I'm developing a dynamic portfolio optimization procedure based on the implementation of the Modified sharpe ratio. The mentioned ratio depends, among other factors, on the skewness and kurtosis of the portfolio. To build the skewness and kurtosis I need to compute the co-skewness and co-kurtosis arrays. In financial literature, there is a great deal of studies which describe how to annualize higher order moments in general (annualized skewness=skewness/sqrt(n) and annualized kurtosis=kurtosis/n), but not how to do it for co-moments such as the co-skewness and co-kurtosis arrays. To sum up: would anyone know how to annualize higher order co-moments?
Thanks in advance