Coskewness is the third central cross-moment between an asset's return and the squared market return, and its estimation from historical data introduces substantial sampling error relative to covariance estimation. The sample coskewness estimator requires a return history roughly three times as long as the covariance estimator for comparable estimation precision, which means that practitioners working with five-year return histories are operating with considerably less reliable third-moment estimates than their mean-variance counterparts. Structured shrinkage toward a theoretically motivated prior, such as the coskewness implied by a factor model, consistently outperforms the raw sample estimator in out-of-sample portfolio construction tests documented in the published literature. The practical implication is that coskewness-based portfolio construction requires explicit attention to the estimation methodology, not just the optimisation framework that consumes the estimates once they are produced.

Skewness preference does not dominate every portfolio construction decision with equal force — the conditions under which the third moment materially changes the optimal portfolio relative to the mean-variance solution are specific and identifiable. The theoretical analysis shows that skewness preference has the largest effect on portfolio weights when the investor's coefficient of relative risk aversion is high, when the cross-sectional dispersion in coskewness across assets is large, and when the overall level of market return asymmetry is elevated. In practice, these conditions are most likely to be met during periods of market stress, when the left tail of the return distribution is most extended and investor demand for positive skewness is most acute. Practitioners who apply higher-moment optimisation only during stable market conditions may be adopting the more complex framework at precisely the time when it matters least, while reverting to mean-variance approximation during the periods when incorporating skewness preference would most materially change the portfolio they construct.

Higher-moment portfolio optimisation introduces several failure modes that do not appear in mean-variance analysis and that practitioners encounter with notable regularity when first applying the framework. The most common is treating coskewness as a fixed characteristic of each asset rather than a property of each asset in relation to the specific portfolio being constructed — coskewness is not an asset-level attribute but a portfolio-level relationship, and it changes as the portfolio composition changes. A second common error is optimising over the third moment without imposing the same constraints on portfolio concentration that are standard in mean-variance practice, which allows the optimiser to take extreme positions in assets with favourable coskewness characteristics regardless of their expected return or variance contribution. A third pitfall is failing to account for the estimation error in coskewness when interpreting the output of the optimiser, leading to a false confidence in portfolio weights that are largely artefacts of sampling noise in the historical return data rather than stable reflections of the underlying return-generating process.