Can The Normality Of The Semi Variance Be Improved?
) Abstract This study examines the financial and statistical properties of the variance and semi variance (SV). Since the mean-variance approach and its extended mean-semi variance approach assume normality of returns, it has been observed that practical and computational problems emerged in the cases of portfolio optimization and estimation risk. The reliability of the semi variance has to be re-examined. This paper shows that the variance and its partial domain (semi variance) produce non normal estimates when the mean returns are normally distributed. Accordingly, a new proposed measure of risk, Mean Semi Deviations (MSD), is introduced which focuses on the measurement of the percentage returns lost from the average. The financial and statistical properties of the three measures of risk are tested and examined taking into account the risk-return theoretical relationship using data from index returns (DJIA and S&P500). The data patterns used are hourly, daily, quarterly and annual da
