Relative mispricing and takeover likelihood

1.   Introduction

Does takeover exposure represent mispricing or risk in the cross-sectional stock returns? Recent paper by Cremers et al. (2009) documents a positive relationship between target likelihood and future stock returns and argues that it is consistent with a risk-based explanation. Target firms are exposed to cash flows shocks or discount rate risk because acquirers have more free cash, or lower required rates of return. Difference in takeover exposure means difference in exposure to asset pricing state variables.

Takeover markets offer a unique testing ground for the risk-based hypothesis. In prefect capital markets, higher returns (or low returns) for high target likelihood firms (or high acquirer likelihood firms) would reflect compensation for higher (or lower) systematic risk. If the link between takeover probabilities and cross-sectional stock returns can be attributed to risk (Cremers et al., 2009), then target likelihood and acquirer likelihood should capture the same risk exposure. This indicates that acquirer likelihood, the likelihood of being an acquiring firm, should have no incremental effect on the cross-sectional stock return beyond target likelihood, the likelihood of being a target firm.

In this paper, we find that stocks with high acquirer likelihood earn significantly lower future returns than similar stocks in both portfolio and regression settings after controlling for target probability. In independent-sorting portfolios on acquirer and target probability, strategies that go long on the lowest acquirer probability portfolio and short the highest acquirer probability portfolio earn significantly positive future returns in all target probability quintiles. The acquirer effect is more pronounced for longer holding periods, and the results are robust to various risk-adjustment techniques. Based on the results in Fama-MacBeth regressions, a one percent increase in acquirer likelihood corresponds to a four percent decline in future one-month stock returns. This is inconsistent with the interpretation of takeover exposure as a proxy for risk.

Alternatively, the evidence in this paper supports the relative mispricing hypothesis. Misvaluation is an important factor in takeover market (Shleifer and Vishny, 2003; Rhodes-Kropf and Viswanathan, 2004). Bidder and target overvaluations reflect expropriation opportunities, information asymmetries and managerial incentives. Bidders profit from purchasing less overvalued (or undervalued) assets using relatively cheap currency (equity). Over-optimistic investment opportunities can induce managers to acquire firms to confirm investor expectations (Polk and Sapienza, 2009).

Under the behavioral approach, market valuation is a determining factor in takeovers. We hypothesize that takeover likelihood can be viewed as a measure of relative overvaluation. Markets are consisting of different scales of misvaluation firms, including overvalued, fair-valued and undervalued firms¹. Shleifer and Vishny (2003) argue that overvalued firms are motivated to acquire fair-valued and undervalued firms to capture real assets². For fair-valued firms, mangers acquire undervalued firms to survive competition or avoid losing private benefits and controls in the acquisition process (Gorton et al., 2009). Morck et al. (1988) find that target managers are likely to be replaced or play subordinate roles in the new firms after being acquired. Potential acquirers tend to be overvalued and potential targets tend to be undervalued stocks, but fair-valued firms may be either.

¹The implication does not change if these firms are changed to more overvalued, median overvalued, and less overvalued firms.

²To capture the benefits of overvaluation from M & A, acquirers are not restricted to use stock as the method of payment. Issuing equity prior to M & A and make cash offers, acquirers also benefit from their overvalued equity as stock acquisition.

Overvaluation determines the potential acquirer and potential target between two firms. Furthermore, a firm is facing an entire market of potential acquirers. If takeover likelihood corresponds to relative mispricing, acquirer probability and target probability should have different influences on future stock returns. Probable investors are likely to short probable acquirers even if these firms do not engage in M & A activities. Investor should go long on probable targets. Several studies find evidence of abnormal volume and price increases during periods of known insider trading (Cornell and Sirri, 1992; Meulbroek, 1992; Meulbroek and Hart, 1997; Chakravarty and McConnell, 1997; 1999; Fishe and Robe, 2004). By examining trading in target firms prior to M & A announcements, other studies (Jarrell and Poulsen, 1989; Gao and Oler, 2012) conclude that the observed abnormal trading activities and the resulting price run-ups are consistent with market anticipation of a takeover announcement. Probable acquirers become less overvalued and probable targets become more overvalued (or less undervalued).

We examine trading strategies based on takeover probability in different mispricing subsets as a further test of the mispricing hypothesis. We find that the takeover effect concentrated in small size, value, high momentum, high investment, and low turnover firms, as well as both high and low net issuance (or accrual) firms. These characteristics are associated with firms that are expensive for investors to arbitrage and are likely to be mispriced³. This evidence supports the relative mispricing hypothesis.

