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Take a hypothetical model that takes a stock as input and outputs "up" or "down" indicating if the stock price will increase or decrease in a fixed time interval T.

Assuming the model is correct >50% of the time, what are the strategies to trade given this information? No indication of how much the stock increases/decreases so a simple buy strategy would obviously fail.

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    $\begingroup$ Input several stock names until you get a stock that is predicted to go up and one which is predicted to go down. Then buy the first and short the second. $\endgroup$
    – nbbo2
    Commented Jan 19 at 17:02
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    $\begingroup$ @nbbo2 But the distribution of increase/decrease signals by the model may not be uniform across all stock prices. $\endgroup$
    – BeefJerky
    Commented Jan 19 at 17:24
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    $\begingroup$ @JulienMaas Yeah that's my point of the question. If a model doesn't give any magnitude, then buy/sell strategies won't work. $\endgroup$
    – BeefJerky
    Commented Feb 18 at 15:04
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    $\begingroup$ @nbbo2 If the stock I bought/(shorted) goes down/(up) 100% with 49% chance and up/down 1% with 51% chance then I lose. $\endgroup$
    – BeefJerky
    Commented Feb 18 at 15:07
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    $\begingroup$ @BeefJerky: you need predicted up and down returns or probabilities of up and down. You can't do anything with what you have. $\endgroup$
    – mark leeds
    Commented Feb 18 at 17:22

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I believe it matters what probabilities are priced into the market. Assuming the market prices a 50/50 percent of up/down at time T, then you could trade a call or put spread to bet on the probability of stock going up or down.

If the stock is fair at 100, and the model says it will go up you could buy a European 100-d/100+d call spread expiring at time T. If d is small enough, this is essentially a bet on probability of stock being above or below 100 at time T.

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