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Kelly calculates optimal leverage for maximising geometric growth. At the same time, any change in leverage does not lead to a change in a risk-adjusted return (i.e. Sharpe). Therefore Kelly cannot be used to improve risk-adjusted return. Talking about the excess vola, in practive one rarely applies Kelly. The bet is usually Kelly/2, Kelly/4 or even less. ...


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They are the same. The maximum growth rate is achieved when the Sharpe ratio is maximized. For the proof, see here.


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Maybe you could find pretty interesting the following papers: Laureti, P., Medo, M., and Zhang, Y.-C. (2010). Analysis of Kelly-optimal portfolios. Quantitative Finance, 10(7): 689–697. and Nekrasov, Vasily, Kelly Criterion for Multivariate Portfolios: A Model-Free Approach (September 30, 2014). The last is available at SSRN. Particularly, ...


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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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