A Note On Portfolio Selection Under Various Risk Measures PDF Download

Decision-making has a long history in many fields, and at the basic level, decision-making is about the selection of an alternative from a group of alternatives. Inevitably, alternatives involve uncertainty and risk. Numerous normative and descriptive theories have been proposed to assist decision-makers in the presence of risk. Measuring the risk associated with each alternative is the most challenging part of each theory and measuring it adequately is pivotal point in each decision theory. Usually, risk of each alternative is measured by a scalar either as dispersion measure, such as standard deviation, or risk measure, such as Value-at-Risk (VaR). Each risk measure should satisfy several good properties such as non-negativity, monotonicity, convexity, and so on. In this study, we develop new dispersion measures based on the expected mean and multiplicative mean which measure risk of each alternative based on reference points. These points represent the extreme expectation of the decision-maker which can be interpreted as the goal (the largest possible gain) and the nadir (the largest possible loss). We show that these measures satisfy non-negativity, subadditivity and convexity. Also, these measures are less sensitive to mean preserving spread noises while the standard risk measures are sensitive and can increase drastically. Furthermore, we show that these measures distinguish the good and bad volatilities. In this study, we investigate the performance of these risk measures in portfolio selection comparing to the traditional portfolio selection models. We develop a model based on each risk measure as well as combination of the both risk measure. Also, we derive the closed form optimal solution of investment when two risky assets are available. Using four different scenario generation methods, we investigate performance of these risk measures in a real data sets and we show that they outperform the existing portfolio selection models.