The idea of pseudo market timing is that many firms make M&As when past returns have been positive and; because higher stock prices imply more downside space and prompt firms do mergers and acquisitions. Firms could make more mergers and acquisitions at higher prices
because managers trust that they result in less earnings dilution and incorrectly believe that stock prices are too high, or for other reasons. Returns of private firms (that potentially may make M&As) and firms that actually make M&As are assumed to follow a simple binomial process.
A simple example:
This thesis follows Schultz (2003) and analyzes the pseudo market timing hypothesis in a two-period model. This thesis examines two-period returns following mergers rather than multi-period returns. The market return is normalized to zero in both periods. We assume that the market earns a return of zero and the aftermarket return of M&A is equal to the market return plus an excess return of either + 10 percent or - 10 percent. Positive and negative excess returns are equal, and are unpredictable. According to the binomial process, (the abnormal return in period 1 (between date 0 and date 1) is denoted by . Similarly, let denote the abnormal return in period 2 (between date 1 and date 2))
I. = +10% and = +10%;
II. = +10% and = −10%;
III. = −10% and = +10%;
IV. = −10% and = −10%.
The abnormal returns in periods 1 and 2 can take four different paths. This thesis assumes that the stock price of each firm is $100 at time zero. For this example, we assume that no firms make M&As if stock prices for potential M&As are $95 or less; There is one M&A if prices are between $95 and $105; There are three M&As if prices exceed $105. When two possible paths excess returns for each period, there are four equally possible paths of mergers and excess returns. Figure 1 corresponds to one of these paths.
Considering the upper path as shown in figure1, it is evident that M&As earn positive excess 6
returns for each period. At time 0, stock prices are $100 and one firm makes mergers and acquisitions.
The M&A earns an excess return of 10 percent following the period. At time 1, with a M&A price of
$110, three firms make mergers and acquisitions. Each of these M&As earns an excess return of 10 percent. In total, there are four M&As for this path: one at time 0 and three at time 1. If we calculate the average excess returns, we weigh each M&A equally and get a mean excess return of 10 percent after mergers.
There are four equally possible stock price paths and only one will occur. Figure I reveals that when the average aftermarket excess returns are calculated in event time, that is weighting each return equally on M&As, the mean excess returns are positive for one path and negative for three paths. Even though the expected aftermarket return for any individual M&A is zero, there is a 75 percent probability that the observed mean aftermarket return will be negative.
In this example, the decision to make mergers and acquisitions is a response to the current price;
It is not made because future returns are predictable. As an illustration, two of the paths have a stock price of $110 at time 1 in the example. On each of the paths, three M&As are issued at time 1. The aftermarket excess return for M&As issued at time1 is positive for one of the paths and negative for the other. Ex-ante, the number of M&As is unrelated with future excess returns.
This thesis observes that although the probability of observing a price path where equal-weighted aftermarket returns are negative is 75 percent, a M&A is never a bad decision ex-ante.
To see this, note that if you weigh each of the four price paths by the number of M&As on each, the expected return is zero. Those price paths with the highest excess returns also have the most mergers.
This example is simple, but it includes the key point of pseudo market timing. First, the likelihood of observing negative abnormal returns in event time far exceeds 50 percent even though the ex-ante expected excess return of every M&A is zero. This is because as the number of M&As increase with higher stocks prices, the M&As will cluster when prices are near their peak. Second,
excess returns are negative in event time and zero in calendar time. The results are still unchanged if more than two periods are considered, if aftermarket returns are calculated over more than one period or if the market earns a non-zero return. Similarly, if the number of M&As increase after the M&As have done well in the aftermarket, the likelihood of losing money on average is high, even though each M&A is a fair game. In this example, the decision to conduct a merger is a response to current price levels; it is not made because future returns are predictable.
Although the example employed here used only two periods, the pseudo market timing is not a small sample. In fact, underperformance is more likely to be observed in a long time series than in a short one. Schultz demonstrates this. He relies on simulations of a binomial model like the one in the Figure I example. The likelihood of observing underperformance increases steadily with the length of the time series. Pseudo market timing is not a small sample problem.
