As we all know that Microsoft has agreed to buy Linkedin for $26.2 Billion on June 13th earlier this month. I thought it would be perfect timing to conduct an event study on Merger and Acquisitions (M&A) and its impact on the stock market.

Also, in order to develop effective trading strategy and algorithm, we need to make sure our model is able to incorporate new market event information effectively and this requires us to extract key asset-specific factors such as the prices trends, liquidity, volatility through the event study before building the strategy. Furthermore, by analyzing the market in general we can also gather the information and find about the proper order size and trade horizon for our strategy. Then combined with investors’ requirements like the benchmark, risk aversion and trading goals we can finalize our algorithm to effectively deliver those requirements.

First, let’s look at the trend graph of the M&As for recent 20 years:

*<Data source:https://imaa-institute.org/>*

We can see that the total number of M&As has increased over time(from the length of the bars and the dashed linear forecasting line above which shows the upward trend). The M&A value(orange line) and a total number(blue bar) of the M&As have their own cycles. Moreover, we can find that the most popular years for M&As was in 1999, 2007, and 2015. Within last few years, the total number of M&As has stayed relatively stable.

The main topic of this article is about the public reaction towards M&A transactions after their respective announcements and its impact on the stock prices of the target and acquiring firms for both short-term and long-term period. A paired sample analysis for both target and acquiring companies has also been conducted by comparing the pre-announcement and post-announcement returns of their stock prices in the event window of ±30 and ±252 days for acquiring company only.

In general, across all the event windows, target firm’s stock price abnormal returns are significantly different from zero. Unlike the target firms, acquiring companies do not show significant differences and some negative returns across all the event windows. But their volumes are significantly higher than usual on the announcement date. The target firms depict that the post-announcement returns are significantly greater than the pre-announcement returns, indicative of the immediate market reaction to this disclose information.

By the end of the article, I will also introduce how to find the arbitrage opportunity through an M&A event, M&A may be one of the few win-win situation if done properly. Usually, people will long the company being acquired(pretty much always the smart move if the deal goes through). You can also choose to short the acquirer depending on the strategic value and investment timeline.

# 1.Close look at LinkedIn and Microsoft

*Source: dialogue gets the data(http://time.com/4366106/linkedin-microsoft-why/)*

From the graph below, I plotted the Microsoft and Linkedin stock prices for the last 2 years(2014–06–24 to 2016–06–24) and for June 2016. We can see an obvious increase in LinkedIn’s stock price at the announcement date. (Even though the stock price of LinkedIn is much higher, the market cap of linked is 25.49Billion compare to the 399.60Billion which is much lower.)

*(1) LinkedIn*

*Momentum*

I also plotted the stock price of the Linkedin and its short-term 50 days and long-term 200 days simple moving averages and asset prices together on the same graph. In order to predict stock momentum, we need to identify the crossover points of two moving averages. We can see that short-term moving average(since they are moving together) is moving closer to the long-term, which is higher right now, and we can expect the short-term moving average will go above the long-term one soon and it may imply an upward momentum in the near future.

The graph below is just to further clarify this trend. I will use moving average ribbon (a technique used in technical analysis to identify the strength of the current trend and which is achieved by placing a large number of moving averages onto the same chart). Whenever identifying all averages are moving in the same direction, you can judge that the trend is strong to some extent. Reversals are confirmed when the averages crossover and head in the opposite direction. Here the ribbon ranged from 25 days to 120 days) and I also use the hamming distance method (which you can find the detailed explanation from my previous article) to capture the signals when those ribbon lines come across and the regime shift.

When there is a ‘BUY’ signal, the distance metrics line(yellow line) will show up a spike and the distance of the ribbon is at a relatively high level. In turn, if the distance metric line moves downward after a spike, it implies a ‘SELL’ signal. We can see that there is a ‘BUY’ signal around the announcement day since we can see the indicator line is building an upward momentum. The next graph here just uses another method to capture and confirm signal which is achieved by measuring the thickness of the ribbon. Every time there is a paradigm shift we can see the spike of the measurement line (brown line). This time, the moving averages ranged from 50 days SMA to 200 days SMA.

