open for trading. Executing both sides of the arbitrage simultaneously can be difficult for companies whose shares are listed on different continents and where opening hours overlap only briefly, if at all.

The stock prices of B2Gold and CGA are shown in Figure 2.4. It can be seen that CGA jumped on September 19, the day of the announcement, from a close of C$2.65 the prior day to an open of C$2.84, rose as high as C$2.95 during the day and closed at C$2.71. B2Gold had closed at C$4.30 before the announcement and fell to a closing price of C$3.79. Articles in the press often attribute such a drop of an acquirer's stock price to skepticism about the merger in the investor community. However, it will be seen that the drop is often the byproduct of arbitrage activity.

Figure 2.4 Stock Prices of B2Gold and CGA

For simplicity, it will be assumed that an arbitrageur enters the position on September 19 at the closing price. The arbitrageur will execute two transactions:

1. Pay C$2.86 per share to buy 1,000 shares of CGA. This is the volume-weighted average price (VWAP) for the day, a realistic level at which investors could have bought CGA.

2. Sell short 740 shares of B2Gold at C$3.95 per share, which is the VWAP for this stock for September 19.

It helps to examine the cash flows and stock holdings after these two trades. They can be found in Table 2.1. There is an expense of C$2,860 to acquire the shares of CGA, and proceeds from the short sale amount to C$2,923.

Table 2.1 Cash Flows in CGA/B2Gold Merger

It can be seen that this transaction leaves the arbitrageur with a net cash inflow of C$63. At the closing of the merger, the 1,000 shares of CGA will be converted into 740 shares of B2Gold. The arbitrageur is then long 740 shares and at the same time short 740. The long position can then be used to deliver shares to the counterparty from which the short position was borrowed. Once the delivery has been completed the arbitrageur no longer has a position in stock, long, or short, but is left with a profit of C$63.

The example of 1,000 shares is useful for illustrative purposes. Rather than looking at the purchase of 1,000 shares, transactions should be calculated on a per-share basis. Each share of CGA is converted into 0.74 shares of B2Gold. For each share of CGA purchased, the arbitrageur must sell short 0.74 shares of B2Gold. By multiplying the exchange ratio with the stock price of B2Gold, it can be seen that per share of CGA an arbitrageur receives C$2.923 (0.74 × 3.95) from the short sale of B2Gold. The spread is hence C$0.063 per share of CGA.

The return calculation is simplified here in that no dividends need to be taken into account. Neither of the two companies has ever paid any dividends, and there was no reason to believe that this would change prior to the closing of the merger.

2.5

where

The gross return on this arbitrage is 2.2 percent.

Calculation of the annualized return works as in the example of a cash merger. Only the calculation of compound returns is shown here; simple interest can be calculated analogously. Unlike in the prior examples, the arbitrageur cannot find a direct reference to the closing date in the press release. “The merger will be implemented by way of a Scheme of Arrangement under the Australian Corporations Act 2001” gives a valuable hint. As I will explain later, a scheme of arrangement follows a well-defined timetable. A five-month time frame is a reasonable estimate. If we assume a closing date of February 28, 2013, then there are 162 days from September 19, the day the position was entered.

Compound interest

2.6

The expected annualized return at the time of entering the position is 5.0 percent. The actual closing of this merger occurred on January 18, 2013, so the actual return on this arbitrage was an annualized 6.9 percent over 121 days.

One of the advantages of stock-for-stock mergers is the simultaneous holding of a long and a short position. Because of the upcoming merger, the two stocks are highly correlated, so that an increase in CGA's stock price is accompanied by an offsetting increase in B2Gold's. If the two stocks were no longer to move in parallel, the spread would change, and the annualized return available to arbitrageurs would either compress or expand.

However, as the fluctuations in the two stocks mostly cancel out due to the short position in B2Gold, the net result for the arbitrageur is a much smoother ride than what an index investor experiences. The evolution of the spread of the CGA/B2Gold merger is shown in Figure 2.5. In the case of a cash transaction, the spread depends on only one variable. In a stock-for-stock merger, it depends on two stock prices. The spread does trend toward zero over time. The spread is not very smooth on an absolute basis. But compared to the gyrations in the index over the same time, the volatility is much lower.

