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Simple Stock Trading An FDA ruling will be handed down in three months, and a stock trader believes this ruling will have a significant effect on the traded value of a company’s stock price. The trader believes that the market views the chance of a favorable outcome of this ruling as 50%, and the outcome will add or subtract $3 (the “Stock Price Increase With Favorable Ruling” model property) to the already volatile (trader believes 30%) stock price, which is currently trading at $13. The trader has knowledge that leads him to believe that the probability of a favorableruling is 55%. Over each of the next 3months, the trader will be watching the FDA closely and expects to get a better idea of which way the ruling will go. The other market participants will not have this information. Specifically, the trader believes that his probability of a favorable ruling could increase or decrease each month by 3% (the “Periodic Probability Change With Knowledge” model property) with a 50/50 chance, depending on what he finds out. The trader also believes that the outcome of this ruling has a relationship with the Market. If the Market goes up by one standard deviation more than average that month, the probability that the trader will obtain knowledge that increases his favorable probability by 3% increases to 55%. This stock is most-easily traded in blocks of 100,000units. The bid/ask spread is 2% (twice the size of the “Percentage Trading Cost” model property)and the fixed trading cost is $10. The trader believes that he will not be able to trade an entire block at the bid or ask price. His buy and sell orders will influence the price artificially, and he will end up getting an average of the starting and ending price. If he buys or sells 1 block, the price will change by 0.5% (the “Traded Block Percentage Change” model property). If he buys or sells 2 blocks, the price will change by 2% (the “Double Traded Block Percentage Change” model property). He believes that in such an illiquid market, he won’t be able to get a reasonable price by buying or selling any more than 2 blocks per month. The stock price will lose its artificial price difference by 0.3% (the “Periodic Percentage Artificial Regression” model property) of the stock price’s value each month until it’s gone. Optimal Trading Strategy The optimal strategy is to wait one month and see if favorable knowledge is gathered. If so and the stock price decreases, the trader should buy 1 block. The stock price matters because it changes how great the $3 effect of the ruling is in percentage terms of the stock price. If the original favorable knowledge is followed by more favorable knowledge, 1 block of stock should be purchased regardless if 1 block has already been bought or not. If the knowledge is unfavorable the second time, the trader should wait for more information. If the original knowledge was unfavorable, no trade should be made at the end of the second month either. The trading strategy immediately before the ruling is complex and conditional on a number of factors. The True Shareholder Value of the optimal trading strategy is $16,669. Analysis The NPV is sensitive to the model properties. Below are tables containing the sensitivity of the NPV to the model parameters in dollar, percentage, or absolute terms. Model Property Stock Initial Value Fixed Trading Cost d $NPV / d $ -2709 -2 d $NPV / d % -23558 -22712 8406 5336 -4298 -2719 -1783 -464 -130 -117 -55 Model Property Percentage Trading Cost Traded Block Percentage Change Periodic Probability Change With Knowledge Initial Probability of Favorable Ruling Market Probability of Favorable Ruling Periodic Percentage Artificial Regression Stock Growth Double Traded Block Percentage Change Risk Free Rate Probability of Favorable Knowledge With 1 Dev Market Rise Stock Volatility Model Property Stock Price Increase With Favorable Ruling Block Size d $NPV / d % 17299 +0
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