Simulação de séries temporais correlacionadas

Abstract

Information availability regarding the risks associated with each choice is of great importance in decision-making. In this sense, the main objective of this work was to investigate the efficiency of the bootstrap simulation technique to analyze the random behavior of stock portfolios value for different investment horizons (from 3 up to 24 months), thus also making possible the measurement of risks and potential gains. It is known that the same cause can simultaneously affect the prices of different stocks and that this correlation directly affects the risk of a portfolio. By using historical data itself in the simulation, the bootstrap technique is able to correlate the logarithmic returns of stock prices. The technique still has the advantage of being able to dispense the use of parametric distributions of probability for simulating the returns. The response variable (output variable) considered in the simulations was the value of portfolio gains or losses, which is obtained by subtracting the initial portfolio value from the simulated value to the portfolio after the investment period (simulation horizon). The simulation is used to calculate the percentiles of the response variable that help to characterize dispersion and risk, so the Value-at-Risk (VaR) measure is also explored. The software Excel and ModelRisk®, in addition to the price history of 18 companies from 12/31/2001 to 12/29/2017, were used in simulations and optimizations. The simulated values for the percentiles of the response variable were confronted, by backtesting techniques, with the values that the portfolio would have performed in practice in each forecast. In general, values of counts performed below the 1th and 5th percentiles (called violations) were higher than expected, whereas values of counts performed below the 95th and 99th percentiles were lower than expected. It was observed that the larger the simulation horizon, the greater the model's slowness in responding to market changes, the lower the independence between violations for predictions on subsequent days. The influence of the historical size used as input for the simulation model was also investigated. The model was very sensitive to market changes, so one of the main contributions of the work was to highlight that changes in the size of the entry history (consequently in the market conditions considered) were able to cause considerable differences in the simulated percentiles and the realism of the model. The importance of the work is also in exploring a very uncharted area in the literature, the long-term risk analysis for portfolios. Optimizations to maximize the 5th percentile of the response variable on 04/01/2010 were carried out for a 3-month investment horizon given a 3-month and 6-month entry history. The optimized portfolios presented average realized values greater than the original portfolio for the period from 01/01/2010 to 12/29/2017, but the differences are small compared to the standard deviations of the realized values.