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-varianceskewness-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.

Sustainable Portfolio Optimization with Higher-Order Moments of Risk

“…The mean-variance optimization possibly does not provide an acceptable solution with various investors' risk preferences. This study's results are in line with those that confirm the skewness and kurtosis presence in other markets [12,13,30] and show a vital link between returns and higher moments of risk (skewness and kurtosis). This is an important phenomenon because traditionally mean-variance optimization is assumed that embeds all the risk associated with returns.…”

“…Therefore, it is essential to include these risk moments while constructing an optimized portfolio [33]. Previously, scholars stress on the inclusion of skewness and argue that incorporation of skewness not only improves the efficiency of mean-variance portfolio but also effect on optimization of portfolio and its selection [1,4,12].…”

“…In recent couple of decades, kurtosis has become a vital part when selecting a portfolio [12] and the inclusion of kurtosis is stressed while selecting and optimizing a portfolio. Inclusion of kurtosis and skewness in a portfolio selection makes it non-convex [2,34,35].…”

“…Furthermore, the addition of the fourth moments of risk in PGP has taken it from three dimensions to four [5]. To construct optimal portfolios of hedge funds multi-dimensional PGP is used [11,12].…”

“…Because of this assumption the optimization process understates the true investment associated risk, as this assumes that variance is an efficient proxy of risk [11]. Many finance studies confirm that return's distribution of an asset is non-normal and can be skewed either positive or negative with excess kurtosis [12,13].…”