Mean-Variance-Skewness-Kurtosis Portfolio Optimization with Return and Liquidity

In this paper, we extend Markowitz Portfolio Theory by incorporating the mean, variance, skewness, and kurtosis of both return and liquidity into an investor’s objective function. Recent studies reveal that in addition to return, liquidity is also a concern for the investor, and is best captured by not being internalized as a premium within the expected return level, but rather, as a separate factor with each corresponding moment built into the investor’s utility function. We show that the addition of the first four moments of liquidity necessitates significant adjustment in optimal portfolio allocations from a mathematical point of view. Our results also affirm the notion that higher-order moments of return can significantly change optimal portfolio construction. 1

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