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:


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

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.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.