Figure 2.5 Evolution of the CGA/B2Gold Spread

It is clear that short sales from arbitrage activity can lead to significant selling pressure on the stock of a buyer after the announcement of a stock-for-stock merger. Often analysts and journalists attribute the drop of a buyer's stock after a merger announcement to fundamental reasons, such as the prospect for the merged entity. One account of the trading activity following the announcement of the merger of Trane Inc. with Ingersoll-Rand is shown in Exhibit 2.3. Ingersoll-Rand fell over 11 percent following the announcement of the merger. The fundamental reasoning behind this merger appeared solid. Some reports suggested that the combination of the two firms created the number-two air-conditioning company in the United States. The long-term prospects of Ingersoll-Rand clearly were not bad and would not have justified an 11 percent drop. It can be explained only by arbitrage activity. Experienced investment bankers warn company management during merger negotiations of the risk to their stock price and suggest structures with a cash component to a stock-for-stock merger in order to reduce short selling.

Exhibit 2.3 Account of Ingersoll-Rand's Acquisition of Trane for $10.1 Billion, Creating Climate Control Behemoth

TRENTON, N.J. (AP) – In a deal worth a cool $10 billion, Ingersoll-Rand Co. will acquire Trane Inc. and create one of the world's largest makers of commercial and residential home air conditioners, refrigerators for trucks and stores, and other climate control products.

But some Ingersoll-Rand shareholders, who had expected the cash-rich company to pour some money into share repurchases, seemed disappointed with the acquisition announced Monday and sold Ingersoll-Rand stock, driving shares down sharply.

Merger arbitrage is attractive to many investors as a portfolio diversifier because of its long/short components. It is assumed that these positions immunize the portfolio against fluctuations in the overall stock market and leave only uncorrelated event risk to the investor, and therefore, the portfolio is market neutral. This argument is revisited in more detail in Chapter 3. Nevertheless, at this point, a short discussion of one of the pitfalls of long/short positions is necessary. A constant percentage spread can lead to dollar paper losses in an extreme bull market, if both the long and the short position increase, but the percentage spread remains constant. Table 2.2 illustrates the problem of a hypothetical increase of CGA and B2Gold when the percentage spread remains constant throughout the increase. The losses discussed here are temporary only and will eventually be recovered once the merger closes.

Table 2.2 Losses Suffered at a Constant Percentage Spread in a Rising Market

Table 2.2 starts in the first row with the actual spread of 2.20 percent at prices of C$2.86 and C$3.95 for CGA and B2Gold, respectively. It shows the profit and loss (P&L) relative to a position entered at the baseline of C$2.86 and C$3.95. If both CGA and B2Gold rise and the percentage spread remains constant, then the spread expressed in dollars must rise (2.2 percent of $5.72 is more than 2.2 percent of $2.86). The simulated price rise in Table 1.3 shows that a spread of $0.063 will widen to $0.126 per share if CGA were to double in value to $5.72 per share. Although B2Gold's stock appreciates by the same percentage as CGA, the difference in dollar terms increases. At $5.72 per share, the arbitrageur's portfolio would record a loss of $0.063 per CGA share (last column).

This scenario does not imply inefficiency in the market. If the hypothetical increase in spreads were to occur on the same day as the position was entered, the annualized return would be unchanged, because the percentage spread is the same whether CGA trades at $5.72 or at $2.86.

It is clear that these losses are only paper losses that are temporary. As long as the merger eventually closes, the arbitrageur will realize a gain of $0.063. Only those who panic and close their position early will suffer a real loss. The arbitrageur is short 0.74 shares of B2Gold for every long position of CGA, and the cash changed hands already when the trade was made. Therefore, the eventual profit is certain as long as the merger closes. In the meantime, however, the account will show a loss.

Whether or not an arbitrageur wants to hedge against paper losses is a matter of personal preference. Any hedging transactions will entail costs and will reduce the return of the arbitrage. Because the spread eventually will be recovered, it makes little sense to hedge against transitory marked-to-market losses.

Now what would happen if stock prices were to fall? It can be extrapolated from this discussion that in the case of a fall in stock prices, the dollar spread will tighten, and the arbitrageur will record a gain even though the percentage spread and the annualized return would remain unchanged.

Sometimes shareholders hold a number of target shares that does not get converted to a round number of buyer shares. For example, a holder of 110 shares of CGA would receive 81.4 shares of B2Gold. However, the fractional 0.4 shares cannot be traded or issued because corporations have whole shares only. (Note that mutual funds are different, even though they are also organized as corporations.) Therefore, companies will liquidate fractional shares and issue only full shares. The investor in our example would receive 81 shares of B2Gold and a cash payment for the value of the fractional 0.4 shares. The cash payment depends on the share price of B2Gold at the time of the closing of the merger.