³See, for example, Ritter (1991), Loughran and Ritter (1995), Stein (1996), Sloan (1996), Teoh et al.(1998b, 1998a), Teoh et al. (1998), Baker and Wurgler (2000), Lee and Swaminathan (2000), Jegadeesh and Titman (2001), Bakeret et al. (2003), Titman et al. (2004), Zhang (2006), Henderson et al. (2006) and Dong et al. (2007).

The rest of the paper is organized as follows. Section we discuss the sample data, summary statistics, and adjustment for outliers and other data problems. In section Ⅱ, we construct a dynamic logit model of target probability and another to estimate acquirer probability. In section Ⅲ, we conduct portfolio analyses based on these likelihoods. Section Ⅳ, we test the takeover effects on different firm characteristics. Section Ⅴ reports my conclusions.

2.   Data and Estimation

Acquirers and targets are identified from the Securities Data Corporation (SDC), which compiles a database with a broad range of M & A activities between January 1981 and December 2009. After filtering the sample (see section C), we obtain 22,008 acquirer observations and 6922 target observations. Table 1 provides summary of the takeover activities over the sample period. There is an obvious increasing pattern before year 2000 for both acquirers and targets. In fact, the number of acquirers (target) is 2477 (1844) in the 80s, but the number becomes 9105 (3127) in the 90s⁴. Takeover activities subsequently stabilize.

⁴The huge unbalance between the number of acquirer and that of target is due to the fact that many targets are privately owned firms, which do not appear in our sample. The empirical results are robust to eliminating non-public target observations.

The dataset also provides information on whether the acquisition is successful, the mode of payment, announcement date, completion date, transaction value, and industry SIC code. We consider all announced deals (both complete and not) since this paper studies the expected level of takeovers. We create two dummy dependent variables. For each month, we assign a value 1 to the acquirer dummy (AC) if a firm announces to acquire another firm and 0 otherwise. At the same time we assign a value 1 to the target dummy (TA) for the corresponding target firm and 0 otherwise.

We obtain daily and monthly stock returns, prices, and trading volumes from CRSP monthly and daily data. Annual accounting data are from COMPUSTAT annual file. IBES covers analyst data, which contains analyst earnings forecasts, long term growth estimates, and recommendations⁵. To align firms with different fiscal year-ends in calendar month, we match fiscal year t-1 accounting data to the monthly market data from May of year t to April of year t+1 based on the assumption that accounting data of fiscal year t-1 is available to all investors on April of year t. Then we match prior quarter analyst data to current month securities data.

⁵We also use EXECUCOMP database and RiskMetrics database in the robustness check section.

Prior literature applies the market-to-book ratio (or analogous variables such as Tobin's Q) to capture the valuation effect on takeover. Motivated by Rhodes-Kropf et al. (2005), we decompose the market to book ratio because market value is a noise measure of fundamental value. Market value reflects both overvaluation and information on future earnings growth prospects. Between observed market price and fundamental value, there is a mispricing componentwhich the literature generally attributes to behavioral causes⁶. Mispricing significantly affects finance decisions (Dong et al., 2012), predicts future abnormal returns (Frankel and Lee, 1998; Lee et al., 1999), and predicts takeover-related activities (Dong et al., 2006). The estimate of residual income value (V) contains forward-looking information, which filters firm characteristics other than misvaluation, such as earnings growth prospects, risk, and managerial problems. We adopt methodology similar to Dong et al. (2006) and Dong et al. (2012).

⁶See Modigliani and Cohn (1979), Shiller (1981), Shleifer and Vishny (1997), Scheinkman and Xiong (2003), Brunnermeier and Julliard (2008), and Chen, Lung, and Wang (2009). Behavioral models imply that B/P is correlated with misvaluation, and therefore is a predictor of abnormal returns (e.g., Barberis and Huang 2001; Daniel, Hirshleifer, and Subrahmanyam 2001).

2.1.   Mispricing measure

We follow the approach of Dong et al. (2006) and Dong et al. (2012) who use Ohlson's (1995) residual income model. There are two obvious advantages of using the residual income model. First, the "clean surplus" calculation allows different accounting treatments and the results are unaffected (Ohlson, 1995). Second it contains forward-looking information from analyst forecasts of future earnings and filters growth expectations not related to misvaluation⁷.

⁷Sell-side analyst forecasts are well-known with their biases due to either strategic actions from analysts or common psychological biases. These biases can only weaken the results of this paper. If that is the case, the results should be interpreted as a conservative version of the results using true misvlauation.

