Modeling, Estimation, and Optimization of Equity Portfolios with Heavy-tailed Distributions

In this chapter we provide a methodology to solve dynamic portfolio strategies considering realistic
assumptions regarding the return distribution. First, we analyze the empirical behavior of some equities, suggesting how to approximate an historical return series with a factor model that accounts for most of the variability and proposing a methodology to generate realistic return scenarios. Then we examine the profitability of some reward-risk strategies based on a forecasted evolution of the returns. Since several studies in behavioral finance have shown that most investors in the market are neither risk averters nor risk lovers, we discuss the use of portfolio strategies based on the maximization of performance measures
consistent with these investors’ preferences. We first argue the computational complexity of reward-risk portfolio selection problems and then we compare the optimal sample paths of the future wealth obtained
by performing reward-risk portfolio optimization on simulated data.