In addition to earning the spread, a stock-for-stock merger has another source of income. When arbitrageurs short a stock, they receive the proceeds of the short sale. In the example from Table 2.1, the arbitrageur received C$2,923 from the short sale of B2Gold. These funds are on deposit at the brokerage firm that executed the short sale. Arbitrageurs can negotiate to receive interest on this deposit. This is easier said than done. In the author's experience, most retail brokerage firms do not pay interest on the proceeds of short sales. At the time of writing, one retail brokerage firm advertised that it had paid interest on balances of short proceeds in excess of $100,000. Institutional investors are better off. They are always offered interest on the proceeds. This is referred to as short rebate in industry parlance.

The example of the CGA/B2Gold merger can illustrate the effect of the short rebate on merger arbitrage returns. Assume that the short rebate is 1 percent. At the time of writing, in a period of historically low interest rates, this would be a high rate. In normal interest rate environments, short rebates are higher and match LIBOR rates. In fact, it is quite normal for rates for short rebates to be below interest rates. In fact, the spread between short rebates and margin rates charged customers who borrow to buy stock is an important source of revenue for brokerage firms. The interest earned on the $2,923 over the 140-day period until the closing of the merger would have been

2.7

This would increase the merger profit from $63 to $74.21 – an increase of almost 18 percent. For simplicity, simple interest is used in this calculation. Most brokers pay interest monthly, so monthly compounding should be used.

The annualized spread increases by the amount earned on the short rebate:

where represents the interest paid on the short rebate.

As discussed in Chapter 3, returns on merger arbitrage tend to be correlated with interest rates as a result of the impact that short rebates have on spreads.

The CGA/B2Gold merger was easy to analyze because neither stock pays any dividends. Stocks paying dividends can be tricky to handle when sold short, because the short seller must pay the dividend on the stock. The long position will generate a dividend; the short position will cost a dividend. A crude calculation to determine the net effect of dividends on the annualized spread is to subtract the dividend yield of the short position from the dividend yield of the long position, and add the result to the annualized return of the merger arbitrage. However, this method can give incorrect results, especially for mergers with a short horizon to closing. The method can be used as a first approximation, but arbitrageurs always must consider the actual dividend dates and dividend amounts.

The gross return in the presence of dividends is calculated for a long/short merger arbitrage in this way:

2.8

where

Mixed Cash/Stock Mergers

Many buyers want to limit dilution in the acquisition of a target company or have access only to an amount of cash insufficient to purchase the target entirely for cash. They structure the acquisition of a target for a dollar amount plus shares, or they offer target shareholders the option to choose between cash and stock, typically with a forced proration.

In the former case, every shareholder of the target company is treated equally. Exhibit 2.4 shows the announcement of the merger of Alterra Capital Holdings Ltd. with Markel Corp, announced in December 2012. This merger was mentioned briefly earlier to illustrate the effect that arbitrage-related short selling can have on a company's stock price immediately following the announcement of a merger.

Exhibit 2.4 Announcement of Acquisition of Alterra Capital Holdings Ltd by Markel Corp

RICHMOND, Va. & HAMILTON, Bermuda–(BUSINESS WIRE)–

Markel Corporation (“Markel”) (MKL) and Alterra Capital Holdings Limited (“Alterra”) (NASDAQ: ALTE; BSX: ALTE.BH) announced today that their respective boards of directors have each unanimously approved a definitive merger agreement. Under the terms of the agreement, the aggregate consideration for Alterra is approximately $3.13 billion, based on a closing price of $486.05 for Markel common stock on December 18, 2012.

At closing, each Alterra common share will be converted into the right to receive 0.04315 Markel common shares (with cash paid for fractional shares) plus a cash payment of $10. Following the merger, Markel's existing shareholders will own approximately 69 % of the combined company on a fully diluted basis, with Alterra's shareholders owning approximately 31 %. Completion of the transaction is contingent upon customary closing conditions, including shareholder and regulatory approvals, and it is expected to close in the first half of 2013.

Alterra's shareholders will receive $10 plus 0.04315 share of Markel. Alterra's shares traded on December 19 at a VWAP of $28.58, whereas those of Markel traded at a VWAP of $444.97. An arbitrageur entering a position at these prices would make a gross return of 2.17 percent:

2.9

where

This gross return should be annualized by one of the methods explained earlier. An arbitrageur would also have to factor in the receipt of at least one additional dividend of $0.16 / share, which, based on Alterra's dividend history, would be paid in the middle of February 2013. A second dividend may be paid in the middle of May, if the merger has not closed by then.

