Portfolio optimisation with higher moments of risk at the Pakistan stock exchange

Abstract

Stock markets play an important role in spurring economic growth and development through diversification opportunities. However, diversification cannot be truly achieved if we continue to ignore additional dimensions of risk, namely skewness and kurtosis. This study incorporates higher moments of risk to form a mean-variance-skewness-kurtosis based framework for portfolio optimisation. Inclusion of higher moments in optimisation framework acknowledges the risk of asymmetric returns and fat-tail risk and can help investors in formulating optimal portfolios of stocks which can be significantly divergent from the ones they obtain through the Markowitz meanvariance optimisation. Our results confirm the presence of tradeoff between returns and additional dimensions of risk in Pakistan Stock Exchange (PSX) and strongly suggest including them in the optimisation framework to avoid sub-optimal decisions and to curtail exposure towards higher moments of risks.