*Stock Price, Trading Volume, Returns, and Volatility*

Let’s take a look at the table below which contains the time(daily), trading volume, open and closing price, daily returns and daily volume % change for the individual stock (here is LinkedIn) from 2014–06–24 to 20160–06–24), the Linkedin’s stock daily return increased by around 46% and its volume increased 1112.27% on the announcement day. It is not hard to interpret this dramatic changes since Microsoft will pay $196 per Linkedin Share, a 50% premium on the social network’s closing price on 2015–06–10.

Also, as I explained at the beginning, as the acquirer offers more per share than the target’s current price, the shareholders of the target company may sell their shares and result in the growth of their value. In other words, an M&A transaction gives its shareholders the opportunity to cash out at a significant premium, especially if the transaction is an all-cash deal like this one.

In order to show the daily movement of the stock returns and volume % changes, I also plotted the graph below to show the daily returns and daily volume % change plus possible error in the same graph(daily return — dark red line; daily trading volume % change — light red). We can see there is a big spike near announcement date for both trading volume and daily return.

From the graph below, it shows daily trading volume % change individually to highlight the dramatic change of trading volume of Linkedin shares on the announcement date. Usually, a rising market should see rising volume since buyers require increasing numbers and increasing enthusiasm in order to keep pushing prices higher.

The graph below is the daily returns distribution graph. We can look at the corresponding intercept on the x-axis of blue line which is the average of the returns and it’s value is around 0(the corresponding y-value which is probability is around 20%). We can also tell that this distribution follows a leptokurtic distribution which happens when the points along the X-axis are clustered resulting in higher peak (higher kurtosis) than the curvature found n a normal distribution. When we analyze historical returns, kurtosis can help us to gauge an assets’ level of risk. A leptokurtic distribution means that small changes happen less frequently because historical values have clustered by the mean. The general range of the daily returns is from -0.10 to 0.10 from the graph with the slightly negative skewness. Based on the skewness, investors can estimate the future returns would most likely be on which side and here the “fruitier” returns are more likely to be more than the mean.

However, the short-term returns distribution shows positive returns with a long tail on the positive side. It is not surprising to see the significant positive returns after the announcement date for the target firm.

The next graph here is the volatility of the stock daily returns. Volatility is a statistical measure of the dissension of returns for a given security. Thus, it refers to the amount of uncertainty or risk about the size of changes in security’s value. A higher volatility means that a security’s value can potentially be spread out over a large range of values. As we expected, the stock returns increase along with the increased volatility of the announcement date.

According to Modern portfolio theory(MPT), volatility creates a risk that is associated with the degree of dispersion of returns around the average. The average volatility of the stock daily returns is around 4% over this period.

The next step for me is to further analyze the stock prices of target company Linkedin. I plotted the histogram below to see the distribution of the stock price. Based on the calculation, I found the average price of Linkedin for last 2 years(2014–06–17 to 2016–06–17) is $199.34 and the standard deviation of the stock price is 44.31 which is very high(especially when you compare it with the standard deviation of Microsoft later).

From the price distribution below, it is clear that the stock prices of Linkedin are located around $200-$220. The short-term graph shows that the price evenly split into either around $130–140 or around $190.

The graph below is created because I also would like to add the volume into the graph as well as the regression line. So you can see from the graph that the y-axis is stock price and the x-axis is the time. As for the size of the dot represents the trading volume over time. You can find there is a huge dot around announcement day recently(when t = 500). Also, from the regression line drawn on the graph the stock price for that last 2 year is moving downward.

For the short-term, there is a divide before and after the announcement date. After the announcement date, we can see that the price is always around $190 and the trading volumes are generally higher than the trades before announcement date.

The next graph is the one I created to measure how the trading volume varies among different stock prices. We can see that the highest trading volume happens when the price is at $192.3.

