Running percentage increases and amount of doubles

[MathiasArendru]

Hello people.

I want to start of with my first question.
What got me thinking about this is actually stock price movements. If a stock rises from 10$ to 15$ on a day, it will have increased by 50% obviously. But what wonders me is what if we break the small movements down. Say that first it rises 25% from 10$ to 12,5$. Now if we then reset the percentage calculator, and the price moves to 15$, the percentage move from 12,5 to 15 is then only 20% and therefore the stock theoretically moved by 45%? If we keep magnifying and making the moves smaller, then we get more deviation... A more extreme example, if a stock starts at 10$ and ends at 30$ for the day, the increase is 200%. But if we take this in two steps and first take the move from 10$ to 20$, its an increase of 100%. If we then take the rest of the 100% increase from 20$ then that would give 40$. Is it only because it is intraday movement that this percent resetting doesn't happen? If anyone knows why is calculated like this then i'd be glad if you could explain.

Another question i actually take from this quote:
"Which in six years rose from 5 to 256, without paying a dividend while its earnings increased from 40 cents to $3.91 per share. (Note that the price advanced five times as fast as the profits...)
How is this calculated, that the price advances five times as fast?

Thanks in advance! Sincerly, Mathias

 

[jtbell]

If a stock rises from 10$ to 15$ on a day, it will have increased by 50% obviously. But what wonders me is what if we break the small movements down. Say that first it rises 25% from 10$ to 12,5$. Now if we then reset the percentage calculator, and the price moves to 15$, the percentage move from 12,5 to 15 is then only 20% and therefore the stock theoretically moved by 45%?

No, you can't "add" percentage increases like that (25% + 20% in this case) because the individual percentages are based on different starting amounts. If you had taken the second increase of $12.50 and found the percentage with respect to the original amount of $10, that would have been 25% again, and you would have been able to add them (25% + 25% = 50%).

For another example of this phenomenon, consider starting with $10.00 and increasing in successive steps of 10%, using the starting amount for each step:

First step: 10% of $10.00 = $1.00; new amount = $11.00 (10% above the original amount)
Second step: 10% of $11.00 = $1.10; new amount = $12.10 (21% above the original amount)
Third step: 10% of $12.10 = $1.21; new amount = $13.31 (33.1% above the original amount)
etc.

This is the principle behind compound interest. In each period (step), you earn interest not only on the original amount, but also on the accumulated interest from previous periods.

 

[MathiasArendru]

Makes good sense. So that would mean that they have defined the original amounts as the opening prices for the trading day... Aha...

 

[Mark44]

Makes good sense. So that would mean that they have defined the original amounts as the opening prices for the trading day... Aha...

Or whatever. When anyone talks about a change of x%, the increase or decrease is relative to some starting value. It doesn't have to be the opening price for the day -- it could be a price at midday.