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It seems to me that Currency Risk can be diversified away and hence one should not get paid for taking it. Do you agree?

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Yes, FX generally does not command a risk premium (expected return = 0, but volatility is not 0), and you can improve the Sharpe ratios of global equity/bond portfolios just by hedging away FX risk. See this excellent AQR paper: Risk Without Reward: The Case for Strategic FX Hedging.

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