3. RESEARCH METHOD
3.1.RESEARCH HYPOTHESIS
According to the definition of managerial timing ability and pseudo market timing, this paper constructs three types of research hypotheses to clarify which theory explains the post-merger abnormal returns correctly.
Hypothesis 1: According to managerial timing ability hypothesis, the correlation between post-merger abnormal returns and a firm’s book-to-market ratio is negative.
According to the managerial timing ability hypothesis, managers decide to merge with other firms because managers predict that their stock price is overvalued. Rau and Vermaelen (1998) discovered that the value firms’ (high book-to-market ratio) abnormal return is higher than the returns of the growth firms’. Thus, the growth firms’ stock price is overvalued more heavily.
According to the managerial timing ability, the growth firms’ post-merger abnormal returns should be lower than the value firms’ post-merger abnormal returns.
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Hypothesis 2: According to managerial market timing hypothesis, the relation between the number of M&A and the future M&A index is negative and event-time abnormal returns after mergers are also negative. However, according to pseudo market timing, event-time abnormal returns after a merger is also negative but the relation between the number of M&A and the future M&A index is not negative.
According to the managerial market timing hypothesis, managers have the ability to predict future prices. When managers predicted that their price is overvalued, they decided to merge with other firms. The relation between the number of M&As and the future M&A index should be negative.
The event-time abnormal return after the merger should also be negative. Furthermore, according to pseudo market timing, firms merger when past returns were positive. However, it presents a case that event-time abnormal returns are also negative but the relation between the number of M&As and the future M&A index should not be negative.
Hypothesis 3: According to managerial market timing hypothesis, the relation between the number of M&As using stock financing and the future M&A index is negative and the event-time abnormal returns of firms using stock financing is also negative.
The full samples hide an important distinction based on the financing of these transactions. In particular, mergers financed with stock, at least partially, have different value effects from mergers that are financed without any stock. Myers and Majluf, (1984) explained that post-merger abnormal returns are the result from the information differences between managers and outside investors. The basic idea is that managers are more likely to merger when they perceive that it is overvalued by the stock market than when they think the company is undervalued. According to managerial market timing hypothesis, mergers financed with stock are more intense with the stock market than mergers that are financed without any stock. The relation between the number of mergers financed with stock and the future M&A on the stock merger index should be more significant than the full M&As and event-time abnormal return also is more significantly negative.
3.2. Definition of Variables
1. Number of M&A:
This paper uses the number of M&A as the announcement activity. Monthly number of M&A is calculated by summing the number of announcement on merger each month from1995 to 2006.
2. The M&A Index
This paper uses the M&A index as a monthly equally weighted performance index consisting of companies characterized as having M&As which date back a maximum of three years. The M&A index is calculated by equally weighing the companies’ monthly prices in computing the results. Analysis of the movement of the post-merger profitability ratios are one of the major objectives in this paper.
3. Abnormal Stock Returns
Abnormal stock returns measures stock performance both prior to and subsequent to the M&A announcement. Abnormal stock returns are calculated by subtracting the expected returns from actual returns in event time. This paper uses BHRs method to calculate the holding returns.
Because of its ability to provide a more meaningful interpretation, much of our analysis relies on an annual buy-and-hold returns approach (BHRs).
4. Cold Months
Figure 2 ranked a three-month moving average of M&A number into quartiles. The cold months are defined as a period of at least three consecutive months where the number of M&As are below the lower quartile (1rd quartile). The variable of cold months is coded “1” if the number of M&As are below the lower quartile; and otherwise it is coded as “0”.
5. Hot Months
Figure 2 ranked a three-month moving average of M&A numbers into quartiles. We define hot periods as occurring for at least three consecutive months where the number of M&As exceed the upper quartile (3rd quartile). The variable for hot months is coded “1” if the number of M&As is
10
above the upper quartile; and otherwise it is coded as “0”.
