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Suppose the SPY index will either go up 10% or down 10% by the end of next week. In addition, you know that the probability
Suppose the SPY index will either go up 10% or down 10% by the end of next week. In addition, you know that the probability of either case occurring is 50%. The index currently sells for $320. Take these details as facts. An associate at your firm (call him trader A) argues that a bull market is on its way, and that there is in fact a 70% chance of the 10% increase, and a 30% chance of a 10% decrease. A second associate (call him trader B) argues that a bear market is on its way, and that the probabilities are just the opposite; a 30% chance of the 10% increase, and a 70% chance of a 10% decrease. Now suppose trader A catches on and won't trade, leaving only trader B willing to buy and sell at a price equal to their own expected value of the stock price. You have $320 for investment. How much money can you make on a quick arbitrage trade using trader B (and perhaps a short sale)? (Assume the interest rate / time value of money = 0. Do not place a $ sign in your answer, but answer in dollars.)
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