This work presents an approximate solution of the portfolio choice problem for the investor with a power utility function and the predictable returns. Assuming that asset returns follow the vector autoregressive process with the normally distributed error terms (what is a popular choice in financial literature to model the return path) it comes up with the fact that portfolio gross returns appear to be normally distributed as a linear combination of normal variables. As it was shown, the log-normal distribution seems to be a good proxy of the normal distribution in case if the standard deviation of the last one is way much smaller than the mean. Thus, this fact is exploited to derive the optimal weights. Besides, the paper provides a simulation study comparing the derived result to the well-know numerical solution obtained by using a Taylor series expansion of the value function.
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