A decision model for portfolio selection

Abstract

This study presents one approach to investing in the financial markets using a decision theory point of view, where the main decision is to choose an investment portfolio, based on economic indexes, in order to predict future investments based on historical data, which minimizes the risk involved. The decision model is based on Decision Theory and Bayesian Analysis and the application uses Brazilian financial market data from

An Approach to Financial Risk in a Portfolio for Planning the Industrial Production of Products Derived From Sugarcane

“…The consequence function is obtained from a statistical analysis of historical data for the assets selected, as a probability distribution (Ferreira et al, 2009). For instance, if the data fit a normal distribution, this function is given by (4):…”

“…The states of nature involved may be explained by a priori knowledge. Thus, it is possible to associate a priori probability distribution over states of nature, which is represented by π(θ) (Bernoulli, 1954;Bernardo & Smith, 1994;Ferreira et al, 2009). For the problem formulated in this paper, a priori distribution can be constructed from the relative frequency of cumulative return rates over time on the sugarcane output commodities.…”

“…Therefore, in a Bayesian risk analysis perspective, r a is a measure that considers a priori knowledge about the state of nature so as to determine the probability of obtaining a certain payoff that plays a significant part in the decision context -in other words, r a measures the risk of an action given that x occurred (Raiffa & Schlaifer, 1961; Berger, 1985;Bernardo & Smith, 1994;Ferreira et al, 2009), given by ( 10) and (11). This metric allows decision rules to be established, where r a is the risk of a decision rule R a given by the utility ratio in a state of nature θ:…”

“…This relation between utility value and gain or loss value, in general, is represented by a utility function (Berger, 1985). A utility function represents a means by which the DM can more fully understand the level of risk involved and this highlights the importance of managing this indicator for the business while considering the different factors that describe the investment context (Aït-Sahalia & Brandt, 2001;Ferreira et al, 2009;Lovisolo & Leal, 2013). Thus, this paper investigates how best to evaluate which sugarcane-derived commodity should be chosen for production when considering a sugarcane surplus as capital to be invested.…”

“…Thus, the likelihood function can be represented by a vector of dimension equal to the number of observations multiplied by the number of states of nature.The combination of the a priori distribution and a likelihood function results in the a posteriori distribution. This distribution is used for the calculations of Bayes's rules to describe the probability of states of nature after a given known variable has been observed(Raiffa & Schlaifer, 1961;Berger, 1985;Bernardo & Smith, 1994;Ferreira et al, 2009):…”