# Decomposition of stock index movements

I want to decompose stock index movements. I know the estimated 12 months earnings growth rate ($$g_1$$), estimated long run earnings growth rate ($$g_2$$) and the index value.

I am about to use two-stage dividend discount model:

$$P=\frac{1+g_1}{1+r} + \frac{\frac{(1+g_1)\cdot(1+g_2)}{r-g_2}}{1+r},$$

which can be simplified as:

$$P=\frac{1+g_1}{r-g_2}.$$

The percentage change is then:

$$\frac{P(t+1)}{P(t)}-1= \frac{1+g_1(t+1)}{1+g_1(t)} \cdot \frac{r(t)-g_2(t)}{r(t+1)-g_2(t+1)}.$$

The problem here is that I don't know $$r$$. Variable $$r$$ cannot be solved because I am considering stock index, not a single equity. What would be the best way to decompose stock market movements using the information I have?