Including leaps in portfolio construction:

The main input for the construction of Markowitz-type portfolios is the distribution of financial asset returns that is usually assumed to be normal. The literature has shown that the incidence of extreme events is more common than the Gaussian distribution predicts. Consequently, this paper aims to analyze the inclusion of Poisson jumps that have proven to be useful in the field of financial derivatives valuation. First, the stochastic equation for the value of the portfolio is found from the distributions of the returns of its components. Based on the above, using data from the North American market during the period 1996-2021, it is shown that: (i) statistically the new distribution is more adequate for modeling returns and (ii) benefits are obtained in the optimization of portfolios under different objectives.