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              <text>Traditionally, academics have suggested that generating excess returns off timing the market, i.e. buying or selling financial products off frequent predictions requires maintaining an unreasonably high level of predictive accuracy. However, recent advancements in machine learning have motivated the adoption of predictive algorithms in financial markets. This highlights the importance of the question: How accurate do predictive algorithms have to be "useful"? To answer this, we study 2 problems related to the value of predictive accuracy in directional models for trading. We obtain results on the relationship between predictive accuracy and returns, and results on quantifying thresholds for when a predictive signal provides significant edge. </text>
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