Portfolio selection using mean-risk model and mean-risk diversification model

With mean-risk and mean-risk diversification models, return distributions are characterised and compared using two statistics: the expected value and the value of a risk measure. This paper uses mean-risk model and risk curve obtained from the same model for portfolio selection problem. Security returns are assumed to be normally distributed. Further, the same mean-risk model is modified by using entropy to diversify the risk; this model can be called as mean-risk diversification model. In both the models, normal distribution is used to calculate the probability of likely losses of portfolio. The idea of mean-risk model is to regard expected return of a portfolio as the investment return and risk curve thus formed as investment risk, and the idea of mean-risk diversification model is to ensure that the portfolio thus formed is well diversified. The objective is to maximise the investor's return at a preset confidence level and minimise the risk. Two numerical examples are presented for the sake of illustration.