6. Stock-financed mergers
Stock-financed mergers refer to the case when bidders use majority payment with stock to obtain absolute control.
7. Book-to-Market Ratio
This paper calculates a firm’s book-to-market ratio by using the book value of common equity divided by the market value of common equity from the COMPUSTAT data. The book value of common equity is subtracted from annual data prior to the announcement date. The market value of common equity is subtracted from the daily data prior to the announcement date. According to the book-to-market ratio degrees, we ranked them into five levels. The highest level defines the high B/M and the lowest level defines the low B/M. The rest of the levels define the mid B/M.
8. Firm Size
This paper calculates firm’s size using numbers of outstanding shares minus monthly prices from the COMPUSTAT data. According to the degree of a firm’s size, we ranked five levels.
3.3. Research Model
In order to analyze the event-time abnormal return, this paper uses the BHARs method to test the hypotheses 1~3 and the bootstrap to perform hypothesis tests in the presence of nonnormality.
In order to analyze the calendar-time relation between M&A activity and the M&A index, this paper uses the negative binominal regression model to test hypothesis 2 and hypothesis 3.
3.3.1. BHAR Method
Although a conventional cumulative abnormal return (CAR) approach is straightforward to estimate, this approach implicitly assumes frequent rebalancing which induces an upward return
bias due to a bid-ask bounc (Conrad and Kaul (1993)). To avoid this problem, we focus on buy-and-hold returns, BHRs.
This thesis tried to calculate the long-horizon buy-and-hold abnormal returns as:
(8)
Where is the t period buy-and-hold abnormal return for sample firm i, is the t period buy-and-hold return of control firms, and is the t period buy-and-hold return of sample firm i. We calculate annual BHRs for each firm in our sample for the year before and the five years following the M&A announcement, where each year is defined as 252 trading days.
This thesis follows the findings from Lee (1997) and Chan, Ikenberry and Lee (2004) and uses five matching firms to reduce the noise that may occur when examining smaller sub-samples.
These control firms are selected by choosing non-M&A firms with the closest B/M ratios relative to the M&A firm which also belong to the same size deciles. It is well-documented that the common stocks of small firms and firms with high book-to-market ratios earn high rates of return (Fama and French (1992), Chan, Jegadeesh, and Lakonishok (1995), Davis (1994), Barber and Lyon (1997b), Fama and French (1997)). Consequently, this thesis considers portfolios or control firms selected on the basis of firm size and book-to-market ratios.
In this research, this method uses either technique:
1 Frequent rebalancing results in the CAR method in calculating return on a portfolio rebalances the portfolio, but firms on M&A announcement don’t rebalance composed firms. In the BHAR method, the control firms and firms of the M&A announcement in calculating returns have no rebalance composed firms
2 Especially for smaller, less liquid stocks, bid-ask bounce can create the illusion of a price change when in fact there wasn't really a change. Recall that in a market, the interested buyers of a stock post the "bid,"
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(1)This thesis uses twenty-five size and book-to-market reference portfolios. These portfolios are formed as follows. Five size reference portfolios are created. Each size portfolio is further partitioned into five book-to-market quintiles in year t.
(2)Portfolio returns are computed based on BHRs of sample firms, assuming an equal-weighted investment strategy. Longer horizon portfolio returns are obtained by compounding annual portfolio returns across event times.
(3)The BHAR is calculated by the portfolio returns minus the return of the matched firm on a size and book-to-market matched sample firm as a proxy for the expected returns.
3.3.2. Statistical Tests and Simulation Method
This section describes the statistical tests that this thesis analyzed in tests of event-time abnormal returns. This thesis describes the simulation method used to evaluate the empirical specification of these tests. The bootstrapping technique was used to calculate the empirical p-values.
This method is recommended by Lyon, Barber and Tsai (1999) as a way to avoid a potential bias caused by skewness in long-horizon returns (Kothari and Warner(1997)). In this approach, the method generates the empirical distribution of long-run abnormal stock returns under the null hypothesis.