Under the "clean surplus" calculation, increases (or decreases) in book value of equity are equal to earnings minus dividends. The intrinsic value (V_t) includes both book value of equity and an additional component to reflect the firm's forecast excess income, which is measured by analysts' earnings forecasts. To measure fundamental value for each stock in month t, we measure the residual income model as follows:

where E_t is the conditional expectation operator, B_t is the book value of equity at time t, ROE_t+τ is the return on equity for period t+τ, ${{\rm{r}}^{\rm{e}}}_{\rm{t}}$ is the firm's annualized cost of equity.

To implement estimation, we replace equity (1) to a finite series of T-1 periods and a terminal value. The terminal value is equal to the present value of perpetual of residual income (Dong et al., 2006; Dong et al. (2012). Since the estimated fundamental value is not sensitive to the choice of the forecast period beyond three years (Lee et al., 1999), we use a three-period horizon to estimate the residual income valuation:

where f(ROE_t+i) is the forecasted return on equity for period t+i. Forecasted ROE is:

where

and where

where f(EPS_t+i) is the forecast EPS for period t+i. payout is the dividend payout ratio and is equal to dividends divided by earnings⁸. If the EPS forecast for any horizon is missing, we replace it with the EPS forecast for the previous horizon. We restrict each of f(ROE)s to be less than one.

⁸Following Lee et al. (1999), we replace negative payout ratio (due to negative EPS) to the ratio of dividends over 6% of total assets. We also delete observations with payout ratio greater than one.

For the annualized cost of equity, ${{\rm{r}}^{\rm{e}}}_{\rm{t}}$, we consider the CAPM and the Fama-French three-factor model. In the tables, we report results based on the CAPM but findings based on the Fama-French three-factor model remain qualitatively the same. Following Fama and French (1992), for each month of each firm, the beta of time t is estimated on the prior 24 to 60 monthly returns (as available). The market risk premium and risk free rate are obtained from Professor French's website. To reduce outlier problems in the beta estimation, we winsorize the annualized cost of equity into the range of 5% to 25%. Following Dong et al. (2006) and Dong et al. (2012), we use V/P, fundamental value (Equation 2) divided by price per share, as a misvaluation proxy.

2.2.   Earnings growth prospects

Past literature documents that B/P, book value per share divided by price per share, is a robust and positive predictor of the cross-section returns. While risk models argue that B/P is correlated with growth, behavior models claim that B/P is related to misvaluation (Daniel et al., 2001). This implies that B/P is likely to be a noisy proxy of firm characteristics, such as earnings growth expectations. By replacing market value with the residual income measure of fundament value, B/V can capture earnings growth prospects better than B/P in filtering out misvaluation. We calculate B/V as a ratio of book equity to fundamental value, which is measured by the residual income model. In the final sample, the correlation of V/B with V/P is fairly low, 0.068, so they may offer useful independent information about growth or misvaluation.

2.3.   Data filtering, outliners, and adjustments

In the raw data, there are serious negative book value of equity problems and outlier problems. Following Cohen et al. (2003), the book value of equity is adjusted by adding 10% of the difference between the market value and the book value of equity. After these changes, we still find less than 1% of sample firms have negative book values of equity. We replace the negative adjusted book values of equity with values of $1. Similar adjustments are made to the book value of assets.

For the outlier problem in our sample, we winsorize all variables at the 1 and 99 percent levels for the entire sample. We implement some additional filtering criteria and adjustments as follow:

1. The observation date is between January 1981 and December 2009. This means the sample for mergers and acquisitions should also fall within these periods

2. Both the acquirer and the target are public and trade in NYSE, AMEX, or Nasdaq

3. Firms are required to have earnings forecast data in IBES

4. Firms are required to have valid information on total assets, the book value of shareholder's equity, the book value of total liability, sales, cash and short-term investment, operating income, market capitalization, and total outstanding shares

5. Observations with negative value in capital expenditure, sales, cash and short-term investment, inventory, capital expenditure, plant, property, and equipment, and price per share are discarded.

6. We replace missing values in plant, property, and equipment with zero

7. V/P and B/V are not missing in the data sample

8. Financial firms (with one-digit SIC of 6) and utility firms (with two-digit SIC of 49) are eliminated.

Next, we explore the summary statistics and characteristics of the filtered and adjusted variables

2.4.   Summary Statistics

Table 2 shows the summary statistics of filtered and adjusted variables. There are 684,437 firm-month observations with complete data available. Panel A of Table 2 reports the distributions of the independent variables for the basic models for all firms. Panel B of Table 2 describes the variables for acquirer and target firms. All variables are free from the outlier problem as the table indicates. Using Panel A as a benchmark, targets and acquirers are distinct from each other and average firms. Acquirers have much higher market-to-book ratio compared to average firms, but targets' market to book ratio is similar to average firms. This indicates that the market to book ratio might not be a good indicator in identifying targets. Of all accounting variables, size stands out as an apparent identifier for acquirers and targets. The average size for acquirers is 6.686 and for target is 5.545, but the average size of sample firms is 5.842. This evidence is consistent with the "eat or be eaten" theory, where size is important factor in determining acquirers or targets.

