Lognormal distribution on stochastic dominance for stock selection

Abstract

As a criteria of choosing risk investment, stochastic dominance is usually used without considering the distribution of return. Likewise, in practical case, investors do not expect that return is assumed to follow normally distribution. In real situation, we can find that data is not normally distributed, for instance stock data. Furthermore, distribution of the return tends to positive skewness. Therefore, considering normal distribution of the data is not suitable anymore. The aim of this research is to apply the interesting properties of first order of stochastic dominance as well as second order of stochastic dominance in which return is considered to follow lognormal distribution. For this purpose, the first step taken is to recaptulate stochastic dominance criteria with lognormal distribution and the second step is to implement the stochastic dominance criteria on the stock price data in the stock market Indonesia. The implementation of the criteria are to determine the properties of the lognormal distribution of the data, to use these properties on the stochastic dominance (SD) criteria, to specify conditions that against SD criteria with lognormal distribution, to apply stochastic dominance to lognormal distribution of stock price data in Indonesia stock market, and to draw the conclusion. From the research, it can be concluded that lognormal distribution can be used for managing the return expectation under stochastic dominance criteria. Based on the data taken i.e. monthly stock price data from March 2015 until February 2018, it can be said that the dominant stock price is ADHI, INCO, and WIKA, and there is no dominance for BBTN. Therfore, ADHI, INCO, and WIKA are preferred by investors.