Different downside risk approaches in portfolio optimisation

Abstract

Variance is commonly used as risk measure in portfolio optimisation to find the trade-off between the risk and return. Investors wish to minimise the risk at the given level of return.However, the mean-variance model has been criticised because of its limitations. The meanvariance model strictly relies on the assumptions that the assets returns are normally distributed and investor has quadratic utility function. This model will become inadequate when these assumptions are violated. Besides, variance not only penalises the downside deviation but also the upside deviation. Variance does not match investor’s perception towards risk because upside deviation is desirable for investors. Therefore, downside risk measures such as semi-variance, below target risk and conditional value at risk have been proposed to overcome the deficiencies of variance as risk measure. These downside risk measures have better theoretical properties than variance because they are not restricted to normal distribution and quadratic utility function. The downside risk measures focus on return below a specified target return which better match investor’s perception towards risk. The objective of this paper is to compare the optimal portfolio composition and performance using variance, semivariance,below target risk and conditional value at risk as risk measure.