Different downside risk approaches in portfolio

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 investo