*Sentiment*

To add more dimensions into our analysis, we can check the sentiment and impact score for last 14 days(Accern’s database). We can see the sentiment for those days are all positive and the impact scores are very high which means the stock price of LinkedIn has a certain positive correlation with the sentiment score(positive sentiment correlated with the positive increase of the stock price). It is not hard to find the increase in the stock price from previous graph.(P.S. I multiply sentiment with 100 in order to match with impact score).

Now, let’s look at LinkedIn’s daily returns compared with the benchmark(S&P500) and its alpha (The abnormal rate of return on a security or portfolio in excess of what would be predicted by an equilibrium model like the capital asset pricing model (CAPM)) and beta (investment indicates whether the investment is more or less volatile than the market) following the CAPM model. Basically, the alpha(alpha = 0.00084) is very small which demonstrates that the daily returns of Linkedin are not outperforming the market as well and its volatility is higher than the S&P500 overall.

A beta which is greater than 1.0 indicates that the security’s price will be more volatile than the market. Here beta equals to 1.077, which is higher than 1.0, that is to say, the volatility of LinkedIn shares is higher than the market.

We can also find the short-term information about alpha and beta through the second graph below. Beta is -8.69 here which implies the LinkedIn stock prices are negatively correlated to the market and it is much more volatile than the market movements.

The graph below shows the cumulative sentiment, the simple moving average (5 days), and the cumulative returns at the same graph for this month We can find that the cumulative sentiment of LinkedIn is increasing over time. The simple moving average of sentiment is moving upward after the announcement day(2016–06–13). The 5 days sentiment moving average keeps being positive after 2016–06–13. Meanwhile, the cumulative returns increase dramatically after the announcement date.

The second graph below is the long-term plot(from 2014–06–25 to 2016–06–25).

# (2)Microsoft

**Momentum**

Following the same analysis as the one, I conducted before on LinkedIn. Here is an interesting single implied in the graph. We can see that the 50 days simple moving average line moved above the 200 days around October 2015 and this trend lasted for a long time until recently. We can see that the 200 days moving average is slowly moving closer to 50 days moving average and they almost come across with each other here which implies the downward trend in the near future if this trend comes true.

From the graph below we can find the ‘BUY’ signal is gradually disappearing and there is a ‘SELL’ signal showing up.(I am using moving averages ranged from 25 days to 120 days).

*Sentiment*

We can also get some insight through the sentiment information about Microsoft for last 14 days. It shows the similar pattern to Linkedin’s sentiment shown as above. The reason is simple. The M&A puts investors in a good mood since corporations are demonstrating that the economy is strong enough for them to spend their cash or obtain some type of bank financing.

I also plotted the sentiment and daily abnormal returns of Microsoft on the same graph to show the similar pattern between daily abnormal returns and sentiment score of Microsoft for this 24 days.(2016–06–01–2016–06–24)

Also, you may find it is interesting that the long-term relationship of the price change of Microsoft and S&P500 seem to have similar fluctuation patterns but the S&P500 is more stable in general.

I also calculated alpha and beta for this pair. (Alpha: is a measure of an investment’s performance compared to a benchmark such as S&P500. It is a mathematical estimate of the return based usually on the growth of earning per share; while the beta is based on the volatility — extreme ups and downs in prices or trading — of the stock or fund. You can think of beta as the tendency of a security’s returns to respond to swing in the market.)

If alpha is close to 1,0, means the fund or stock has outperformed its benchmark index by 1%. We can see that the alpha here is 0.0003 which is very small. Thus, we can conclude that Microsoft hasn’t really outperformed benchmark S&P500 very much.

In this case, the beta over the last years of Microsoft stock is 1.185 >1.0. For the short-term, beta is around 1.25 > 1.0 too. It is not hard to find this pattern from the graph and it is obvious that the price change of Microsoft moves up and down much more dramatically than the benchmark S&P500.

From the graph and the result, we can relate to CAPM(link) model which expresses an asset’s returns in terms of the expected returns from the market the those of risk-free asset. Based on this mode, the asset’s risk may be split into both systematic and idiosyncratic risk.