A different incarnation of mixed cash/stock transactions does not specify a set dollar amount to be received per share but instead sets a fraction of the total consideration that will be paid in cash. Frequently used ratios are 50/50 cash/stock, 40/60, or 20/80.

The acquisition by Vulcan Materials Company of Sunoco Inc. by Energy Transfer Partners, LP had the frequently used ratio of 50 percent cash and 50 percent stock. The press release is shown in Exhibit 2.5.

Exhibit 2.5 Acquisition of Sunoco Inc. by Energy Transfer Partners, LP

DALLAS & PHILADELPHIA–(BUSINESS WIRE)–Apr. 30, 2012–Energy Transfer Partners, L.P. (NYSE: ETP) and Sunoco, Inc. (NYSE: SUN) today announced that they have entered into a definitive merger agreement whereby ETP will acquire Sunoco in a unit and cash transaction valued at $50.13 per share, or a total consideration of approximately $5.3 billion, based on ETP's closing price on April 27, 2012. This combination will create one of the largest and most diversified energy partnerships in the country by expanding ETP's geographic footprint and strengthening its presence in the transportation, terminaling and logistics of crude oil, NGLs and refined products.

The merger consideration, which consists of $25 in cash and 0.5245 of an ETP common unit, or approximately 50 percent cash and 50 percent ETP common units, represents a 29 percent premium to the 20-day average closing price of Sunoco shares as of April 27, 2012.

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Other Transaction Details

Under the terms of the merger agreement, which has been unanimously approved by the boards of directors of both companies, Sunoco shareholders can elect to receive, for each Sunoco common share they own, either $50.00 in cash, 1.0490 ETP common units, or a combination of $25.00 in cash and 0.5245 ETP common units. The aggregate cash paid and common units issued will be capped so that the cash and common units will each represent 50 percent of the aggregate consideration. The cash elections and common unit elections will be subject to proration to satisfy this cap. Upon closing, Sunoco shareholders are expected to own approximately 20 percent of ETP common units. In addition, $965 million of Sunoco's existing notes will remain outstanding.

Mixed transactions with election rights can be difficult to calculate because they require some guesswork. Arbitrageurs are used to making assumptions, as we have seen in the estimation of closing dates and now again when dealing with cash/stock proration ratios. Shareholders can choose to receive either cash or stock. Arbitrageurs and some shareholders will pick the option that is worth the most. In this transaction, if the value of Energy Transfer Partners shares to be received is above $50.00 at the time of the merger, profit-maximizing shareholders will want to receive shares. If the value of these shares is less than $50, shareholders will prefer $50 in cash instead of the less valuable shares. In either case, no shareholder will accept a blend of shares and stock. The buyer would either have to pay all stock or all cash, which is not what it intended to do. For this reason, these transactions have a proration provision, so that the buyer of the firm can make the blended cash/stock payment of 50 percent stock and 50 percent cash. However, not all shareholders will seek to be paid in cash when the shares are below $50. Some shareholders fail to make a selection and will be allocated the less valuable consideration by default. Many long-term shareholders will select shares even when the cash payment is more valuable because they intend to continue to hold the shares. Strategic investors or managers will hold on to their shares. Some asset allocators may find it easier to roll their shares into the buyer's stock than reinvest themselves. Finally, the most important group selecting stock rather than cash are long-term holders who have significant appreciation in their holdings of target stock. They would be faced with an immediate tax bill if they realized a gain in the merger. By selecting stock, they can defer realization of a taxable gain into the future. Because all of these investors have a preference for stock even if the cash component is worth more at the time of the merger, slightly more cash will be paid to shareholders who select cash than if proration were applied at the stated ratio.

In the case of Sunoco, 73.92 percent of shareholders elected to receive cash, 4.25 percent elected all stock, 2.61 percent requested to receive the 50/50 proration, and the remaining 19.22 percent did not make a selection. Shareholders who did not make a selection also received the 50/50 mix. Out of luck were shareholders who elected to receive all cash: Due to proration, they received $26.47 in cash and 0.49373 shares of Energy Transfer Partners. This shows that aiming for one of the extremes – all cash or all stock – can be a risky undertaking. An arbitrageur who hoped for an all-cash allocation would have ended up with almost half of the position exposed to the market – not quite an arbitrage. Most of the time, it is optimal to target the prorated allocation. With some experience and a study of the shareholder base, it is possible to make a rough estimate of the final proration.