In Panel B, the mispricing measure (V/P) in acquirers and targets are significantly lower than average firms, which indicates that these firms are overvalued relative to average firms. More importantly, acquirers are growth firms with higher V/B and targets are value firms with lower V/B compared to average firms. For example, average V/B of average firm is 1.86, where that of acquirer is 2.13 and that of target is 1.74. For the entire sample, there are 3% acquirer observations and 1% target observations.

3.   The logistic models of takeovers

3.1.   Acquirer and target models

For each sample month, we estimate (separately) logistic regressions of the likelihood of acquirer and target on various independent variables as appropriate. The basic assumption is that the probability of a firm to be an acquirer or target in the next month is logistically distributed. The logistic model can be represented as follows:

where ${z}_{t}^{i} = \alpha +\beta {x}_{t}^{i}$, P is the probability measure, Y is either the acquirer dummy (AC) or the target dummy (TA), α is the constants term, β is a vector of coefficients, and x is a vector of independent variables. The larger is the value of z, the higher is the likelihood that a firm will be an acquirer or target.

We construct the dummy variable, BLOCK, which is equals to 1 if one or at least one blockholder with more than 5% ownership at the end of previous year and 0 otherwise. Thompson/CDA spectrum provides data on institutional share holdings on quarterly basis from SEC 13f filings. Industry dummy variable is SIC 4 digits code to capture the clustering of takeover activity with industry. The time dummy variable is constructed using a combination of year and month.

Table 3 describes the results of logistic regressions. The first and the second columns are for the acquirer model and the last two columns are for the target model. We present a version of the basic model as Model 1 for acquirer and Model 3 for target with independent variables used in prior literature⁹. In Model 1, all explanatory variables are significant predictors on the likelihood of being an acquirer. Acquirers have less fixed asset, cash, leverage and have higher market-to-book ratio and profitability than the average firm. They also tend to be large firms with large blockholders, where the coefficient of size is 0.22 in 1% significant level. Model 1 has Pseudo R² of 0.03.

⁹See, for example, Hasbrouck (1985), Palepu (1986), Ambrose and Meggison (1992), and Cremers et al. (2009).

Model 2 replaces the market-to-book ratio with the mispricing measure (V/P) and growth measure (V/B). The coefficient of –0.018 (t = –6.85) on V/P is a significantly negative predictor in the acquirer model, which indicates that greater mispricing leads to higher acquirer likelihood. This is consistent with the overvaluation hypothesis of Dong et al (2006). In addition, V/B has negative predictive power on the likelihood of being an acquirer. The coefficient of V/B is –0.006 with t-statistics of –2.48, indicating that acquirers tend to have lower earnings growth prospects than average firms. All other variables have similar coefficients with similar significant levels relative to Model 1 except for leverage. The Pseudo R² of Model 2 (0.03) is similar to Model 1.

Model 3 of Table 3 is the target basic model. The market-to-book ratio has significant and positive power in predicting the likelihood of being a target unlike Cremers et al. (2009). This is puzzling under the normal theory of takeovers because the market-to-book ratio has been claimed to be a measure of productivity or growth opportunities¹⁰. However, it is consistent with the misvaluation theory of Dong et al. (2006). Target firms can be overvalued firms, but less overvalued than acquirer (the coefficient of MB on Model 1 and that of Model 3). Targets tend to have higher cash, leverage, lower fixed assets, and ROA. They are also likely to be small firms with large blockholders. This is consistent with the "eat or be eaten" theory, which states that small firms are vulnerable to takeovers. Model 3 has Pseudo R² of 0.02, which is similar to prior literature.

¹⁰Discussion about the market-to-book ratio can be found in Hasbrouck (1985). Cremers et al. (2009) and Bates et al. (2008) find a significant relation between Q and takeover targets but Palepu (1986) and Ambrose and Megginson (1992) uncover no link. Also see the work on Tobin's Q and takeovers of Lang et al. (1991), Servas (1991), Martin (1996), and Jovanovic and Rousseau (2002).

