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The financial markets lay the grounds for an enormous game board of essentially an infinite number of strategies and an apparent risk-free opportunity to win, as the Eintsteins of Lehman Brothers, Merrill Lynch, and AIG so clearly saw before the Financial Crisis of 2008.  Of course, all games have risk involved, and the game of investing is no exception.

The game of investing has two players: the investor and the market. The investor can gain an advantage in this game through gathering publicly-available information and analyzing financial data to find trends. Investments are made based on the investor’s formulated trends of markets, economies, and specific assets, such as stock in Walmart. The investor has X money to invest and his or her return value is positively correlated with the amount of money made.

Because the enormity and complexity of this game, it is only possible to determine a  dominant playing strategy on a large-scale, general basis. We can relate the general properties of this game with that of the card game Blackjack where there is a player and a dealer. If the player were to place a random bet on any given hand, the player has about a 50% chance of increasing his pool of money. If he decides to count cards and gather data, he can use that information to increase his chances of winning.

Let us say that the player has counted cards for a whole game and has determined that his chances of winning are higher than normal. How should he bet? Should he put all his money on the next hand or develop a long-term strategy where he bets a larger-than-normal amount every time his chances are high? If he chooses the former, his possible return is very high, but the risk involved would be losing all his money, the worst possible score in this game. Walking away from the table with more money is only expected if the money is divided into smaller bets and placed over many high-chance hands, just as it is expected that half the time a quarter is flipped it will land on heads only when it is flipped a large number of times.

The scenario where the player puts all his money on one high-chance hand is remarkably similar to Lehman Brothers putting all of its money into mortgages. When all of the sudden the housing market collapsed, so did the investment banks and insurance companies that had bet too heavily in this market. These companies ignored general principles of probability and because of their poor risk management, ultimately lost the game.

The smart card-counters invested their money by allocating risk to their investments. Privately-owned hedge fund Bridgewater Associates, LP is a prime example of such an investor. During the financial crisis, while most investors were losing money, Bridgewater founder Ray Dalio was beating the markets. Is this a simple random event, or was Mr. Dalio using a dominant strategy? Bridgewater diversifies its investments to stocks, currencies, commodities, shorts, bonds, options, and various other derivatives, so no single market slump will pull the whole fund’s money with it.  Risk allocation is a major part in the management of Bridgewater’s investment portfolio and offers a unique strategy to this financial game. The company analyzes its portfolio of investments as a whole to determine possible risk in any single market or financial instrument losing value. A portfolio made up of nothing but stocks in the auto-industry is practically a game of Corporate Russian Roulette. It relies entirely on one industry, which is susceptible to bearish trends like any other. A portfolio consisting of stocks in the tech, retail, automobile, and entertainment industries would be a smarter allocation of assets; however, the performance of all of these investments are heavily correlated with one common factor, the stock market. A financial crisis, such as the credit crunch in 2008, would be detrimental to such a portfolio. By diversifying investments and allocating assets that are highly uncorrelated, such as stock in Apple and the commodity Wheat, risk can be manipulated so that it is minimized, all while positive returns are being made.

Tony Keller, a journalist for the Financial Post, discusses the Investing game strategy of asset allocation in a recent article published here. In this article, Keller argues that high-risk does not necessarily correlate with high-return. He demonstrates that extending investments to multiple markets and financial instruments is the best way to optimize long-term returns. This unique strategy ties back with game theory in CS 2850 with a slight twist on what we have learned. In a game that is based on multiple decisions over a long period of time, the dominant strategy would involve minimizing the risk of short-term returns. Through minimizing risk, expected return will be optimized.



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