Arbitrageurs must use experience and guesswork to determine the ratio that is most likely to apply. In the next discussion, it is assumed for simplicity that the ratio of cash/stock that the arbitrageur will receive is that of the stated proration factor.

To calculate the gross return,

2.10

where

This gross return can be annualized by analogy with the previous examples.

Mergers with Collars

The CGA/B2Gold merger discussed above had a fixed exchange ratio of 0.74. This exposes both CGA and B2Gold to a certain market risk: If the value of B2Gold's stock increases significantly, then the 0.74 shares that CGA shareholders will receive for each share will also increase in value. In this case, the value of the transaction will be much higher than $4 billion. While CGA shareholders will be happy with this outcome, the investors in B2Gold will wonder whether they could have acquired CGA by issuing fewer shares and suffering less dilution. Conversely, if B2Gold's stock falls, then CGA's shareholders will receive less valuable shares for each B2Gold share. They would have been better off with a higher exchange ratio.

For this reason, many merger agreements include provisions to fix the value of stock received by the target company's shareholders at a set dollar amount or at a fixed exchange ratio. The exchange ratio is adjusted as a function of the share price of the acquirer. Two reference prices are determined.

Two types of collars are common:

1. Fixed-value collars. Target shareholders will receive a set dollar value's worth of shares of the acquirer as long as the acquirer's share price is within a certain collar. This collar is buyer-friendly. The exchange ratio can change within the collar range. This type of collar is so common that the term fixed value is often dropped. References to a generic “collar” relate to fixed-value collars.

2. Fixed-share collars. A set number of shares is given to the target shareholders as long as the acquirer's share price is within a certain range. If the acquirer's share price rises above the maximum, the exchange ratio declines. This collar is seller-friendly. The exchange ratio is fixed within the collar range.

The November 2012 acquisition of investment bank KBW, Inc., by Stifel Financial Corp. contained a fixed-value collar, shown in the press release in Exhibit 2.6.

Exhibit 2.6 Acquisition of KBW, Inc. by Stifel Financial Corp

Stifel Financial Corp. (NYSE: SF) and KBW, Inc. (NYSE: KBW) today announced that they have entered into a definitive merger agreement to create the premier middle-market investment bank with a specialized focus on the financial services industry.

Under the terms of the agreement, which was unanimously approved by the boards of directors of both companies, KBW shareholders will receive $17.50 per share, comprised of $10.00 per share in cash and $7.50 per share in Stifel common stock. Additionally, holders of certain restricted KBW shares, that will continue to vest post closing, will receive $17.50 in Stifel common stock. The stock component of the consideration is fixed at $7.50 per share, subject to a collar, provided that the volume weighted average closing price of Stifel common stock for the ten days prior to closing is between $29.00 and $35.00 per share. If the volume weighted average price rises above $35.00 per share, the exchange ratio will be fixed at 0.2143 shares of Stifel common stock for each share of KBW, and if it falls below $29.00 per share, the exchange ratio will be fixed at 0.2586 shares of Stifel common stock for each share of KBW.

The transaction is valued in excess of $575 million, which includes the outstanding shares and restricted stock awards of KBW. Approximately $250 million in excess capital on KBW's balance sheet is expected to be immediately available to Stifel upon closing.

In this acquisition, KBW shareholders will receive a package worth $17.50 as long as the share price of Stifel is between $29 and $35. In this case, they will receive $10 in cash and $7.50 worth of Stifel stock. For example, if the price of Stifel is $31, they will receive $10 plus 0.2419 shares of Stifel. The ratio of 0.2419 is calculated by dividing $7.50 by $31. If the price of Stifel stock falls below $29, then the ratio will be fixed at 0.2586, so if Stifel stock is worth only $25, then the value received by KBW shareholders will be only $16.47 ($10 cash, plus Stifel stock worth $25 × 0.2586). Below the lower collar boundary, KBW shareholders will participate in any depreciation of Stifel shares, as they would if the ratio had been fixed, and will receive less value than $17.50. Similarly, for a share price above the upper boundary of the collar, the value received will exceed $17.50. For example, for a price of Stifel shares of $40, KBW shareholders will receive a package worth $18.57 ($10 cash, plus Stifel stock worth $40 × 0.2143). Certainty as to the value exists only within the collar.

Readers are fortunate that the press release in Exhibit 2.6 is very explicit about the boundary prices of 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 REIT

Merger 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 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