Simple Long vs Short position % return question

Say a currency pair is at parity 1 dollar to 1 dollar. I have $1,000 account and decided to trade it all long. Assuming no fees etc, I have 1,000 units and then that currency goes to 3:1. I now have 3,000 dollars so I sell and make $2,000 or a 200% return.

Now say I short the currency still at 3:1 with $1,000. I get 333 units and then it drops back to 1. I buy back my 333 units for 1 dollar and make $667 profit or a return of 66.7%.

The absolute change of the currency is the same on both sides but one side I made 200% and the other only 66%. Is this correct or am I having a brain fart?

Can anyone answer?
I'd like to know the answer as well.

OK, this made my brain hurt to start with, but I got there in the end.

The maths is correct for what you are doing but what you are doing is incorrect in that you are not comparing like with like.

In the first transaction you buy then sell and express your profit as a percentage of the buying price.

In the second transaction you sell then buy and express your profit as a percentage of the selling price.

Turn the second transaction round to match the first. You bought for $333, sold for $1000, profit $667. Profit ($667) as a percentage of buying price is 667/333=200%

You could if you wanted rework the first transaction as a percentage of selling price which comes out as 66% and it then matches your second calculation.

David.

It's correct: it arises because in-between the two transactions, the relative values of the currencies changed from parity to 3/1, and 200 is three times 66.7.

(I think David, above, has just said the same as me but in slightly different words.)