# Cointegration between prices and dividends. How do I get the following expression?

Actually, I have two questions:

• 1.

Let us assume that expected returns are constant. Then, we have the following expression for how the prices should be determined, provided that the operators are rational:

(1) $$P_t=E_t[\sum_{i=1}^{\infty} (1/1+K)^i D_{t+i}]$$

Campbell, Lo, McKinley in 'The Econometrics of Financial Markets' claim that, if the dividend follows a unit root process, such as:

$$D_t=D_{t-1} + \epsilon_t$$

And $$P_t=D_t/K$$

Then, if we subtract $$D_t/K$$ from (1) we get: (2)

$$P_t - D_t/K = (1/K)E_t[\sum_{i=1}^{\infty} (1/1+K)^i \Delta D_{t+1+i}]$$

I am not able to get (2) from (1). Can you help me, please?

• 2.

Suppose the Dividend follows a RW with drift process:

$$D_t=u+D_{t-1}+ \epsilon_t$$

Than $$E_t[D_{t+i}]= u*i + D_t$$ In a book, the author claims that, because of (3), the rational valuation formula becomes:

(4)

$$P_t=u(1+K)/K^2+ D_t/K$$

I am not able to prove the result just claimed, these are the steps I have been able to do so far: $$P_t=E_t[\sum_{i=1}^{\infty} (1/1+K)^i D_{t+i}]=E_t[\sum_{i=1}^{\infty} (1/1+K)^i (u*i+D_t)]=[\sum_{i=1}^{\infty} (1/1+K)^i (u*i)]+E_t \sum_{i=1}^{\infty} (1/1+K)^i (D_t)=[\sum_{i=1}^{\infty} (1/1+K)^i (u*i)]+D_t/K$$

I would really appreciate your help. Thank you.