The decomposition of MB in model 4 confirms the results from the basic model. The mispricing measure (V/P) is a negative but insignificant predictor of target likelihood. Consistent with the misvaluation theory, targets are less overvalued than acquiring firms¹¹. On the contrary, the coefficient of V/B is –0.005 (t = –1.87), indicating that targets are low growth firms (or firms with management problems) and disciplinary actions will initiate in financial markets. The Pseudo R² is 0.02. All other variables have similar coefficients with similar significant levels relative to Model 3. The Pseudo R² of Model 2 (0.02) is similar to Model 3.

¹¹Target shareholders choose to be taken over by overvalued firms because either target managers want to cash out from their current holdings (Shleifer and Vishny, 2003) or asymmetrical information sets between bidders and targets (Rhodes-Kropf and Viswanathan, 2004).

Figure 1 shows monthly aggregate measures of realized and predicted takeover percentages. The model of acquirer likelihood captures the majority of variation in realized acquirer percentage, with some minor errors. The gradual increment in the percentage of acquirer from 1981 to 2000 and the gradual decline from 2000 to 2005, and in 2010, are well captured by the model. However, it slightly overpredicts the likelihood of being an acquirer during the period 2000–2009.

It is clear that aggregate realized target percentage varies and is mean-revering. Our model of target likelihood has not performed as well as our model of the acquirer likelihood, but it does capture the trend of aggregate realized target percentage. The lack of fit may be due to a number of factors. First, targets may be private firms, for which data are not available. Second, the likelihood of being a target is more idiosyncratic than the likelihood of being an acquirer. Finally, the aggregate measure may not represent targets well since targets tend to disappear from the sample after the acquisition.

3.2.   Robustness check and alternative specifications

Following the corporate governance literature on merger and acquisition, we run a critical robustness check on the sample with alternative specifications. Masulis et al. (2007) find that corporate governance mechanisms affect the profitability of firm acquisitions. Moreover, Cramers et al. (2009) demonstrate that corporate governance has a significant effect on predicting target likelihood.

Following their research, we test two models on both acquirer and target with different corporate governance variables, including a complement of G-index (EXT), and an interaction variable of BLOCK and EXT (EXT_BLK). Similar to Cramers et al. (2009), the corporate governance index (G-index), incorporating 24 different provisions (Gompers et al. 2003), is taken from the Risk Metrics-Governance Legacy Data, formerly known as the Investor Research Responsibility Center (IRRC). The dataset used to construct the indices are available from 1990 through 2006. The index EXT is a complement index to the G-index, which is equal to 24 minus G-index. A higher value of EXT represents a greater shareholder rights. The second corporate governance proxy is a dummy variable for the present of an external blockholder. As Cremer and Nair (2005) point out, corporate governance can be divided further into internal governance and external government. The effect of corporate control on equity value is amplified when internal and external governance mechanisms interact. We obtain the equity percentage for outside blockholders from the Blockholders database, which contains blockholder data on 1,913 companies for the period 1996–2001. We use a data cleaning procedure following Dlugosz et al. (2006). We construct a dummy variable (BLOCK) that is equal to one if a firm has outside blockholders who own more than 5% of equity shares.

Table 4 presents alternative model estimates controlling for the corporate governance effect. Models 5 and 6 are acquirer models and Models 7 and 8 are target models. Following Cremers and Nair (2005) and Cremer et al. (2009), we use EXT and the interaction term of EXT and BLOCK. In all models, sample size reduces significantly to 140,445, compared to 684,437 in previous models. Models 5 and 6 show that EXT and EXT_BLK have significantly negative effects on the acquirer likelihood, indicating that the empire-building agency problem of the acquiring firms motivates managers engaging in acquisitions. In contrast, these variables do not affect the target likelihood¹². Acquirers tend to have overvalued equity, but targets tend to be like average firms.

¹²The difference in the results between ours and Cremer et al. (2009) is caused by different database for outside blockholders. Cremer et al. (2009) use data on institutional share holdings from Thompson/CDA Spectrum.

The goodness of fit of alternative models is marginal. For acquirers, alternative models have lower pseudo R² (0.02) than the original models in Table 3. For targets, the alternative models slightly decrease the pseudo R² to 0.01. However, total observations decrease substantially after we include corporate governance proxies due to data availability. Considering all of the alterative models, we find qualitatively similar results.

In the next section, we use Model 2 to estimate acquirer likelihood and Model 4 to estimate target likelihood and then sort firms into portfolios. To remove look-ahead bias, we use only historical data in estimating both likelihoods, which guarantees all likelihoods are based on past information. In a robustness check, we also estimate models using 10-year rolling windows or the entire sample. Then, we construct portfolios by these likelihoods and analyze these portfolio returns, finding consistent results.

