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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.

      […]

      Other Transaction Details

      Under the terms of the merger agreement,

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