Professional risk arbitrageurs (active arbitrageurs)4 claim to profit by providing insurance and liquidity to the investors and shareholders of target firms. They also play an active role in the deal-making process. Generally, after a merger or acquisition has been announced, investors having positioned themselves vis-à-vis a target firm, face completion risk. Some shareholders may wish to secure their risk by selling their shares. In an efficient
4 There are two roles arbitrageurs can play in the acquisition process. First, active arbitrageurs influence acquisition outcomes and terms. They can change holding periods and influence stock price reversals during the period of deals. Second, passive arbitrageurs do not influence acquisition terms and outcomes. Our paper will focus on passive arbitrageurs. These are naïve investors, who invest in deals that the market expect to succeed. Usually, we would observe a gradual increase in arbitrage holdings over time (Baker & Savasoglu, 2002).
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capital market, the stock prices of target firms will fully and immediately reflect all acquisitions information. We can anticipate that stock prices will exceed the offer price after the announcement date. In reality, shareholders sell to a limited numbers of capital-constrained investors (passive arbitrageurs) and financial institutions specializing in risk arbitrage. As a result of this pressure, the price of the target firm’s shares can fall below their effective market price. This market inefficiency is also called limited arbitrage (Shleifer
& Vishny, 1997). Therefore, to measure the magnitude of price revisions, we had to split risk arbitrages returns into spread returns (also called speculation spread) and revision returns.
Greater detail follows.
3.1 The components of risk arbitrage returns
We define investors as anyone purchasing shares subsequent to an acquisition announcement. They include general or passive arbitrageurs as well as active risk arbitrageurs, such as private equity funds, financial institutions and so on. Assume these investors respond to an acquisition announcement and purchase shares of a target at price P and hold them to the completion date. Holding a target firm’s shares until completion date will yield holding risk arbitrage returns, which can be calculated as
)
where i is per cash offer deal, Riis the realized holding returns of risk arbitrage for successful or failed deal;PiOis the offered price of target firms; PiFis the final price sold to the acquirers; Pi is the target’s closing stock prices on the announcement day;Di is the accumulated dividend paid by the target firms during the holding periods, andci is the percentage of transaction and holding cost. Duration is the period between announcement date and completion date for a successful deal or withdrawing date for failure. RewritingPiF −Pi
as
( ) (
iO)
P − + − , we see that total arbitrage returns have two components, SR and RR, and we get the formula:
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) 2
i (
i i
i SR RR c
R = + −
Where
(
i)
iO i
i P P P
SR = − / is the spread return for deal i, and ( ) i O i F i
i P P P
RR = − / is the revision return for deal i. Stock price movement will be upward, downward or unchanged. Three outcomes are shown in the Figure 1 and Table 2. Here is an example: we assume that an acquirer declares to offer $20 per share to acquire a listed firm on the announcement day, and an investor buys the target stock at a closing market price per share of $15. The stock price traded on the completing day is $18.50, and the period of deal is 180 days (we ignore dividends and trading costs). We know that the spread return is (20-15)/15 = 33 %, and total risk arbitrage is (18.5-15)/15 = 23% for the period. The stock value moved downward and revision return is about 10%.
Table 2 show that most of target firms in leveraged buyouts have negative revision returns, which are quite different the general cash offers, would actually affect the total realized arbitrage returns. However, Jindra & Walkling (2004) investigated the cash offering deals during the period of 1981~1995 in the U.S. and found 80 % of target firms enjoy positive revision returns. As a result, we speculate private equity funds could rig the price to buy target firms’ shares at the lower price. Besides, by splitting risk arbitrage returns, we find that spread returns are realized returns for investors in successful deals. In comparison of previous papers, risk arbitrage returns (the difference of market price on the announcement and completion day) are realized returns for investors.
3.2 Variables construction
In the literature review we proposed that certain variables influence spread returns. We need to explain further how we derived these variables. They include two ex post variables:
revision returns and durations, and characteristics of deals and target firms: bid premiums, price-to-book ratio (P/B), unsystematic risk and bid-ask spread ratio.
(1) Duration (Dur) of the deals is the numbers of days between the announcement date and the completion date for successful deals, and the withdrawal date for fail deals.
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(2) The bid premium (BP) is
(
b)
b Oi P P
P − / , where Po is offer price, and Pb is the closing price one day prior to the announcement day.
