How to calculate the gain or loss percentage in short sell?

[Bruno Tolentino]

A stock, in the first year, cost 128 dollars; in the second, cost 64...

D - Price
1 - 128
2 - 64
3 - 32
4 - 16

If I buy 100,000 dollars of this stock @ 128 dollars / share, so, in the second year I will lost 50,000 dollars (50% of 100K). In the third... ok, ok, easy...

When I buy stock, my capital is directly proportional to share's price and the percentual variation is equal to stock' percentual variation. Ok. No doubts about this.

My doubt is about when I short selling a stock, because the capital is not propotional to stock's price and the percentual variation is not equal between the capital and the price.

If I short selling the same share in the first example with a financial volume of 100,000 dollars. My capital will be:

D - Capital
1 - 100,000
2 - 150,000
3 - 175,000
4 - 187,500

So, exist some implicit rule of proportionality in short selling? Some math relationship using log function?

Since now, thanks guys...

 

[andrewkirk]

The percentage will be determined by the collateral arrangements.
To short sell you have to borrow the stock and then sell it. The lender of the stock will require you to post collateral - usually in the form of cash. At first they might require anything between 90% and 120% of the value of the stock. Say it's 100%. Then the collateral equals what you get from selling the stock, so you have outlaid no net money. Hence any profit or loss you make is infinite on a percentage basis.

Now say the collateral required is 120%. Then you have to put in $20,000 of your own, and whatever profit or loss you make is a percentage of that $20,000. In your example where the value of the stock holding reduces to 64,000, your gain is 36,000 off an investment of 20,000, which is a percentage gain of 180%.

As you can see, short-selling strategies are very highly leveraged. In practice they are often conducted as part of a long-short portfolio that is accompanied by a much larger index portfolio, so that the leverage is heavily diluted. In such a case, it is the percentage profit on the combined index and long-short portfolios that is of most interest.

 

[Student100]

I'm kind of confused by the post, since a ten dollar drop on a short sell is equivalent to a ten dollar gain with a long position, ignoring commissions, margin, taxes, yadayada. In a short sell, the max gain is 100% when the stock drops to zero. Max loses are "infinite" (but not really, since you'd be called long before then). Long positions are the opposite. Max loses are 100%, while gain is technically "infinite."

With 100,000 dollars at 128 stock price you can buy 781 shares for a cost of 99,968. If the shares drop to 64 dollars you now have 49,984 dollars in stock. At 32, you have 24,992. Inversely, if you short sell 781 shares of a stock at 128 and it falls to 64 you've made 49,984 dollars, 32, you've made 49,984 + 24,992 dollars.

Does this answer your question?

 

[mfb]

In the third... ok, ok, easy...

Not that easy. In the third year you lose 25,000, relative to the initial amount that is 25%. The same percentage as you win (relative to your initial amount) in the short-selling scenario.

The short-selling scenario has a different relative change from year 2 to year 3 because you made money already, while in the first scenario you lost money already. If you know how much, you can take this into account. No magic involved.

 

[Bruno Tolentino]

Yeah! Conceptually, I understand the short selling and I know how to calculate the gain or loss using a notional amount. But, I wouldn't like to use the notional amount because this requires refined calculations. I'm working an asset and I do backtests. I know that is possible to calculate the gain or loss of a long position abstracting the notional, ie, without use of financial volume. Simple, if buy a stock that grow up 10%, so I gain 10%, if then I buy a second stock and it drop 20%, my capital will decrease 20% too.

...

In other words, acttualy, in a table...

Year - Price - Capital
1 - Price(1) - Capital(1)
2 - Price(2) - Capital(2)
3 - Price(3) - Capital(3)

Capital(2) = Capital(1) x Price(2)/Price(1)
Capital(3) = Capital(2) x Price(3)/Price(2) = Capital(1) x Price(3)/Price(1)

I want to say, my capital is proportional to stock' price and my gain or loss in % is equal to variation in % of the stock.

...

So, what I'm looking for is a math equation that give me the capital in function of price and capital in a short position:

Capital(n) = F(Price(n), Price(n-1), Capital(n-1))

So, anyway, since now, I aprreciate your helps and answers! :) THx!

 

[andrewkirk]

Simple, if buy a stock that grow up 10%, so I gain 10%, if then I buy a second stock and it drop 20%, my capital will decrease 20% too.

You are not using the word 'capital' correctly. Capital is money that an investor places at risk of total loss if things go badly. It is not the same thing as Gross Assets, which is what you appear to be using it for. In the case of a limited liability company, capital is usually much smaller than Gross Assets. Whether that matters in this context depends on what the purpose of your calculation is, which has not been made clear.