For the systematic risk which represents the market risk across all the traded assets. Thus, we may add to the conclusion that the large part the risk of the Microsoft stock related to the market risk since they present a similar pattern.

The next graph is a little bit complicated. First, we can look at the yellow line: which are the cumulative sentiments score for the last 2 years. It is growing over time. As for the green line which is the 50 days sentiment moving average. We can see the upward trend around the June this year of the green line. The red line represents the cumulative returns of the stock(price). You can see that the cumulative returns started to grow around the beginning of 2016 and now is around 0.20 for the last 2 years.(I preprocessed the cumulative sentiment: using cumulative sentiment divided by 1000).

*Stock Price, Trading Volume, Returns, and Volatility*

I also constructed the table with the timestamp, trading volume, open_price,close price, daily returns and volume % change for Microsoft for the last 2 years. The daily return declined slightly, but the trading volume grew by 221.31% on the announcement day.

Based on the table above, I plotted the daily returns and daily volume % change at the same graph for both long-term and short-term period. We can see that the daily return is relatively stable over last 2 years and there is a peak of trading volume with possible error added to the graph on announcement date from the second graph.the moving pattern of daily returns and trading volume are quite similar too.

The first graph below is the long-term daily returns distribution, which has the mean around 0 and leptokurtic distribution as well as slightly positive skewness. However, the second graph shows the-the returns distribution for this June only. We can see that the mean returns are negative.

The announcement data is at t=8. As we expected, the stock returns drop significantly.

The same graph as the one I explained for Linkedin. On the first graph below, the price is on the y-axis and time is on the x-axis. The size of the dot shows the size of the trading volume on a certain day at a certain price. We can see the dots are generally clustered with each other which means the stock prices did not change much for Microsoft for the last 2 years. You can check this out by looking at the graph below. The second graph shows the most recent month’s distribution and regression line, which is moving downward with the large trading volume and the low trading price at announcement date.

This is the price distribution plot about Microsoft stock price for last 2 years. You can see the average price for this 2 year is around $47.66 and the standard deviation of the stock price is very low which is 4.25 compared to the LinkedIn’s stock price(which is 44.31). Most time the stock prices are bouncing around $44-$48 from the distribution graph below. The highest value here is around $57.

The last graph shows the price distribution for the June. We can see a clear **bimodal distribution** which is a continuous probability distribution with two different modes. This distribution shows the distinguishable split of the stock price within June 2016. One mode would be around $47 and the other one would be around $51. The highest value here is around $52.5.

We can see that when the stock price is at $50.15 there is the highest trading volume in June.

The next graph is the one I created to measure how the trading volume varies among different stock prices. We can see that when the stock price is at $50.15 there is the highest trading volume.

As I explained before, M&A are amongst the biggest investment a company is capable of conducting as it is a reasonable way to enhance company value. There are plenty of M&A cases happened every year. I am curious about the stock price reaction of the target and acquiring companies due to the merger announcement. This simple event study using abnormal asset returns to measure stock’s performance. The announcement of the M&A is considered as an event in this study.

# 2.M&A Event Study

# — Study time frame:2006.12.31–2015.1.1

# — Data source:EventVestor: Mergers and Acquisitions

**My objectives here are:**

- To check whether the publicly available announcement information drives the observed price pattern around the announcement day for both target and acquiring companies.
- Examine the effect of M&A announcement on both target and acquirer quantitatively before and after the announcement.
- Measuring the uncertainty of the abnormal returns to offer the insight to look at the result.
- Added the volume % change(the volume rate of change is the indicator that shows whether or not a volume trend is developing in either an up or down direction) into the research in order to find the movement of the volume % change pattern around the announcement day for both target and acquire companies.

I have published few event studies article before such as the financial event study about positive and negative news and their impacts on the stock market. Usually, financial event study examines the impact of an event no the stock returns of a firm and normally we directly translated into the value of the firm.