4.   Acquirer Likelihood and Equity Returns

4.1.   Portfolios based on acquirer likelihood

We first present results on univariate sorting. Each month from January 1981 to December 2009, firms are grouped into quintile portfolios based on acquirer likelihood. To indentify the cross-sectional effect, acquirer portfolios are constructed each month. This guarantees that any effect here is not caused by time-series variations in equity returns. The average value of each portfolio is calculated for each month. Then, the time-series mean of equity returns is computed for each portfolio.

In this section, we test whether acquirer likelihood affects equity returns based on univariate sorting and double sorting of the firm's takeover measures. We also present multivariate regression tests. We focus on equal-weighted portfolios, but results of value-weighted portfolios show similar patterns with slightly lower magnitude.

Table 5 reports results of quintile portfolios based on acquirer likelihood (acquirer portfolio) from Model 2 and the model is re-estimated using historical data for each month. Each row represents each portfolio mean as well as the difference between top and bottom acquirer likelihood firms. There are remarkable patterns in characteristics and risk loadings across acquirer portfolios. In Panel A of Table 5, firms with high acquirer likelihood tend to be large, high growth, and high momentum firms. These stocks also have high market beta loadings and lower loadings on HML and SMB betas, indicating that low acquirer likelihood stocks have lower HML and SMB risks. The results raise concerns that these return differentials are driven by characteristics or risk loadings. To address these concerns, we perform both risk adjustments, and characteristic adjustments on equity returns.

Panel B of Table 5 reports results of 1-month holding period abnormal returns relative to the risk free rate, 3-factor model (Fama and French, 1993), 4-factor model (Carhart, 1997), 5-factor model (Pastor and Stambaugh, 2003), and characteristics-adjusted returns¹³ (Daniel et al., 1997). There is a clear pattern on abnormal returns among different acquirer portfolios. High acquirer likelihood portfolios generally earn lower abnormal returns compared to low acquirer likelihood portfolios. The average excess returns over risk free rate of quintile 5 are 0.72% per month, where quintile 1 earns 1.24% per month average excess returns. This pattern is monotonically declining and is not caused either by traditional risks or common characteristics. The long-short strategy which buys the lowest acquirer portfolio and sells the highest acquirer portfolio has average excess returns of 0.51% per month. Decile portfolios also show similar results. The long-short strategy earns 0.66% per month in excess returns.

¹³All factors and risk free rates are available at Professor Kenneth R. French's website. The DGTW's (1997) benchmark portfolio cutoffs and returns are available at Russ Wermers' website. Definition of firm Characteristics is similar to DGTW (1997).

Panels C to E of Table 6 confirm the patterns among acquirer portfolios. For example, for a 12-month holding period, the average excess returns over risk free rate is 16.66% per year in portfolio 1 where portfolio 5 earns 9.25% excess returns per year. The long-short quintile portfolio earns average returns of 7.41% per year and the long-short decile portfolio earns average returns of 10.31% per year.

Overall, the evidence from the univariate sorts indicates that acquirer likelihood is negatively related to equity returns. Consistent with the relative mispricing hypothesis, investors anticipate a takeover and they position themselves to capture these premiums.

4.2.   Portfolios based on acquirer likelihood and target likelihood

The previous section showed how acquirer likelihood affects equity returns. To study whether takeover probability is driven by risk, we test whether acquirer likelihood has predictive power over target likelihood. For each month, firms are sorted into quintile portfolios independently based on the two likelihood measures. This procedure creates total 25 portfolios with 94 stocks on average. The mean value of excess returns over the risk free rate is computed each month for each portfolio. Then the time-series mean for each portfolio is calculated.

Table 6 shows the time-series average of double sorting. For brevity, we report only excess returns over the risk free rate of quintile portfolios, but all other abnormal returns with respect to risks and characteristics of quintile portfolios or decile portfolios have qualitatively similar results. We also report the interquintile return difference along high takeover likelihoods. Table 6 confirms that acquirer likelihood is a negative and significant predictor on stock returns even after controlling for target likelihood. The long-short strategy of buying the lowest acquirer portfolio and selling highest acquirer portfolios earns 0.34% excess returns per month at target portfolio 1, and a similar strategy at target portfolio 5 earns 0.40% per month. We also construct a strategy that buys the lowest acquirer likelihood and the highest target likelihood portfolio and sells the highest acquirer likelihood and the lowest target likelihood portfolio. This strategy earns 0.59% per month, 1.64% per quarter, 3.68% per semi-annual, and 8.55% per year in excess returns. These returns are statistically significant.

