Dynamic Optimization of Portfolios 2018 to 2024

Abstract

Investors are always willing to receive more data. This has become especially true for the application of modern portfolio theory to the institutional asset allocation process, which requires quantitative estimates of risk and return. When long-term data series are unavailable for analysis, it has become common practice to use recent data only. The danger is that these data may not be representative of future performance. Although longer data series are of poorer quality, are difficult to obtain, and may reflect various political and economic regimes, they often paint a very different picture of emerging market performance. This paper presents an application of a stochastic nonlinear optimization model of portfolios including transaction costs in the Brazilian financial market. In order to have that, portfolio theory and optimal control were used as theoretical basis. The first strategy tries to allocate the whole available wealth, not considering the risk associated to portfolio (deterministic result). In this case the investor obtained profits of 7,23% a month, taking into account the three risk aversion levels during the whole planning period [see column (7)]. On the contrary, the results from of the stochastic algorithm obtained profits of 1,34% a month and 18,06% a year, if the investor has low risk aversion. The profits would be 0,88% a month and 11,02% a year for a medium risk aversion investor. And with high risk aversion, the investor obtains 0,62% a month and 7,66% a year.