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I have a portfolio of foreign stocks. All stocks are denominated in foreign currency. I need to compute returns and risk metrics in national currency which is different from stocks currency. Stocks`s weights in the portfolio may change during optimization, but currency position always has the weight equal to one (no stocks from other exchanges). How to implement this in portfolio optimization procedure? Maybe I should add some constraint to my portfolio? How to deal with such a constraint as that the sum of all other assets weights must be equal to 1?

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I think for multi currency portfolios you will have to seperate out equity risk and currency risk. For example, if you own Gazprom stocks with current value of 1M RUB, then you have company specific risk (equity risk) and Ruble risk (currency risk). Since your investment has two risk sources, you should calculate risk and return metrics both for equity and currency. Then you can optimize your portfolio accordingly. On the other hand, you could hedge out your currency exposure entirely, then move on optimizing your portfolio only considering equity risk.I am not completly sure if these are robust approaches.

There are several research papers out there that discuss this subject:

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