Exploiting Game Theory for Profit in the Stock Market

It has been observed that the decision taken by a player not only depends on his own choice but also on the decisions taken by other person who are involved in the game. Now taking this idea forward it will be seen how a smart trader makes money out of the financial market through trading.

But prior to that the idea of Risk arbitrage has a significant weight in analyzing how profit can be made out. So Risk Arbitrage is a relatively low risk strategy of turning a profit by carefully analyzing the market situation through the lens of a constantly changing environment in which one must predict the actions of other players in order to figure out the best strategy for himself. One way to do so is to analyze historical data of past trades to figure out the trend. According to Prof Brown while entering into a trade a trader must identify the company he wants to take position in. Then he should go forward and analyze the goal for which he has entered the trade. The next step is finding out the pay off diagram for each player involved in the trade. However the author feels that a mere use of Game Theory will not help in making profit. Hence a smart trader should adopt Game Theory as well as Statistical analysis while taking his trade forward. But since the various factors at play in the stock market have a very big bearing on the global economy so one should have a clear idea about the overall macroeconomic and micro economic factors. (Brown, N.D.)

The Game Theory approach to make profit form a trade can be taken forward with the help of another example.

There is a hypothetical case where a company X is going to acquire a company called Y by the share swap mechanism. The overall mechanism involves swapping one share of X with two shares of Y. The price of X's shares is 50 pounds and that Y's shares are 20 pounds. So in order to take this merger forward the fair price of Y shares should be 25 pounds. However the share price of Y is currently quoting at 24 pounds. So a riskless arbitrage opportunity appears where a trader can buy 2 shares of Y and short 1 share of X and in the process make a riskless profit of 2 pounds. So by applying risk less arbitrage model a profit of 2 pound is made. However the process is not always riskless as there are chances that the process of merger might not work out

which may result in a loss for the trader.
From the light of Game Theory we need to find out the decision makers involved in the total process of merger. So the decision makers involved could be the management of X, management of Y, investors and market regulators. Thus each decision maker will have his own pay off diagram. However the involvement of so many decision makers makes the situation complex. To make it simple Game Theory is applied with Statistical Analysis.

In 1991 Time Warner the world's largest media and Entertainment Company known for its brands like Fortune, Time, People and Sports Illustrated had decided to raise fresh capital through a right issue to existing shareholders.
The term of the offer was made in such a way that ultimately forces the existing shareholder.
It was decided that

a) If 100% shareholder participation takes place in the right issue then the price of right would be fixed at $105 and the number of shares for each participant would increase by 60 % after the offer closes.

b) If 80% shareholder participation takes place in the right issue then the price of right would be fixed at $84

c) If 60% shareholder participation takes place in the right issue then the price of right would be fixed at $64.
However the decision was not taken positively by the shareholders and the stock tanked over 25% in a few days after the announcement. The stock fell from $105 and finally settled at $85 in the NYSE (New York Stock Exchange).
Let us construct a pay off matrix where we have taken the price purchase of the share at $90 and decision to take part in the right issue by 100%, 80% and 60% participants from the three scenarios decided upon by the company.

Cost pay off matrix for the problem

So clearly it can be seen that if the market price of the stock price can be brought down below the prices of right then the shareholders can be forced to participate in the deal. Instead the shareholders can purchase shares of the company and increase their stake in the company directly from the market and therefore not take part in the right issue as buying form the market offers a much cheaper alternative for the shareholders. Thus the fall of share price was logical enough to counter the decision of the firm.

Taking the best possible scenario for the shareholders the price of the right issue should have been fixed at $63. However from the valuation perspective the price around $80 was cheap and fair for the deal to go forward.
This move completely took Time Warner off guard and the company decided to fix the price of right issue at a fixed price of $80.The market gave a big thumps up to the decision and the stock soared up in the NYSE (New

York Stock Exchange) after the news broke out.
So this clearly gives us an idea as to how Game Theory was used to analyze the various outcomes of the entire event and how the best outcome was obtained from the perspective of both parties involved.