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What are you saying is not completely correct. What kelly criterion maximizes is the average growth of the capital invested. In fact, if I want to invest a fraction $f$ of my 1000 units the amount that I will have after $M$ trades will be $1000\Pi_{i=1}^{M} (1+f\phi_i)$ What we need to maximize is expected long-term growth rate. Growth rate is given by ...

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