# Examine price changes vs price returns

In empirical financial analyses, is there a difference when examining stock price changes and stock price returns? Would a model with a response variable price changes tell a different story than price returns? Thank you in advance.

• Nov 24 '21 at 0:19

Given a time series $$\{y_t\}=(y_1,\dots,y_t)$$, you can obtain both price changes $$d_t:=y_{t}-y_{t-1}$$ and price returns $$r_t:=\frac{y_{t}-y_{t-1}}{y_{t-1}}$$. For any model of $$d_t$$, you can write an equivalent model of $$r_t$$ by dividing both sides of the model's equation by $$y_{t-1}$$. For any model of $$r_t$$, you can write an equivalent model of $$d_t$$ by multiplying both sides by $$y_{t-1}$$. Therefore, there does not have to be a difference. Consequently, any difference between the models for $$d_t$$ and $$r_t$$ is your choice rather than a necessity. And if the models are telling different stories, it is by the modeller's choice, not by necessity.