# Calculating stock prices falls and rises

Let's say I close my investment of \$25 in a stock which is currently down from 313 to 123, I calculate my loss with this equation:

`( ( Close - Open ) / Open ) * 100 = %change`

Which would leave me with \$10, or 60% down.

If I then re-invest that \$10 and the stock goes back up to 313, using that same equation, I would have a profit of \$15 or 154%.

Are my calculations correct for how the stock market actually works?

• The intuitively strange thing about results is that -60 + 154 is not 0. To properly calculate cumulative profits, you can mark first day as Close/Open = 39.3%, and second day 254.5%. Then 0.393 * 2.545 = 1.0 as you'd expect.
– jpa
Dec 24, 2022 at 17:01

Yes.

And the %'s are weird because you're using a different baseline for each %.

However, they are inverses of each other. Your first trade fell to 40% of purchase price (so: 60% down). You second trade rose to 250% of purchase (so 150% up).

1/250% = 40%
1/40% = 250%
40% x 250% = unity

Let's simplify this by ignoring the fact that it's a stock.

To find out what percentage X is of Y, divide X by Y and multiply by 100.

123/313*100 is roughly 39.29, so the stock is now worth a bit under 40% of what it was before. Subtract that from 100% and you can see that it has lost a bit over 60% of its earlier value.

313/123*100 is roughly 254.47, so the stock is now worth a bit over 2.5 times what it was worth before. Subtract the original 100% and you can see that it has gained 154% of its earlier value.

So, yes, it's all simple mathematics (however you happen to write the formulas) and your numbers are correct.

Of course in the real world, nobody but a quant cares about opening price vs. closing price. They care about what they pay for it versus what they can sell it for.