Estimating Downside Co-Moments for Currency Hedging

Summary

The document raises modeling and portfolio attribution questions about minimum lower partial moment hedging with order two, in the setting of currency hedges for international equity portfolios. It contrasts downside co-moments with covariance matrices, noting that the former are asymmetric and asking whether exponentially weighted moving averages could estimate asset-currency co-LPM relationships.

It also asks whether currency hedging can use a partitioned matrix like the one used in multi-currency mean-variance analysis, with local-currency asset and currency blocks plus their cross relationships. Finally, it asks whether Euler decomposition can assign asset- or currency-specific risk contributions, which depends on whether portfolio LPM of order two is homogeneous of degree one. The document provides no answers, empirical results, or citations beyond a reference to a portfolio risk book, so it serves as a research agenda rather than a validated method.

Key ideas

• Order-two lower partial moments measure downside risk and can produce asymmetric co-moment relationships.
• The author asks whether EWMA can forecast asset-currency co-LPMs for international equity hedging.
• A partitioned asset and currency risk matrix may offer a framework analogous to multi-currency mean-variance hedging.
• Euler risk attribution requires examining whether portfolio LPM of order two is homogeneous of degree one.
• The document poses these questions without resolving them or presenting empirical evidence.

Tags

# Minimum Lower Partial Moment (n=2) hedging ratio


# Minimum Lower Partial Moment (n=2) hedging ratio












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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