(3) Price-to-book ratio (P/B) is the ratio of a target firm’s market value divided by equity book value; book value is the target equity value at the end of the most recent fiscal year prior to the announcement, and market value is the target equity market price calculated by multiplying the total number of target shares outstanding by the target stock price on the announcement day.
(4) We computed unsystematic risk (Risk) in the market model. At first, we calculated the market model beta of target firms, so as to determine the systematic volatility during the period of deals. Then we subtract systematic volatility from total volatility to obtain unsystematic risk. Target firms’ stock returns and market returns (S&P 500 NYSE/AMEX/NASDAQ value-weighted market index) are obtained from the CRSP; the period of returns is one month before and after announcement date.
(5) The bid-ask spread ratio (Spread) is abnormal spread divided by normal spread; the spread
is ( )
)
2(
1
bid ask
bid ask
P P
P P
+
− , where Pask,Pbid are the asking price and the bid price on transaction day
(the abnormal spread for this measurement is the average ratio in the interval of t = -42 to t = +2, normal spread is the average ratio in the interval of t = –50 to t = –25; t is the announcement date).
3.3 Research hypotheses
Hypothesis 1: Given offer price and the duration, spread returns would be negatively relative to revision returns and positively relative to durations.
This hypothesis is intuitive. First of all, all prices are driven by the expectation of subsequent returns. If spread returns are relatively smaller, higher expected revision returns for certain acquisition generate higher immediate prices. This assertion is consistent with the findings of Jindra & Walkling (2001). They do a regression analysis of spread returns cf.
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revision returns resulting in a significantly negative coefficient. Second, longer holding duration should lower the total realized arbitrage returns and spread returns. However, Table 1 shows that spread returns seem to be positively associated with expected duration, measured as the period from announcement to completion. We speculate that investors enjoying higher spread returns prefer to hold their shares longer.
Hypothesis 2: Target stocks with both higher bid premium and lower liquidity yield higher spread returns.
This suggests that investors will buy target firms with not only higher bid premium but lower liquidity. Bid premium (the ratio of closing price one day prior to the announcement day scaled by offer price) will lead to higher spread returns and higher total risk arbitrage returns. During the deal, acquirers would acquire shares from the stock markets, and most investors would sell their shares at fair prices on the completion day5. In reality, as Table 2 shows, 70% of our observations tend downward, and that the price of the target firm can fall below its offer price on the completion day. This phenomenon may result from the possibility that more arbitrageurs engage in the bidding process and sell out their shares prior to the completion day. If more arbitrageurs hold shares of target firms, these target firms will be less liquid in the market.6 Agrawal et al. (2004) showed that stocks with a greater proportion of
5 Investors can sell off their shares at market price to an acquirer on the completion date.
However, most target firms’ stock prices do not equal the offer price on completion day; and investors should sell their stocks at the offer price to an acquirer. As a result, spread returns would equal to realized arbitrage returns.
6 The institutional ownership of a target firm is a good indicator of liquidity, but we can not acquire this information from the SDC databases. The Securities Exchange Act stipulates that institutional investors can be exempted from the 13F filing requirements of disclosing ownership of target firms. This is the confidential treatment (CT) rule, which is applicable to an arbitrage position throughout the period of deals. Besides, private equity funds in leveraged buyouts are not required to disclose their asset holdings to the SEC. Therefore, we would use bid-ask spread to measure liquidity.
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informed institutional investor will tend to lower the liquidity of target firms. This implies that if target firms have both higher bid premium and lower liquidity, arbitrageurs will earn considerable risk arbitrage returns with certainty.
Hypothesis 3: Target firms with less liquidity could easily reverse their stock price post the announcement day.
We support the assertion that the higher the bid-ask spread will be, the greater the proportion of informed investors who will tend to have better information than general investors (Agrawal et al., 2004). There are two ways that informed investors can sell their shares. They can sell their shares to general investors or acquirers in the stock market, or they may negotiate with private equity funds (acquirers) for a reasonable price during the deal.
Whatever option they take, targets firms with a higher ownership of informed investors will lower their liquidity. As a result, those target firms tend to reverse prices post the announcement day. An intriguing question is whether less liquid target firm stocks could easily loose value and result in lower total risk arbitrage returns.