In summary, Table 6 confirms the findings for the one-way sorts by acquirer likelihood. It documents that acquirer likelihood has predictive power on equity returns beyond target likelihood. For given target likelihood, higher acquirer likelihood firms earn lower future stock returns. The evidence contradicts the risk-based hypothesis (Cremers et al., 2009) on the relationship between takeover probability and equity returns.

4.3.   Predictive ability in cross-sectional stock returns

The prior two tests uncover the predictive power of acquirer likelihood and the results raise doubt on the interpretation that takeover exposure is a risk. To test whether these results are driven by uncontrolled effects from growth, risk, or other factors, we employ Fama-MacBeth regressions, where standard errors are adjusted using the Newey-West Methodology. Four return holding periods are considered, including 1-month, 3-month, 6-month, and 12-month.

This test relies on implementing the correct functional form of expected returns. Since the correct specification is not known in the finance literature, we employ several independent variables including firm size (SIZE), the book-to-market ratio (BM), momentum (MOM), investment (IV), asset growth (AG), turnover (TO), issuance (IS), and accruals (AU). MOM is defined as prior 12 month returns (Jegadeesh and Titman, 1993). IV is the sum of changes in property, plant, and equipment and changes in inventory from the prior year relative to total assets (Titman et al., 2004). AG is the percentage change in total assets from the prior year (Cooper et al., 2008). TO is trading volume for the previous 3-months, relative to total shares outstanding (Scheinkman and Xiong, 2003). IS is the log value of shares outstanding less the log value of the prior year's shares outstanding (Pontiff and Woodgate, 2008). AU is the change in current assets less the sum of changes in cash and short term investment, changes in long-term debt, and changes in depreciation, depletion, and amortization from the prior year relative to total assets (Sloan, 1996).

Table 7 shows the results of panel regressions. Four holding periods are under consideration, where Panel A reports results t+1 month ahead, Panel B reports results t+3 months ahead, Panel C reports results t+6 months ahead, and Panel D reports results t+12 months ahead, each with excess returns as the dependent variable. Five specifications allow comparison by considering:

1. univariate model (acquire likelihood, pAC)

2. multivariate model with takeover proxies (acquire likelihood, pAC, and target likelihood, pTA)

3. multivariate model with takeover proxies and common risk (or characteristic) proxies

4. multivariate model with takeover proxies and anomalies

5. multivariate model with takeover proxies and all other proxies

The coefficient on pAC measure in the first specification is negative, which is statistically and economically significant for all holding periods. For example, in model (1) of Panel A, a one percent increase in pAC will lead to a 0.08% decrease in monthly cross-sectional returns with a t-statistic of –2.28. Average adjusted–R² ranges from 0.78% to 1.03%. When considering a specification that includes both takeover measures simultaneously, pAC remains negative and statistically significant. In addition, pAC in other specifications exhibits consistent results.

In the third specification, which controls for common risks and characteristics, the sign of the slope coefficients on SIZE, BM, and MOM is consistent with prior literature¹⁴. The coefficient on SIZE is negative but not significant. Although the estimate of the slope coefficient is similar to Fama and French (1992), the effect of SIZE can be captured by pAC. The slopes on BM and MOM are positive and significant.

¹⁴Various studies have claimed the meaning of these factors. Fama and French (1992) argues that size and the book-to-market ratio capture unobserved state variable related to financial stress or marginal ability of surviving in market meltdowns. On the other hand, De Long et al. (1990), Hong and Stein (1999), Barberis and Shleifer (2003) claim that these factors are related to behavioral reasons, such as style investing.

The fourth specification consists of multivariate models with additional variables, which control for other empirical anomalies, including investment (IV), asset growth (AG), turnover (TO), issuance (IS), and accruals (AU). Results of Model 4 show that all variables of interest are aligned with prior literature. When all independent variables are considered simultaneously, the coefficient on pAC is less pronounced, yet significant. For example, model 5 of Panel D shows that a one percent increase in pAC is associated with a 0.12% increase in stock returns per year with a t-statistic of –2.87.

Overall, acquirer likelihood predicts stock returns better than target likelihood. We interpret these results as evidence against the risk-based explanation of takeover probability. The longer the holding period, the better is the predictability of pAC measure. All results in this section are consistent with analyses from previous sections.

5.   Mispricing and takeover

We document that acquirer likelihood is a significant predictor of future stock returns over target likelihood, which is inconsistent with the risk-based explanation for takeover probability. Alternatively, previous results are consistent with the relative mispricing hypothesis. First, in the model construction (Table 3 and 4), the mispricing measure (V/P) is a significant predictor of takeover activities. The predictive value of takeover likelihood is likely to be associated with mispricing. Furthermore, if takeover likelihoods are proxies for the level of mispricing relative to the market, both acquirer likelihood and target likelihood may have predictive power on cross-sectional returns. Table 5–7 confirm this argument.

