![]() ![]() In his seminal paper, Kelly utilizes the logarithmic function for the solution of investment problems. It derives from the work of John Larry Kelly Jr, who was a researcher at Bell Labs. An alternative approach is the Kelly criterion. One of the most famous is proposed by Markowitz. In literature, many researchers have come up with different solutions for the investor problem. When an investor allocates his money in the market, what he aims to is making much money as possible at the lowest level of risk. In a dynamic setting, the rolling Kelly portfolio outperforms competitors particularly in the case of rebalanced portfolios optimized with a 2-years window width. Finally, we implement a dynamic strategy applied on the European stock market data and compare the results between the tangent and the optimal Kelly portfolios. Next, we optimize a portfolio with the Kelly criterion with no leverage and no short selling conditions and show that this portfolio lays in the mean-variance efficient frontier and has higher expected return and higher variance, although it is less diversified, respect to the tangent portfolio optimized under the Markowitz approach. We also show that, under a normal distribution of returns, the Kelly criterion has the best performance in the long run. In particular, it maximizes the expected growth rate and the median of the terminal wealth. Under few conditions, using Monte Carlo simulations with different scenarios we prove that the Kelly criterion beats any other approach in many aspects. We develop a general framework to apply the Kelly criterion to the stock market data, and consequently, to portfolio optimization. Department of Business and Economics, University of Cagliari, Cagliari, Italy.
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