As I explained before, after the M&A announcement the stock price of acquired company usually goes up, the stock price of the acquiring company usually goes down. This is daily because the premium paid for the target company more than the company is worth. But depending on how the deal is being paid for, how long it is expected to take to close and any speculation about ta competing offer. There are some arbitrage opportunities to exploit for speculators regarding this event as I mentioned before.

# (1)Short-term 30 days before and after announcement day

*Average Cumulative abnormal returns*

*— Target Company*

Here we can see from the graph, the ‘target’ companies stock’s daily abnormal returns over time from [t-30, t+30] and t = 0 represents the announcement date. The red dash line is the mean value of the daily abnormal returns for them which is around -0.08%. Also, you can see the total observations we collected to plot the graph is 1358(N=1358 shows on the legend part of the graph) for this case. We plot the average cumulative abnormal returns for them.

The line shows ‘Z’ shape here which has a dramatic jump at t =0. It implies that the abnormal returns increase dramatically on the announcement day and the trend becomes sort of flat afterward. The red dashed line shows the average returns over this period.

It seems like the M&A news incorporated into the stock prices efficiently. At announcement date, the stock returns show a dramatic increase. This upward momentum of abnormal returns last from the few days before day 0 to 30 days after the day 0. The slope seems to be constant throughout this period.

This is the standard deviation of the abnormal returns over this period. The high standard deviation implies that the further investigation awaits for us to conduct next and the possible solution could be that we categorize the stocks based on their sectors, indexes, or some other mixing factors to filtering down the stocks and to get more accurate result.

*— Acquiring Company*

Similarly, I also plotted the cumulative abnormal returns 30 days prior to and after the announcement date for Acquirer with the corresponding standard error plot. We can see that the mean stock price drops on day 0. And the stock cumulative abnormal returns continue to be relative low after announcement date for the next 30 days as well. From the error graph, we can see that the standard error at t=0 is generally small which verifies the fact I explained. However, the volatiles of those stock abnormal returns is still high in general.

*Average Cumulative Abnormal Volume % Change*

*— Target Company*

From the graph below we cannot identify a distinguishable trend. The trend is volatile in general and It seems like the M&A news may not be incorporated into the stock volume that efficiently based on the graph. But we can still see the increase in the trading volume after day 0 compared with the days before day 0.

*— Acquiring Company*

Here is the short-term trading volume % change for Acquirer. We can find the obvious spike on the day 0 and the general flat cumulative abnormal volume percentage change except at the days around announcement date. The following graph is the standard error graphs which intend to show the accuracy of the first graph, we can see there are very high errors overall except at t=0.

# (2)Long-term 252 trading days before and after announcement day for Acquirer:

Let’s look at more details about Merger and Acquisitions(M&A) transactions. There are some anomalies may happen such as M&As overall are estimated to only have 50% chance of success. As I mentioned before, M&A activity has longer-term ramifications for the acquiring company.A good management team, coupled with a good integration strategy, can significantly improve the share price of the acquiring company in the long term. However, there are no guarantees that any deal, even with the best of management teams, will result in higher long-term stock prices. Also, when a buyer finances a takeover with shares of its own stock, shares of the target company may continue to trade independently for months until the deal is finalized. Thus, it is not very meaningful to study the long-term performance of the target company if their stocks are delisted or stopping trading independently anymore.

So I plotted the long-term(1year which is around 252 trading days before and after the announcement day) cumulative abnormal returns before and after the announcement day 0. The general trend is as followed.

*Average Cumulative Abnormal Returns*

From the following graph, we can see that the cumulative abnormal returns are decreasing overall especially after the announcement date.

*Average Cumulative Abnormal Volume % change*

We can find the significant spike on the announcement date for the cumulative abnormal volume percentage % change for Acquiring company.

(3) Conclusion

If the capital market is efficient stock price should adjust quickly with respect to the public information, the acquired company’s share price will shoot up to a level that is still at a discount to the announcement price. What’s more, the entire wealth effect of the mergers or acquisitions should be incorporated into stock prices by the time all uncertain disappeared. Nowadays, a growing body of work has been done for long-term post-acquisition returns. According to the graph about the abnormal returns 1 year before and after the announcement date, it provides the evidence of negative post-merger stock performance.

