The Kelly Criterion: implementation, simulation and backtest

In dieser Masterarbeit wird das asymptotisch optimale Kelly Portfolio, im Gegensatz zum Mittelwert/Varianz Ansatz, implementiert und in einer Simulationsstudie, wie auch auf empirischer Basis getestet. Das hauptsächliche Ziel von Kelly (1956) ist die Maximierung des erwarteten Logarithmus des Vermögens, welche, wie Breiman (1961) bewiesen hat, zu einer asymptotisch, optimalen Strategie in einer unabhängigen, stationären Welt führt, welche aber auf verschieden verteilte, zeitabhängige Renditen erweitert werden kann.In this thesis the Kelly growth-optimum criterion, as one strand of portfolio theory, besides the widely used mean-variance approach, is implemented and tested in a simulation study and on empirical basis. The main objective of Kelly (1956) is the maximization of the expected logarithm of growth, leading to, as Breiman (1961) proves, the asymptotically optimal strategy in an i.i.d. world, which can be extended to arbitrary and time-dependent returns. Under different parametric distribution assumptions for the outcomes, closed-form solutions for the growth-optimum strategy will be presented. Within a simulation study it will be shown that, sampling from the assumed data generating process naturally supports the asymptotic outperformance. As the assumption of the known process is loosened and the Kelly strategy needs to be implemented upon past, limited data, draw-down risks are increased and the portfolio maximizing the expected logarithm of end wealth is shifted to fractional Kelly bets. This holds for the empirical out-of-sample test. As the main statistical focus remains the improvement of the moment estimates in terms of errors, conditional moments are estimated by econometric time-series models. Setting the conditional mean forecast to zero if the conditional volatility forecasts surpasses the unconditional volatility, leads to a cancellation of positions in times of high uncertainty, which, one the one hand, decreases errors in the mean estimate and on the other hand, decreases portfolio draw-downs substantially