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From Wikipedia article on foreign exchange reserves:

The central bank may, however, profit from a depreciation of the foreign currency or incur a loss on its appreciation.

Why does the depreciation of a foreign currency held in reserves yield a profit to the central bank holding these reserves?

I would think it’d be the opposite — if Country A has 50 of Country B’s currency in reserve and Country B’s currency depreciates, wouldn’t this reduce the value of the reserve (read: be a loss)?

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A central bank’s balance sheet is denominated in its domestic currency. Thus, all else being equal, a depreciation in the domestic currency (with respect to the currency that the reserves are denominated in) will result in a mark-to-market gain on the central bank’s foreign currency holdings (as they will now be worth more in terms of the domestic currency). Conversely, an appreciation in the domestic currency will result in a mark-to-market loss on these holdings.

So you are correct. That sentence should read:

The central bank may, however, profit from an appreciation of the foreign currency or incur a loss on its depreciation.

A point of clarification on the use of “gain” and “loss”: The preceding sentence in the article refers to carry gains, whereas the sentence you quote specifically refers to mark-to-market gains and losses. These latter “paper” gains are only realised if the central bank were to transfer these funds into the domestic currency.

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  • $\begingroup$ Go edit the wiki page? $\endgroup$
    – BrsG
    Jul 21, 2022 at 13:24

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