I would like to better have understanding on the minimum-LPM hedging. I have understood that the co-LPM matrix cannot be modeled by GARCH type models that are used to estimate to the covariance matrix, because the co-LPM matrix is asymmetric. However, in the context of international equity portfolio currency hedging, could it be
feasible to estimate the asset-currency co-LPM matrix with EWMA? Is there any research on forecasting co-LPM matrices/downside covariances/semicovariances?
possible to use similar approach as the multi-currency mean-variance? In the approach, the covariance matrix is a 2x2 partitioned matrix including an asset covariance matrix (returns measured in local currencies) and a currency covariance matrix (base currency excluded) on diagonal, and two local asset-currency matrices in the other corners. As an example, this approach on minimum variance currency hedging is described in the book Portfolio Risk Analysis by Connor et al.
possible to evaluate asset (or currency) specific risk contributions on overall portfolio using Euler's decomposition; is portfolio's LPM ($n=2$) homogeneous of degree one?
Thanks for correcting my possible misunderstandings about the topic and for answering any of the questions.