Question about a weird strategy

I heard a weird strategy from my friend and I was wondering what your take on it is:

Consider the following trading strategy:

Two currencies are at parity (1:1)

An investor holds 100 units of both.

Now, there is a movement, and one of the currencies appreciates. Now the ratio is (2:1).

Our careful investor seeks to maintain the same amount of both currencies, so he dumps a bit of the more expensive currency and now has 150 of one currency and 75 of the other.

Now, the price drops back suddenly to 1:1 – but he holds 225 total units, up from 200 before.

Thus, he made a profit of 25 units.

Why doesn’t this strategy work in real markets (with more realistic numbers, such as 1-2% gains)?

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