Before I start to discuss Merger arbitrage. Let’s look at some important rules of the M&A trading:

- When a company makes public its interest to buy another, it has
**28 days**to either make a formal offer or announce that it doesn’t intend to make one. - If it does not make an offer, it usually has to wait six months before it can put itself in a position to do so again. However, if the target agrees, the bidder may be allowed to launch an offer after three months.
- All shareholders must be given the same information and misleading or inaccurate information must be publicly correctly immediately. There is a strict timetable setting out what the bidder and target may publish and when they must do it.
- Special deals for certain shareholders are not allowed. All shareholders must be offered the same terms.
- If the bidder acquires shares in the target after making an offer and pays a higher price for these than the initial offer, it must raise its offer to make up the difference.
- Any shareholder that acquires shares that control 30 percent or more of the voting rights in a company must make a cash offer to the remaining shareholders of the company. The price has to be at or above the highest price it paid in the last 12 months when acquiring those shares.
- If the transaction is being paid in all cash, the shares should disappear from your account on the date of closing, and be replaced with cash. If the transaction is cash and stock, you’ll see the cash and the new shares show up in your account. It’s pretty much that simple.
- If the acquirer pays partly in cash and partly in its own stock, the target company’s shareholders would hold a stake in the acquire, and thus have a vested interest in its long-term success. For the acquire, the impact of an M&A transaction depends on the deal size relative to the company’s size.

*<Source:* *Understanding M&As>*

Next, I would like to talk more about the M&A arbitrage since I believe that is most investors concern and focus.

First, let’s look at the merger arbitrage is the business of trading stocks in companies that are subject to takeovers or mergers. Usually, takeovers normally involve a big price premium for the target company. So long as there is a price gap, there is potential for a sizable reward even though betting on mergers can be very risky business.

For most arbitrageur, they will go long once the terms of potential merger become public, or buy shares of the target company, which in most cases trade below the acquisition price now. At the same time, the arbitrageur will short sell the acquiring company by borrowing shares and then repaying them back later with lower cost shares.

As we all know, the target company’s stock price should eventually rise to reflect the agreed acquisition price. As for the acquirer’s price, it should fall to reflect what is paying for the deal. In general, the wider the spread between the current trading prices and their prices valued by the acquisition terms, the better the arbitrageur’s potential returns.

While this all sounds straightforward, in real life, things don’t always go as predicted. The entire M&A arbitrage business could be a very risk in which takeover deals can fizzle and prices can move in unexpected directions. There are also the situations in which the target company may trade below the announced offer price. It could happen when part of the purchase consideration is to be made in the acquirer’s shares and the stock plummets when the deal is announced. As for the opposite situation the target’s shares trade above the offer price when investors are indicating that they believe the target company may receive a higher bid from another buyer or if they believe there is likely to be a competing bid from another suitor. Also, the shares of target company may remain below the offer price if there is doubt over whether the takeover will go ahead.

As for the acquirer’s price, it should fall to reflect the premium paying for the deal or if investors think the target is overpriced based on inflated P/E ratio or other metrics, they might push the stock price of the acquiring company down even further . But think for a long-term, the acquiring company stock may initially fall, if all goes smoothly, it is often a good investment in the long-run. But it only works when the market’s estimate of the probability that the deal will go through.

Thus, alternatively some traders may bet on the transaction will not happen even though the chance is very low. They could take advantage of this situation by buying a long-term put — but you may need to pay the premium for the put. This strategy is extremely speculative but the upside could be very large should the merger not occur. The reason of this situation could be the financing problems, due diligence outcomes, and regulatory objections and so on. Hostile bids are more likely to fail and longer the deal takes to close, the more things can go wrong to scuttle it.

Sometimes growing number of specialists funds moving into this part of the market has caused, greater market efficiency and subsequently few chances to profit from the price of the target company’s shared will jump to the agreed per-share acquisition which completely eliminates the price spread opportunity.

