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A natural question which was likely studied in academic literature (even though Kelly is not particularly popular among portfolio managers). I guess you could generalize Eq. (6.87) of this book. If $f(R)$ is the joint probability density of the returns of your $N$ assets (so $R$ is $N$-dimensional vector), for example Gaussian, $$ f(R)\propto\exp(-(1/2)\...

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