(1) Specifically, this thesis randomly replaces each sample firm with another firm with the same size and B/M group at the time of the M&A announcement, and thus formed a “pseudo”
portfolio.
(2) This thesis tried to calculate BHRs and then BHARs for this particular portfolio as if it is our sample portfolio.
(3) This thesis repeated this process for a 1,000 times to form an empirical distribution of abnormal returns.
(4) The statistical significance of the sample portfolio abnormal performance is measured by the empirical p-value.
(5) The null hypothesis occurs when the mean long-run abnormal return is zero; The null hypothesis tested by approximating the empirical distribution of the mean long-run abnormal returns which is defined as being when the mean long-run abnormal return equals the mean long-run abnormal return for the 1,000 portfolios. This hypothesis is rejected at the significance level if:
(9)
The two y* values are determined by solving
Pr[ Pr[ = (10)
where are the p = 1, . . . ,1,000 mean long-run abnormal returns generated from the portfolios.
This section summarized the statistical methods that this thesis evaluated.
3.3.3. Negative Binomial Regression Model
This thesis estimates the context that the decision to merge is a response to current price levels; and is not made because future returns are predictable.
In order to control for the discrete and non-negative natures of the variables, this thesis applies a count data regression model A natural starting point is the poisson regression model, where the dependent variable follows a Poisson distribution with mean
in each time point t.
ut
3 See Green, 2003, p. 740. Dahlquist and De Jong (2004) apply similar count data regression models in order to analyze pseudo market timing in the US. Schultz (2003), however, ignores the count data characteristics of the number of IPOs and applies linear regression models.
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t n t Unfortunately, the Poisson distribution with density
exp( )
has only one free parameter which at the same time corresponds to the mean and the variance of the distribution.
ut
As in our sample, the count data usually shows more variability than what can be accounted for by the Poisson distribution. Hence, we introduce a stochastic parameter ε to allow for unobserved heterogeneity:
=exp(β0+β1 1,x t +β2 2,x t+ +... βnxn t,) exp( )ε (4) This equality of the mean and variance is referred to as equidispersion. When the variance is larger (smaller) than the mean, we have overdispersion (underdispersion).
Empirically, overdispersion is common (for example, we have noted that the number of M&As is unconditionally overdispersed). To allow for overdispersion, we let the number of M&As in a month to be drawn from the mixing of a Poisson distribution and a gamma distribution.
Let the unobservable random variable z=exp( )ε follow a gamma distribution with density
and with parameters α>0, β>0. Setting β=1/α, this gamma distribution has mean 1 and
variance α and therefore does not bias the model, but introduces unobserved heterogeneity.
Especially, for α→0 we yield the simple poisson regression model since z equals 1 deterministically. The distribution of the dependent variable now results from the marginal distribution with density come up with the negative binomial regression model which nests the poisson regression model, as noted earlier
If possible, the natural logarithms of the independent variables enter the regression models to avoid a fixed exponential link, but allow for different functional links between the independent variables and the dependent variable.
3.4. Source of Data
This thesis’s analysis begins with all firms trading on the NYSE/AMEX/NASDAQ exchange with available data on the monthly stock returns; monthly price, daily price and daily stock return files are created by the Center for Research in Security Prices (CRSP). In addition, the book value of equity per share and the number of outstanding shares are obtained from COMPUSTAT data. This thesis eliminated all firms whose information was not present on the CRSP or whose accounting information was not available on the annual Compustat records.
4 For a more detailed derivation of the negative binomial model see Cameron/Trivedi (1998), pp.100.
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4. RESEARCH RESULTS
4.1.DESCRIPTIVE STATISTICS
This thesis obtained the useful sample sets of material mergers and acquisitions from the Securities Data Corporation Worldwide Mergers and Acquisitions database (SDC). Table 1 presents the data that uses the following criteria:
(1)All acquiring and target firms are US public firms;
(2)The announcement date is from 1995 to 2006 inclusively;
(2)The announcement date is from 1995 to 2006 inclusively;