The merger arbitrage business is largely the domain of specialist arbitrage firms and hedge funds. The advice to avoid big loss could be: try to predict which proposed takeovers will succeed and avoid those will fail; A diversified collection of bets on announced deals can make steady returns for these firms.

Meanwhile, to offset some of the risks, arbitrageurs need to be more creative. For instance, they can bulk up returns by leveraging their bets(by using borrowed funds), or they can take mix-up traditional moves, sometimes shorting acquisition targets and going long the acquirer then selling calls on target shares. If the merger falls apart and the price falls, the sellers profits from the price paid for the call; If the merger closes successfully, the call reflects much of the difference between the current price and the closing price.

***In the end, I would like to share with you an example of how to take advantage of arbitrage opportunity when the deal is paid by stock. You could take a look if you are interested:

When a company B(Buyer) is going to buy company S(Seller)at $100M, they need to create the equivalent this amount of money in stock shares to make this transaction happen. That is to say, they are going to create $100M shares. They will give these amount of shares to company S’s shareholders in exchange for all the shares of company S. Assume promised acquired stock price for company S is twice as high as company B nowadays. In the transaction, every shareholder from company S will have 2 shares of company B’s stock theoretically. Or the company B could give company S’s shareholders all $100M directly to finish the transaction in exchange the ownership of company S.

Usually, the company B will give a premium to the company S’s stock price to acquire S, so we can measure company S’s stock price based on the trend of company B’s stock price since every share of S is going to convert into 2 shares of B, so if we assure that the transaction will happen. Every share of S should worth exactly at twice the value of B shares

What will happen here is after the announcement of this acquisition, the stock price of S is going to be exactly the twice as the price of the company B and then they should always trade at double of B’s shares in theory.

If they trade less than this amount, instead buying B shares, people would like to buy S shares or they could buy half of S shares. In other word, if here is someone are about to buy 2 of B shares and instead of buy 2 B shares he can get the same amount of B shares with less money by buying 1 share from S(since the value of S share is going to be worth than 2 shares of in the future if the transaction happens).

Now let’s look at the situation if the price of S is trading less than 2*B:

As I said it could because some people don’t think the transaction will happen, they don’t expect the full premium from B. If you try to get some arbitrage opportunity from the M&A activity, here is a case:

Imagine you are working at a hedge fund company, you may want to hedge this risk from if the transaction will not happen in the future –The best way to do it is to set up a pair trade here. Remember you assumption is the transaction is going to happen:

- You will buy 1 share of S– LONG
- You will sell 2 shares of B — SHORT

Right now 2 shares of B is going to be 1 share of S. At any point since S is trading a little bit of a discount so 2 shares of B is going to do more than 1 share of S in the future. When you short 2 shares of B you are going to get 2*B(earning of short) > S(cost to long).Your net profit would be $(2*B — S).

In the future when the transaction happens for 1 share of S you can exchange for 2 shares of B. You get 2*B to cover your short position that you borrowed from other people from the beginning. So you will make total (2*B — S) for your profit and hedge the risk if S is trading lower than 2*B. However, it may be a temptation to take advantage of differential by buying the target’s stock and shorting the proper ratio of the acquirer’s stock. The strategy itself has a very poor risk/reward ratio as the downside can be many times the possible upside.

*Reference:*

*http://www.investopedia.com/articles/stocks/06/mergerarbitrage.asp*

*http://smallbusiness.chron.com/happens-stockholders-business-merged-20901.html*

*http://www.learningmarkets.com/how-mergers-and-acquisitions-affect-stock-prices/*

*https://dspace.fandm.edu/bitstream/handle/11016/4167/Shaheen.pdf?sequence=1*

*http://www.accountingtools.com/acquisition-payment-methods*

*http://www.fool.com/knowledge-center/what-happens-to-a-companys-stock-when-a-buyout-is.aspx*

*http://finance.zacks.com/stock-prices-increase-after-takeover-6973.html*