In this section, we investigate whether takeover likelihoods are related to mispricing by implementing trading strategies on different mispricing subsamples. If the relative mispricing hypothesis explains the relationship between takeover likelihoods and stock returns, trading strategies based on these likelihoods are concentrated in firms that are more sensitive to mispricing. For instance, small firms tend be mispriced because they are less diversified and have more severe information asymmetries. In this case, the takeover effect may be more prominent among small stocks.

To explore this argument, we form portfolios by first sorting stocks based on characteristics into 3 portfolios. Then for each characteristic portfolio we independently double-sort stocks based on acquirer likelihood and target likelihood into 3x3 portfolios. Finally, for each characteristic portfolio, we construct a strategy of buying the highest pTA and lowest pAC portfolio (1, 3) and selling the highest pAC and lowest pTA portfolio (3, 1). we consider firm size (SIZE), book-to-market ratio (BM), momentum (MOM), investment (IV), asset growth (AG), turnover (TO), issuance (IS), and accruals (AU), since these characteristics are associated with sensitivity to mispricing in the literature¹⁵.

¹⁵SIZE (Zhang, 2006), BM (Lakonishok et al., 1994), MOM (Jegadeesh and Titman, 1993), IV (Titman et al., 2004), AG (Cooper et al., 2008), TO (Scheinkman and Xiong, 2003), IS (Pontiff and Woodgate, 2008), and AU (Sloan, 1996).

Table 8 presents the average value of trading strategy profits attributed to different firm characteristics. Five returns are considered: abnormal returns relative to risk free rate, the CAPM, the Fama and French (1993) 3-factor model, the Carhart (1997) 4-factor model, the Pastor and Stambaugh (2003) 5-factor model. We apply the above strategy on each characteristic portfolio. All returns are future one month returns with and without risk adjustment. Table 8 (top) reports results of the three most common characteristics from literature. It is consistent with the relative mispricing hypothesis that takeover effect appears only in small stocks and growth stocks. All MOM portfolios show significant returns based on the long-short strategy, but the magnitude is larger among high momentum firms. All risk adjustments reveal consistent results.

We extend the analysis to other firm characteristics. In the second and third rows of Table 8, we present the results for investment (IV), asset growth (AG), turnover (TO), issuance (IS), and accruals (AU). The long-short portfolio earns significant returns on all IV, IS, and AU portfolios, but more notably among High IV, low TO, and high IS. The evidence for IS portfolios is consistent with the literature, as prior studies propose that equity issuance is closely related to valuation-driven merger and acquisition¹⁶. More interestingly, the takeover effect seems to exist only on median and low TO portfolios. One possible explanation for this pattern is that high turnover stocks trade constantly and information can be instantaneously reflected in prices without obstacles. On the other hand, prices of low turnover stocks respond to news slowly. This indicates high sensitivity to mispricing in low TO firms.

¹⁶Pontiff and Woodgate (2008) are motivated by post-SEO and post-stock merger long-run returns and find significant relationship between equity insurance and stock returns.

Furthermore, both high and low AU portfolios reveal significant trading profits from the long-short strategy. This is consistent with Sloan's (1996) earnings fixation hypothesis, which indicates that high accrual and low cash flow firms tend to be overvalued, and low accrual and high cash flow firms tend to be undervalued. Overall, the evidence is consistent with the relative mispricing hypothesis.

5.   Conclusions

Mergers and acquisitions have been viewed as the disciplinary action taken in the markets for corporate control to ensure proper management of corporate resources. Prior studies point out that acquirers generally lose and targets gain in M & A actions. However, the implication of takeovers on asset valuation has been largely ignored until recent article by Cremers, Nair, and John (2009). Whether takeover probability is a proxy for risk is still an open question.

In contrast to prior literature, this paper presents evidence that acquirer likelihood is a significant and negative predictor on future stock returns over target likelihood in both portfolios and regression settings. This is inconsistent with the risk-based explanation of Cremers et al. (2009) of takeover likelihood.

The results in this paper are consistent with the relative mispricing hypothesis. We find that trading strategy based on both acquirer likelihood and target likelihood is concentrated in firms that are more sensitive to mispricing. Specifically, profits are significantly higher in small, high growth, high momentum, high investment, high issuance, low turnover, as well as both high and low accrual firms.

Conflict of interest

The author declares no conflicts of interest in this paper.