# Do stock prices go up and down by percentage or by dollar?

I am studying the term volatility drag. The common example is that I invest \$1000 in a company stock. Say, the stock goes down 50% and than goes up 50%. This would result in \$250 loss. I would only have \$750 after the swing (\$1000 -> \$500 -> \$750), even though the stock go down 50% and come back up 50%.

My question is that does stock go up and down by percentage or by dollar? The volatility drag would only be a problem when the stock goes up and down by percentage. In my previous example, say this company I invested in, lost Y percent revenue from their original revenue X. Assuming there is no other factors, the stock from \$1000 a share went down 50% to \$500 a share. In the next season, this company was undergoing changes, that has earned the extra Y percent revenue back into their original revenue X. Does the stock only go up 50%, or does it go up to the original dollar amount \$1000 a share? If the stock only go up 50%, than I could see how volatility drag hurts me. But, if the stock goes up to the original dollar amount \$1000, than I don't see why volatility drag would be an problem to me. Since a company revenue went down and come back up to its original performance, the stock value would make up the difference of the volatility drag.

• Yes. It's just how you do the math, and the example is just demonstrating how percentages work, for the mathematically challenged. Dec 29, 2017 at 3:19
• What do you mean by "do they" go up or down by percentage or dollar? They do both. When any number goes up from, say, 10 to 11, it also goes up by 10%. It's not like it went up by one "or" went up by 10%; it did both, because they are just two ways of describing the same change. Dec 29, 2017 at 5:45

## 2 Answers

Stocks are denominated in the currency of the country where the stock market it's sold on resides. In the US, that's obviously the US Dollar, and the fraction is the cent. (Back in the day, the fraction was a power of 2: 1/2, 1/4, 1/8 and occasionally 1/16 and 1/32.)

We refer to growth in percentage because a \$10 rise in what was a \$30 stock (that's 33%) is much more dramatic than a \$10 rise in a \$350 stock (that's 2.85%).

Volatility drag is just a construct for ordinary investors who only knows arithmetic average. See this article from CFA.

https://blogs.cfainstitute.org/investor/2015/03/23/the-myth-of-volatility-drag-part-1/

Moreover, volatility in finance is measured in logarithmic returns, which guarantees symmetry.

https://en.m.wikipedia.org/wiki/Rate_of_return#Comparing_ordinary_return_with_logarithmic_return