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Why does the calculation for percentage profit vary based on whether a position is short vs. long?
The problem with rate of return calculation on short positions is, that the commonly used approach assumes an initial investment creating a cash outflow. If we want to apply this approach to short selling, we should look at the trade from another perspective. We buy money and pay for this money with stock. Our investment to buy 50$ in your example is 1 share.  When closing the short position, we effectively sell back our money (50$) and receive 2 shares. Our profit on this position is obviously 1 share. Setting this in relation to our investment of 1 share yields a performance of 100%   in reality, we do not sell back the entire cash but only the amount needed to get back our investment of 1 share. This is actually comparable to a purchase of stock which we only partially close to get back our invested cash amount and keep the remaining shares as our profit