# Do stocks move up and down in value or in proportion to how much they cost?

Do stocks change in value or in proportion to how much they cost? If a stock costs 100 dollar will it generally change value at the same rate as a 700 dollar stock (IE: both will move about 2 dollars in a day) or will they both change at the same proportion as each other(IE: both move about 2% each day)? Thank you for your time and help!

I'm a beginner like you, but i would like to take my shot at this.

First way is represented by Malick's answer above: you try to come up with a model that seems to fit reality well enough, you apply the question to the model, and whatever answer the model gives you, you say it applies to reality. In this case the model says the change in the stock price is percentage based.

Second way in my opinion is to look at data, a lot of it, without using a model. You just look at hundreds of thousands of stocks, maybe group them by price range, and you test your hypothesis. The drawback of this approach is it's a lot of work everytime you ask a new question.

The third way I see would be to ask: "What makes a stock price change ?". This is more of a behavioral approach. If I am an investor and I see a stock that I want to buy at price P, what would be my bid if P=10 and if P=100 ?

I realize I'm not really answering your question (because I don't actually know the answer), just food for thought...

Theoretically in proportion : the classical Geometric Brownian motion (GBM) for stock price is defined as follow :

$dS_{t} = \mu S_{t}dt + \sigma S_{t}dW_{t}$

Where $S_{t}$ is the stock price, $W_{t}$ a wiener process and $\mu$ and $\sigma$ are percentage drift and volatility term.

Then a infinitesimal change in price ($dS_{t}$) is proportional to the stock price :

$dS_{t} = S_{t} (\mu dt + \sigma dW_{t})$

Note that it is also why the stock price can never go bellow zero.

When analyzing stock price movements mathematically it is generally assumed that each stock has a specific 'volatility' (expressed in percent) that measures the tendency of that particular stock to move. So if Stock A has a volatility of 25% and Stock B of 20%, then Stock A has a tendency to make bigger moves in percentage terms than B. However, if we know nothing about Stock A and Stock B, we might, to keep things simple, assume that they have the same volatility. In that case the situation would be as you first described: the stocks would change in proportion to the original price (for example they would have the same probability of being up more than 2% on any day).

The second hypothesis you described: that the stocks would tend too move by the same dollar amount, is not taken seriously by anyone as far as I know.

option pricing scale invariant times a constant, meaning that percentages matter, not absolute price .

If you multiply the strike and spot price in the black sholes equation by the same constant, you'll see.