Why does the calculation for percentage profit vary based on whether a position is short vs. long?

In this link here, the point:

In a market in which upswings are likely to equal or exceed downswings, heavier position should be taken for the upswings for percentage reasons - a decline from 50 to 25 will net only 50% profit, whereas an advance from 25 to 50 will net 100%

... is a bit confusing. Why will a decline from \$50 to \$25 give a 50% gain, for a short position? If the profit % is calculated based on the buy price, then it does not matter if you buy and then sell, or sell short and then buy to cover. So shouldn't a \$25 gain based on a buy price of \$25 equal 100% profit?

There are different perspectives from which to calculate the gain, but the way I think it should be done is with respect to the risk you've assumed in the original position, which the simplistic calculation doesn't factor in.

There's a good explanation about calculating the return from a short sale at Investopedia. Here's the part that I consider most relevant:

[...]

When calculating the return of a short sale, you need to compare the amount the trader gets to keep to the initial amount of the liability. Had the trade in our example turned against you, you (as the short seller) would owe not only the initial proceeds amount but also the excess amount, and this would come out of your pocket.

[...]

Refer to the source link for the full explanation.

Update:

As you can see from the other answers and comments, it is a more complex a Q&A than it may first appear. I subsequently found this interesting paper which discusses the difficulty of rate of return with respect to short sales and other atypical trades:

Excerpt:

[...]

The problem causing this almost uniform omission of a percentage return on short sales, options (especially writing), and futures, it may be speculated, is that the nigh-well universal and conventional definition of rate of return involving an initial cash outflow followed by a later cash inflow does not appear to fit these investment situations. None of the investment finance texts nor general finance texts, undergraduate or graduate, have formally or explicitly shown how to resolve this predicament or how to justify the calculations they actually use.

[...]

Simple math: 50-25=25, hence decline from 50 to 25 is a 50% decline (you lose half), while an advance from 25 to 50 is 100% gain (you gain 100%, double your 25 to 50).

Their point is that if you have more upswings than downswings - you'll gain more on long positions during upswings than on short positions during downswings on average. Again - simple math.

• "you lose half" only applies in the case where one is long the stock, but the OP is asking about a short position. – Chris W. Rea Jun 1 '13 at 13:55
• @littleadv - I think that was a typo. The short seller gains the 50% the stock fell, as the buyer lost half. – JTP - Apologise to Monica Jun 1 '13 at 14:02
• @Chris I understood that they're trying to compare short positions during downswings and long positions during upswings. In this case, long positions during upswings will gain more, and that is what they were trying to say. – littleadv Jun 2 '13 at 1:06

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