# Calculating % profit on my investment of a short sale based on % loss of the stock price

Basically, when a stock price goes down by 50%, my profit is 100% of my sell price. When a stock goes down by 75%, my profit is 300% of my sell price.

I'm curious what the relationship is between the % decrease of a stock's price and the % gain on my investment.

Here is a chart that shows what I'm asking. If the price of a stock goes down by the number in red, my profit is the number in green. One line is linear and one is logarithmic, but I cannot find the relationship between these 2 numbers. It's so simple it seems like there would have to be a pretty direct relationship there. This is more of a mathy question, but I'm hoping someone here might have insight. Taking the % down a stock is and converting it to your profit seems very useful when you have a short position and you're watching a stock's price.

• I don't understand why your profit is measured in terms of your "sell price". Why isn't it measured in terms of your "entry price"? Jun 2 at 5:01

Basically, when a stock price goes down by 50%, my profit is 100% of my sell price. When a stock goes down by 75%, my profit is 300% of my sell price.

I disagree with your premise. When you short a stock, the most that you can make is the proceeds that you receive or 100% of the liability.

If you short a \$100 stock, \$10k is deposited into your account. If the stock drops 20%, you have a \$2k profit which is 20% of the proceeds received. If it drops to zero which is a 100% loss of share price, you get to keep 100% of the proceeds. IOW, the relationship is 1:1 linear. And if XYZ doubled in value from \$100 to \$200, you'd have a 100% loss.

The Reg T initial margin requirement is 50% of the short proceeds. So if you want to calculate ROI based on your initial margin requirement then it's a 2:1 relationship (for every 10% that the stock drops, you make 20% of the initial margin requirement). Note that each 10% drop is based on 10% of the initial price.

Where this gets much more complicated is calculating the return on investment. The ROI would be the sum of the four items below divided by the initial margin:

+Sale Proceeds

-Repurchase cost

-Borrow cost

-Dividends paid (if any)

• Thank you. You are right, I am wrong. Based on my verbiage, it would be "When a stock goes down by 75%, my profit is 300% of my Buy to Cover price." I can't downvote my own question but I tried. Jun 3 at 6:33
• Don't sweat it. There's no need to feel bad for asking questions when in search of clarification and for that reason, I removed your apology from your question. Jun 3 at 13:52

I think you're just doing a variant on percent change.

Percent change calculation is:

``````(new value/old value) - 1
``````

So to do this with only the percent change, since percent is just "per 100" just do the calculation with base 1. And since you're doing short sales you reverse the new and old values as the sale occurs before the purchase.

``````(1/(1+change)) - 1
``````

So in the case of a 75% decline you'd use:

``````(1/(1-0.75)) - 1 = 3
``````

It's essentially the same as using (100/25)-1, as though you bought for \$25 and sold for \$100 (which is a 75% reduction from your entry point).