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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.

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